Table of spherical codes

Maintained by Henry Cohn

This data is archived at https://hdl.handle.net/1721.1/153543. If you cite the table, please refer to that data set, not this web page.

A spherical code is a configuration of points on the surface of a sphere, with the goal of maximizing the minimal angle between the points. The following table lists numerically optimized codes, with cases that are known to be optimal marked with *. Each entry links to coordinates for the code. Along with references, in some cases the table lists the minimal polynomial of the cosine of the minimal angle, in which case a code with this exact angle has been proved to exist.

The table is limited to 32 dimensions and 1024 points, with a few exceptions. It omits cases that have been systematically solved, namely dimensions below three and n-dimensional codes with at most 2n points (see R. A. Rankin, The closest packing of spherical caps in n dimensions, Proc. Glasgow Math. Assoc. 2 (1955), 139–144, doi:10.1017/S2040618500033219). The entries labeled “needs more optimization” have not fully converged to a local optimum, while most of the others probably have. There are two records listed in Ericson and Zinoviev's book (Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001) that I have not included below: for 80 points in 7 dimensions, their construction describes only 78 points, and for 1024 points in 16 dimensions, I am unable to get their construction to work.

You can access a plain text table here, which includes some polynomials too large to fit below, and upload additions or improvements here.

Dimension Number of points Cosine of minimal angle References and notes
3 7* 0.210138312731 K. Schütte and B. L. van der Waerden, Auf welcher Kugel haben 5, 6, 7, 8 oder 9 Punkte mit Mindestabstand Eins Platz?, Math. Ann. 123 (1951), 96–124, doi:10.1007/BF02054944.
3⁢x3−9⁢x2−3⁢x+1
3 8* 0.261203874964 K. Schütte and B. L. van der Waerden, Auf welcher Kugel haben 5, 6, 7, 8 oder 9 Punkte mit Mindestabstand Eins Platz?, Math. Ann. 123 (1951), 96–124, doi:10.1007/BF02054944.
7⁢x2+2⁢x−1
3 9* 0.333333333334 K. Schütte and B. L. van der Waerden, Auf welcher Kugel haben 5, 6, 7, 8 oder 9 Punkte mit Mindestabstand Eins Platz?, Math. Ann. 123 (1951), 96–124, doi:10.1007/BF02054944.
3⁢x−1
3 10* 0.404394325217 K. Schütte and B. L. van der Waerden, Auf welcher Kugel haben 5, 6, 7, 8 oder 9 Punkte mit Mindestabstand Eins Platz?, Math. Ann. 123 (1951), 96–124, doi:10.1007/BF02054944; L. Danzer, Finite point-sets on S2 with minimum distance as large as possible, Discrete Math. 60 (1986), 3–66, doi:10.1016/0012-365X(86)90002-6.
7⁢x3−4⁢x2−2⁢x+1
3 11* 0.447213595500 K. Schütte and B. L. van der Waerden, Auf welcher Kugel haben 5, 6, 7, 8 oder 9 Punkte mit Mindestabstand Eins Platz?, Math. Ann. 123 (1951), 96–124, doi:10.1007/BF02054944; L. Danzer, Finite point-sets on S2 with minimum distance as large as possible, Discrete Math. 60 (1986), 3–66, doi:10.1016/0012-365X(86)90002-6.
5⁢x2−1
3 12* 0.447213595500 L. Fejes [Tóth], Über eine Abschätzung des kürzesten Abstandes zweier Punkte eines auf einer Kugelfläche liegenden Punktsystems, Jber. Deutsch. Math.-Verein. 53 (1943), 66–68.
5⁢x2−1
3 13* 0.542636486830 K. Schütte and B. L. van der Waerden, Auf welcher Kugel haben 5, 6, 7, 8 oder 9 Punkte mit Mindestabstand Eins Platz?, Math. Ann. 123 (1951), 96–124, doi:10.1007/BF02054944; O. R. Musin and A. S. Tarasov, The strong thirteen spheres problem, Discrete Comput. Geom. 48 (2012), 128–141, doi:10.1007/s00454-011-9392-2.
x8−24⁢x7−12⁢x6+8⁢x5+38⁢x4+24⁢x3−12⁢x2−8⁢x+1
3 14* 0.563950300361 K. Schütte and B. L. van der Waerden, Auf welcher Kugel haben 5, 6, 7, 8 oder 9 Punkte mit Mindestabstand Eins Platz?, Math. Ann. 123 (1951), 96–124, doi:10.1007/BF02054944; O. R. Musin and A. S. Tarasov, The Tammes problem for N=14, Exp. Math. 24 (2015), 460–468, doi:10.1080/10586458.2015.1022842.
4⁢x4−2⁢x3+3⁢x2−1
3 15 0.592605902926 K. Schütte and B. L. van der Waerden, Auf welcher Kugel haben 5, 6, 7, 8 oder 9 Punkte mit Mindestabstand Eins Platz?, Math. Ann. 123 (1951), 96–124, doi:10.1007/BF02054944; D. A. Kottwitz, The densest packing of equal circles on a sphere, Acta Cryst. Sect. A 47 (1991), 158–165, doi:10.1107/S0108767390011370.
13⁢x5−x4+6⁢x3+2⁢x2−3⁢x−1
3 16 0.612294616483 K. Schütte and B. L. van der Waerden, Auf welcher Kugel haben 5, 6, 7, 8 oder 9 Punkte mit Mindestabstand Eins Platz?, Math. Ann. 123 (1951), 96–124, doi:10.1007/BF02054944.
23⁢x6+6⁢x5+5⁢x4+4⁢x3−3⁢x2−2⁢x−1
3 17 0.628094415071 L. Danzer, Finite point-sets on S2 with minimum distance as large as possible, Discrete Math. 60 (1986), 3–66, doi:10.1016/0012-365X(86)90002-6.
4⁢x10−92⁢x9+24⁢x8+128⁢x7−58⁢x6−78⁢x5+35⁢x4+32⁢x3−4⁢x2−6⁢x−1
3 18 0.648695832224 T. Tarnai and Zs. Gáspár, Improved packing of equal circles on a sphere and rigidity of its graph, Math. Proc. Cambridge Philos. Soc. 93 (1983), 191–218, doi:10.1017/S0305004100060485.
216⁢x11+108⁢x10+118⁢x9+209⁢x8−100⁢x7−160⁢x6+40⁢x5+46⁢x4−20⁢x3−12⁢x2+2⁢x+1
3 19 0.673116887561 D. E. Lazić, V. Šenk, and I. Šeškar, Arrangements of points on a sphere which maximize the least distance, Bull. Appl. Math. (Technical University Budapest) 47 (1987), 7–21.
Minimal polynomial listed in plain text data
3 20 0.676477138130 B. L. van der Waerden, Punkte auf der Kugel. Drei Zusätze, Math. Ann. 125 (1952), 213–222, doi:10.1007/BF01343118.
21⁢x3−9⁢x2−5⁢x+1
3 21 0.699498431067 D. A. Kottwitz, The densest packing of equal circles on a sphere, Acta Cryst. Sect. A 47 (1991), 158–165, doi:10.1107/S0108767390011370.
3 22 0.710306258580 D. A. Kottwitz, The densest packing of equal circles on a sphere, Acta Cryst. Sect. A 47 (1991), 158–165, doi:10.1107/S0108767390011370.
Minimal polynomial listed in plain text data
3 23 0.722846984869 T. Tarnai and Zs. Gáspár, Arrangement of 23 points on a sphere (on a conjecture of R. M. Robinson), Proc. Roy. Soc. London Ser. A 433 (1991), 257–267, doi:10.1098/rspa.1991.0046.
3 24* 0.723078468334 R. M. Robinson, Arrangements of 24 points on a sphere, Math. Ann. 144 (1961), 17–48, doi:10.1007/BF01396539.
7⁢x3+x2−3⁢x−1
3 25 0.747398628578 D. A. Kottwitz, The densest packing of equal circles on a sphere, Acta Cryst. Sect. A 47 (1991), 158–165, doi:10.1107/S0108767390011370.
Minimal polynomial listed in plain text data
3 26 0.754278177121 D. A. Kottwitz, The densest packing of equal circles on a sphere, Acta Cryst. Sect. A 47 (1991), 158–165, doi:10.1107/S0108767390011370.
Minimal polynomial listed in plain text data
3 27 0.758389210777 T. Tarnai and Zs. Gáspár, Improved packing of equal circles on a sphere and rigidity of its graph, Math. Proc. Cambridge Philos. Soc. 93 (1983), 191–218, doi:10.1017/S0305004100060485.
Minimal polynomial listed in plain text data
3 28 0.773230262338 D. A. Kottwitz, The densest packing of equal circles on a sphere, Acta Cryst. Sect. A 47 (1991), 158–165, doi:10.1107/S0108767390011370.
3 29 0.780281415949 D. A. Kottwitz, The densest packing of equal circles on a sphere, Acta Cryst. Sect. A 47 (1991), 158–165, doi:10.1107/S0108767390011370.
3 30 0.781551875095 B. W. Clare and D. L. Kepert, The closest packing of equal circles on a sphere, Proc. Roy. Soc. London Ser. A 405 (1986), 329–344, doi:10.1098/rspa.1986.0056.
Minimal polynomial listed in plain text data
3 31 0.791118613299 J. Strohmajer, Über die Verteilung von Punkten auf der Kugel, Ann. Univ. Sci. Budapest. Eötvös Sect. Math. 6 (1963), 49–53.
Minimal polynomial listed in plain text data
3 32 0.793616614872 L. Danzer, Finite point-sets on S2 with minimum distance as large as possible, Discrete Math. 60 (1986), 3–66, doi:10.1016/0012-365X(86)90002-6.
Minimal polynomial listed in plain text data
3 33 0.806397613648 D. A. Kottwitz, The densest packing of equal circles on a sphere, Acta Cryst. Sect. A 47 (1991), 158–165, doi:10.1107/S0108767390011370.
3 34 0.810984337204 D. A. Kottwitz, The densest packing of equal circles on a sphere, Acta Cryst. Sect. A 47 (1991), 158–165, doi:10.1107/S0108767390011370.
3 35 0.815937771500 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
3 36 0.817248185290 D. A. Kottwitz, The densest packing of equal circles on a sphere, Acta Cryst. Sect. A 47 (1991), 158–165, doi:10.1107/S0108767390011370.
3 37 0.824892480240 D. A. Kottwitz, The densest packing of equal circles on a sphere, Acta Cryst. Sect. A 47 (1991), 158–165, doi:10.1107/S0108767390011370.
3 38 0.826583259422 E. Székely, Sur le problème de Tammes, Annales Universitatis Scientiarum Budapestinensis de Rolando Eötvös Nominatae 17 (1974), 157–175, http://annalesm.elte.hu/annales17-1974/Annales_1974_T-XVII.pdf.
363⁢x14+7685⁢x12+34299⁢x10−77139⁢x8+68985⁢x6−31833⁢x4+6561⁢x2−729
3 39 0.833991322411 D. A. Kottwitz, The densest packing of equal circles on a sphere, Acta Cryst. Sect. A 47 (1991), 158–165, doi:10.1107/S0108767390011370.
3 40 0.837162072474 B. W. Clare and D. L. Kepert, The closest packing of equal circles on a sphere, Proc. Roy. Soc. London Ser. A 405 (1986), 329–344, doi:10.1098/rspa.1986.0056.
3 41 0.841236343029 D. A. Kottwitz, The densest packing of equal circles on a sphere, Acta Cryst. Sect. A 47 (1991), 158–165, doi:10.1107/S0108767390011370.
3 42 0.843331551639 E. Székely, Sur le problème de Tammes, Annales Universitatis Scientiarum Budapestinensis de Rolando Eötvös Nominatae 17 (1974), 157–175, http://annalesm.elte.hu/annales17-1974/Annales_1974_T-XVII.pdf.
Minimal polynomial listed in plain text data
3 43 0.847208865437 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
3 44 0.848201378305 D. A. Kottwitz, The densest packing of equal circles on a sphere, Acta Cryst. Sect. A 47 (1991), 158–165, doi:10.1107/S0108767390011370.
3 45 0.854249474082 D. A. Kottwitz, The densest packing of equal circles on a sphere, Acta Cryst. Sect. A 47 (1991), 158–165, doi:10.1107/S0108767390011370.
3 46 0.857534166865 D. A. Kottwitz, The densest packing of equal circles on a sphere, Acta Cryst. Sect. A 47 (1991), 158–165, doi:10.1107/S0108767390011370.
3 47 0.859122361410 D. A. Kottwitz, The densest packing of equal circles on a sphere, Acta Cryst. Sect. A 47 (1991), 158–165, doi:10.1107/S0108767390011370.
3 48 0.859292295076 R. M. Robinson, Finite sets of points on a sphere with each nearest to five others, Math. Ann. 179 (1969), 296–318, doi:10.1007/BF01350775.
34⁢x5+15⁢x4−12⁢x3−14⁢x2−6⁢x−1
3 49 0.866691479049 D. A. Kottwitz, The densest packing of equal circles on a sphere, Acta Cryst. Sect. A 47 (1991), 158–165, doi:10.1107/S0108767390011370.
3 50 0.868173209127 E. Székely, Sur le problème de Tammes, Annales Universitatis Scientiarum Budapestinensis de Rolando Eötvös Nominatae 17 (1974), 157–175, http://annalesm.elte.hu/annales17-1974/Annales_1974_T-XVII.pdf.
Minimal polynomial listed in plain text data
3 51 0.871484364931 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
3 52 0.872966708781 D. A. Kottwitz, The densest packing of equal circles on a sphere, Acta Cryst. Sect. A 47 (1991), 158–165, doi:10.1107/S0108767390011370.
Minimal polynomial listed in plain text data
3 53 0.876189803956 D. A. Kottwitz, The densest packing of equal circles on a sphere, Acta Cryst. Sect. A 47 (1991), 158–165, doi:10.1107/S0108767390011370.
3 54 0.877004306358 D. A. Kottwitz, The densest packing of equal circles on a sphere, Acta Cryst. Sect. A 47 (1991), 158–165, doi:10.1107/S0108767390011370.
3 55 0.880785046525 D. A. Kottwitz, The densest packing of equal circles on a sphere, Acta Cryst. Sect. A 47 (1991), 158–165, doi:10.1107/S0108767390011370.
3 56 0.881731578410 D. A. Kottwitz, The densest packing of equal circles on a sphere, Acta Cryst. Sect. A 47 (1991), 158–165, doi:10.1107/S0108767390011370.
3 57 0.884363737604 D. A. Kottwitz, The densest packing of equal circles on a sphere, Acta Cryst. Sect. A 47 (1991), 158–165, doi:10.1107/S0108767390011370.
3 58 0.886555745177 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
3 59 0.887855737148 D. A. Kottwitz, The densest packing of equal circles on a sphere, Acta Cryst. Sect. A 47 (1991), 158–165, doi:10.1107/S0108767390011370.
3 60 0.889473567590 D. A. Kottwitz, The densest packing of equal circles on a sphere, Acta Cryst. Sect. A 47 (1991), 158–165, doi:10.1107/S0108767390011370.
3 61 0.892008443283 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
3 62 0.893496850569 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996; J. Buddenhagen and D. A. Kottwitz, Multiplicity and symmetry breaking in (conjectured) densest packings of congruent circles on a circle, undated manuscript.
3 63 0.895036180815 D. A. Kottwitz, The densest packing of equal circles on a sphere, Acta Cryst. Sect. A 47 (1991), 158–165, doi:10.1107/S0108767390011370.
3 64 0.896988167538 D. A. Kottwitz, The densest packing of equal circles on a sphere, Acta Cryst. Sect. A 47 (1991), 158–165, doi:10.1107/S0108767390011370.
3 65 0.898259108584 D. A. Kottwitz, The densest packing of equal circles on a sphere, Acta Cryst. Sect. A 47 (1991), 158–165, doi:10.1107/S0108767390011370.
3 66 0.899195777484 D. A. Kottwitz, The densest packing of equal circles on a sphere, Acta Cryst. Sect. A 47 (1991), 158–165, doi:10.1107/S0108767390011370.
3 67 0.901198227760 D. A. Kottwitz, The densest packing of equal circles on a sphere, Acta Cryst. Sect. A 47 (1991), 158–165, doi:10.1107/S0108767390011370.
3 68 0.902856921522 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
3 69 0.903831506358 James Buddenhagen and D. A. Kottwitz, 1997.
3 70 0.905043036803 D. A. Kottwitz, The densest packing of equal circles on a sphere, Acta Cryst. Sect. A 47 (1991), 158–165, doi:10.1107/S0108767390011370.
3 71 0.906396736776 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
3 72 0.906849285445 D. A. Kottwitz, The densest packing of equal circles on a sphere, Acta Cryst. Sect. A 47 (1991), 158–165, doi:10.1107/S0108767390011370.
3 73 0.909571628656 James Buddenhagen and D. A. Kottwitz, 1997.
3 74 0.910532623502 D. A. Kottwitz, 1997.
3 75 0.911390904652 D. A. Kottwitz, The densest packing of equal circles on a sphere, Acta Cryst. Sect. A 47 (1991), 158–165, doi:10.1107/S0108767390011370.
3 76 0.912633133084 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996; J. Buddenhagen and D. A. Kottwitz, Multiplicity and symmetry breaking in (conjectured) densest packings of congruent circles on a circle, undated manuscript.
3 77 0.913536344688 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996; K. J. Nurmela, Constructing spherical codes by global optimization methods, Research Report A32, Digital Systems Laboratory, Helsinki University of Technology, 1995, https://research.ics.aalto.fi/publications/info/bibdb.HUT-TCS-A32.shtml.
3 78 0.914034438768 D. A. Kottwitz, The densest packing of equal circles on a sphere, Acta Cryst. Sect. A 47 (1991), 158–165, doi:10.1107/S0108767390011370.
3 79 0.916195009441 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
3 80 0.916690360742 James Buddenhagen, 1997.
3 81 0.918117193791 D. A. Kottwitz, The densest packing of equal circles on a sphere, Acta Cryst. Sect. A 47 (1991), 158–165, doi:10.1107/S0108767390011370.
3 82 0.919172412416 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
3 83 0.919937881756 D. A. Kottwitz, The densest packing of equal circles on a sphere, Acta Cryst. Sect. A 47 (1991), 158–165, doi:10.1107/S0108767390011370.
3 84 0.920151698890 D. A. Kottwitz, The densest packing of equal circles on a sphere, Acta Cryst. Sect. A 47 (1991), 158–165, doi:10.1107/S0108767390011370.
3 85 0.922004026342 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
3 86 0.922710627798 D. A. Kottwitz, The densest packing of equal circles on a sphere, Acta Cryst. Sect. A 47 (1991), 158–165, doi:10.1107/S0108767390011370.
3 87 0.923567597265 D. A. Kottwitz, The densest packing of equal circles on a sphere, Acta Cryst. Sect. A 47 (1991), 158–165, doi:10.1107/S0108767390011370.
3 88 0.924093912593 D. A. Kottwitz, The densest packing of equal circles on a sphere, Acta Cryst. Sect. A 47 (1991), 158–165, doi:10.1107/S0108767390011370.
3 89 0.925099726146 D. A. Kottwitz, The densest packing of equal circles on a sphere, Acta Cryst. Sect. A 47 (1991), 158–165, doi:10.1107/S0108767390011370.
3 90 0.926173483336 D. A. Kottwitz, The densest packing of equal circles on a sphere, Acta Cryst. Sect. A 47 (1991), 158–165, doi:10.1107/S0108767390011370.
3 91 0.926844825210 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
3 92 0.927003416243 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
3 93 0.928418531906 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
3 94 0.928979461777 James Buddenhagen and D. A. Kottwitz, 1997.
3 95 0.929811497467 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
3 96 0.930285673249 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
3 97 0.931051674650 X. Lai, D. Yue, J.-K. Hao, F. Glover, and Z. Lü, Iterated dynamic neighborhood search for packing equal circles on a sphere, Comput. Oper. Res. 151 (2023), Paper No. 106121, 17 pp., doi:10.1016/j.cor.2022.106121.
3 98 0.931239991046 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
3 99 0.932727363300 James Buddenhagen and D. A. Kottwitz, 1997.
3 100 0.933385128903 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
3 101 0.934025767057 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
3 102 0.934480088172 James Buddenhagen and D. A. Kottwitz, 1997.
3 103 0.935207723062 James Buddenhagen and D. A. Kottwitz, 1997.
3 104 0.935711381000 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
3 105 0.936434497689 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
3 106 0.937042014619 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
3 107 0.937517802204 James Buddenhagen and D. A. Kottwitz, 1997.
3 108 0.937862018289 James Buddenhagen and D. A. Kottwitz, 1997.
3 109 0.938798085650 James Buddenhagen and D. A. Kottwitz, 1997.
3 110 0.939026290863 James Buddenhagen and D. A. Kottwitz, 1997.
3 111 0.939729959842 Henry Cohn, 2024.
3 112 0.940339774660 James Buddenhagen and D. A. Kottwitz, 1997.
3 113 0.940847649045 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
3 114 0.941205445297 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
3 115 0.941916896842 James Buddenhagen and D. A. Kottwitz, 1997.
3 116 0.942351017116 James Buddenhagen and D. A. Kottwitz, 1997.
3 117 0.942866795114 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996; J. Buddenhagen and D. A. Kottwitz, Multiplicity and symmetry breaking in (conjectured) densest packings of congruent circles on a circle, undated manuscript.
3 118 0.943283453359 X. Lai, D. Yue, J.-K. Hao, F. Glover, and Z. Lü, Iterated dynamic neighborhood search for packing equal circles on a sphere, Comput. Oper. Res. 151 (2023), Paper No. 106121, 17 pp., doi:10.1016/j.cor.2022.106121.
3 119 0.943652307933 James Buddenhagen and D. A. Kottwitz, 1997.
3 120 0.943662307333 R. M. Robinson, Finite sets of points on a sphere with each nearest to five others, Math. Ann. 179 (1969), 296–318, doi:10.1007/BF01350775.
1364⁢x10+1230⁢x9−709⁢x8−1468⁢x7−688⁢x6+136⁢x5+286⁢x4+108⁢x3+4⁢x2−6⁢x−1
3 121 0.944678061273 Henry Cohn, 2024.
3 122 0.945086237318 X. Lai, D. Yue, J.-K. Hao, F. Glover, and Z. Lü, Iterated dynamic neighborhood search for packing equal circles on a sphere, Comput. Oper. Res. 151 (2023), Paper No. 106121, 17 pp., doi:10.1016/j.cor.2022.106121.
3 123 0.945482265531 James Buddenhagen and D. A. Kottwitz, 1997.
3 124 0.945780154584 James Buddenhagen and D. A. Kottwitz, 1997.
3 125 0.946396812867 X. Lai, D. Yue, J.-K. Hao, F. Glover, and Z. Lü, Iterated dynamic neighborhood search for packing equal circles on a sphere, Comput. Oper. Res. 151 (2023), Paper No. 106121, 17 pp., doi:10.1016/j.cor.2022.106121.
3 126 0.946752784732 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
3 127 0.947264465646 X. Lai, D. Yue, J.-K. Hao, F. Glover, and Z. Lü, Iterated dynamic neighborhood search for packing equal circles on a sphere, Comput. Oper. Res. 151 (2023), Paper No. 106121, 17 pp., doi:10.1016/j.cor.2022.106121.
3 128 0.947573544865 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
3 129 0.947971561157 James Buddenhagen and D. A. Kottwitz, 1997.
3 130 0.948266309315 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
3 131 0.948765511183 X. Lai, D. Yue, J.-K. Hao, F. Glover, and Z. Lü, Iterated dynamic neighborhood search for packing equal circles on a sphere, Comput. Oper. Res. 151 (2023), Paper No. 106121, 17 pp., doi:10.1016/j.cor.2022.106121.
3 132 0.948962593971 X. Lai, D. Yue, J.-K. Hao, F. Glover, and Z. Lü, Iterated dynamic neighborhood search for packing equal circles on a sphere, Comput. Oper. Res. 151 (2023), Paper No. 106121, 17 pp., doi:10.1016/j.cor.2022.106121.
3 133 0.949572658198 X. Lai, D. Yue, J.-K. Hao, F. Glover, and Z. Lü, Iterated dynamic neighborhood search for packing equal circles on a sphere, Comput. Oper. Res. 151 (2023), Paper No. 106121, 17 pp., doi:10.1016/j.cor.2022.106121.
3 134 0.949971678353 X. Lai, D. Yue, J.-K. Hao, F. Glover, and Z. Lü, Iterated dynamic neighborhood search for packing equal circles on a sphere, Comput. Oper. Res. 151 (2023), Paper No. 106121, 17 pp., doi:10.1016/j.cor.2022.106121.
3 135 0.950317557456 X. Lai, D. Yue, J.-K. Hao, F. Glover, and Z. Lü, Iterated dynamic neighborhood search for packing equal circles on a sphere, Comput. Oper. Res. 151 (2023), Paper No. 106121, 17 pp., doi:10.1016/j.cor.2022.106121.
3 136 0.950634777737 X. Lai, D. Yue, J.-K. Hao, F. Glover, and Z. Lü, Iterated dynamic neighborhood search for packing equal circles on a sphere, Comput. Oper. Res. 151 (2023), Paper No. 106121, 17 pp., doi:10.1016/j.cor.2022.106121.
3 137 0.951024783277 X. Lai, D. Yue, J.-K. Hao, F. Glover, and Z. Lü, Iterated dynamic neighborhood search for packing equal circles on a sphere, Comput. Oper. Res. 151 (2023), Paper No. 106121, 17 pp., doi:10.1016/j.cor.2022.106121.
3 138 0.951358398188 X. Lai, D. Yue, J.-K. Hao, F. Glover, and Z. Lü, Iterated dynamic neighborhood search for packing equal circles on a sphere, Comput. Oper. Res. 151 (2023), Paper No. 106121, 17 pp., doi:10.1016/j.cor.2022.106121.
3 139 0.951683443186 X. Lai, D. Yue, J.-K. Hao, F. Glover, and Z. Lü, Iterated dynamic neighborhood search for packing equal circles on a sphere, Comput. Oper. Res. 151 (2023), Paper No. 106121, 17 pp., doi:10.1016/j.cor.2022.106121.
3 140 0.951979740880 X. Lai, D. Yue, J.-K. Hao, F. Glover, and Z. Lü, Iterated dynamic neighborhood search for packing equal circles on a sphere, Comput. Oper. Res. 151 (2023), Paper No. 106121, 17 pp., doi:10.1016/j.cor.2022.106121.
3 141 0.952385754295 Henry Cohn, 2025.
3 142 0.952693726748 X. Lai, D. Yue, J.-K. Hao, F. Glover, and Z. Lü, Iterated dynamic neighborhood search for packing equal circles on a sphere, Comput. Oper. Res. 151 (2023), Paper No. 106121, 17 pp., doi:10.1016/j.cor.2022.106121.
3 143 0.952998670435 Henry Cohn, 2024.
3 144 0.953228409663 Henry Cohn, 2025.
3 145 0.953609890346 X. Lai, D. Yue, J.-K. Hao, F. Glover, and Z. Lü, Iterated dynamic neighborhood search for packing equal circles on a sphere, Comput. Oper. Res. 151 (2023), Paper No. 106121, 17 pp., doi:10.1016/j.cor.2022.106121.
3 146 0.953890527065 Henry Cohn, 2024.
3 147 0.954232032048 Henry Cohn, 2024.
3 148 0.954536757950 Henry Cohn, 2025.
3 149 0.954857978400 X. Lai, D. Yue, J.-K. Hao, F. Glover, and Z. Lü, Iterated dynamic neighborhood search for packing equal circles on a sphere, Comput. Oper. Res. 151 (2023), Paper No. 106121, 17 pp., doi:10.1016/j.cor.2022.106121.
3 150 0.955020893900 X. Lai, D. Yue, J.-K. Hao, F. Glover, and Z. Lü, Iterated dynamic neighborhood search for packing equal circles on a sphere, Comput. Oper. Res. 151 (2023), Paper No. 106121, 17 pp., doi:10.1016/j.cor.2022.106121.
3 151 0.955409384784 Henry Cohn, 2024.
3 152 0.955652691422 X. Lai, D. Yue, J.-K. Hao, F. Glover, and Z. Lü, Iterated dynamic neighborhood search for packing equal circles on a sphere, Comput. Oper. Res. 151 (2023), Paper No. 106121, 17 pp., doi:10.1016/j.cor.2022.106121.
3 153 0.955934479813 Henry Cohn, 2025.
3 154 0.956200715693 Henry Cohn, 2024.
3 155 0.956523743427 X. Lai, D. Yue, J.-K. Hao, F. Glover, and Z. Lü, Iterated dynamic neighborhood search for packing equal circles on a sphere, Comput. Oper. Res. 151 (2023), Paper No. 106121, 17 pp., doi:10.1016/j.cor.2022.106121.
3 156 0.956672320428 Henry Cohn, 2024.
3 157 0.957096132346 X. Lai, D. Yue, J.-K. Hao, F. Glover, and Z. Lü, Iterated dynamic neighborhood search for packing equal circles on a sphere, Comput. Oper. Res. 151 (2023), Paper No. 106121, 17 pp., doi:10.1016/j.cor.2022.106121.
3 158 0.957339288658 Henry Cohn, 2024.
3 159 0.957588843682 Henry Cohn, 2024.
3 160 0.957856569962 X. Lai, D. Yue, J.-K. Hao, F. Glover, and Z. Lü, Iterated dynamic neighborhood search for packing equal circles on a sphere, Comput. Oper. Res. 151 (2023), Paper No. 106121, 17 pp., doi:10.1016/j.cor.2022.106121.
3 161 0.958127175342 Henry Cohn, 2024.
3 162 0.958288809704 X. Lai, D. Yue, J.-K. Hao, F. Glover, and Z. Lü, Iterated dynamic neighborhood search for packing equal circles on a sphere, Comput. Oper. Res. 151 (2023), Paper No. 106121, 17 pp., doi:10.1016/j.cor.2022.106121.
3 163 0.958615566728 X. Lai, D. Yue, J.-K. Hao, F. Glover, and Z. Lü, Iterated dynamic neighborhood search for packing equal circles on a sphere, Comput. Oper. Res. 151 (2023), Paper No. 106121, 17 pp., doi:10.1016/j.cor.2022.106121.
3 164 0.958889976688 Henry Cohn, 2024.
3 165 0.959124889495 Henry Cohn, 2024.
3 166 0.959323846675 X. Lai, D. Yue, J.-K. Hao, F. Glover, and Z. Lü, Iterated dynamic neighborhood search for packing equal circles on a sphere, Comput. Oper. Res. 151 (2023), Paper No. 106121, 17 pp., doi:10.1016/j.cor.2022.106121.
3 167 0.959625833713 X. Lai, D. Yue, J.-K. Hao, F. Glover, and Z. Lü, Iterated dynamic neighborhood search for packing equal circles on a sphere, Comput. Oper. Res. 151 (2023), Paper No. 106121, 17 pp., doi:10.1016/j.cor.2022.106121.
3 168 0.959759331314 Henry Cohn, 2025.
3 169 0.960021869084 Henry Cohn, 2025.
3 170 0.960117137568 X. Lai, D. Yue, J.-K. Hao, F. Glover, and Z. Lü, Iterated dynamic neighborhood search for packing equal circles on a sphere, Comput. Oper. Res. 151 (2023), Paper No. 106121, 17 pp., doi:10.1016/j.cor.2022.106121 (see footnote 1).
3 171 0.960456738161 Henry Cohn, 2025.
3 172 0.960629559055 X. Lai, D. Yue, J.-K. Hao, F. Glover, and Z. Lü, Iterated dynamic neighborhood search for packing equal circles on a sphere, Comput. Oper. Res. 151 (2023), Paper No. 106121, 17 pp., doi:10.1016/j.cor.2022.106121.
3 173 0.960986467408 Henry Cohn, 2025.
3 174 0.961153945452 X. Lai, D. Yue, J.-K. Hao, F. Glover, and Z. Lü, Iterated dynamic neighborhood search for packing equal circles on a sphere, Comput. Oper. Res. 151 (2023), Paper No. 106121, 17 pp., doi:10.1016/j.cor.2022.106121.
3 175 0.961330724045 Henry Cohn, 2024.
3 176 0.961593582498 Henry Cohn, 2024.
3 177 0.961828786663 X. Lai, D. Yue, J.-K. Hao, F. Glover, and Z. Lü, Iterated dynamic neighborhood search for packing equal circles on a sphere, Comput. Oper. Res. 151 (2023), Paper No. 106121, 17 pp., doi:10.1016/j.cor.2022.106121.
3 178 0.961965173662 Henry Cohn, 2024.
3 179 0.962096013263 X. Lai, D. Yue, J.-K. Hao, F. Glover, and Z. Lü, Iterated dynamic neighborhood search for packing equal circles on a sphere, Comput. Oper. Res. 151 (2023), Paper No. 106121, 17 pp., doi:10.1016/j.cor.2022.106121.
3 180 0.962128794086 T. Tarnai, Packing of 180 equal circles on a sphere, Elem. Math. 38 (1983), 119–122, doi:10.5169/seals-37194.
Minimal polynomial listed in plain text data
3 181 0.962508969964 X. Lai, D. Yue, J.-K. Hao, F. Glover, and Z. Lü, Iterated dynamic neighborhood search for packing equal circles on a sphere, Comput. Oper. Res. 151 (2023), Paper No. 106121, 17 pp., doi:10.1016/j.cor.2022.106121.
3 182 0.962801835015 X. Lai, D. Yue, J.-K. Hao, F. Glover, and Z. Lü, Iterated dynamic neighborhood search for packing equal circles on a sphere, Comput. Oper. Res. 151 (2023), Paper No. 106121, 17 pp., doi:10.1016/j.cor.2022.106121.
3 183 0.962987455061 Henry Cohn, 2024.
3 184 0.963227493195 X. Lai, D. Yue, J.-K. Hao, F. Glover, and Z. Lü, Iterated dynamic neighborhood search for packing equal circles on a sphere, Comput. Oper. Res. 151 (2023), Paper No. 106121, 17 pp., doi:10.1016/j.cor.2022.106121.
3 185 0.963400251151 X. Lai, D. Yue, J.-K. Hao, F. Glover, and Z. Lü, Iterated dynamic neighborhood search for packing equal circles on a sphere, Comput. Oper. Res. 151 (2023), Paper No. 106121, 17 pp., doi:10.1016/j.cor.2022.106121.
3 186 0.963602302299 X. Lai, D. Yue, J.-K. Hao, F. Glover, and Z. Lü, Iterated dynamic neighborhood search for packing equal circles on a sphere, Comput. Oper. Res. 151 (2023), Paper No. 106121, 17 pp., doi:10.1016/j.cor.2022.106121.
3 187 0.963858096099 X. Lai, D. Yue, J.-K. Hao, F. Glover, and Z. Lü, Iterated dynamic neighborhood search for packing equal circles on a sphere, Comput. Oper. Res. 151 (2023), Paper No. 106121, 17 pp., doi:10.1016/j.cor.2022.106121.
3 188 0.964002261472 X. Lai, D. Yue, J.-K. Hao, F. Glover, and Z. Lü, Iterated dynamic neighborhood search for packing equal circles on a sphere, Comput. Oper. Res. 151 (2023), Paper No. 106121, 17 pp., doi:10.1016/j.cor.2022.106121.
3 189 0.964190407206 Henry Cohn, 2024.
3 190 0.964292984546 X. Lai, D. Yue, J.-K. Hao, F. Glover, and Z. Lü, Iterated dynamic neighborhood search for packing equal circles on a sphere, Comput. Oper. Res. 151 (2023), Paper No. 106121, 17 pp., doi:10.1016/j.cor.2022.106121.
3 191 0.964504935278 X. Lai, D. Yue, J.-K. Hao, F. Glover, and Z. Lü, Iterated dynamic neighborhood search for packing equal circles on a sphere, Comput. Oper. Res. 151 (2023), Paper No. 106121, 17 pp., doi:10.1016/j.cor.2022.106121.
3 192 0.964585751396 X. Lai, D. Yue, J.-K. Hao, F. Glover, and Z. Lü, Iterated dynamic neighborhood search for packing equal circles on a sphere, Comput. Oper. Res. 151 (2023), Paper No. 106121, 17 pp., doi:10.1016/j.cor.2022.106121.
3 193 0.964893730830 X. Lai, D. Yue, J.-K. Hao, F. Glover, and Z. Lü, Iterated dynamic neighborhood search for packing equal circles on a sphere, Comput. Oper. Res. 151 (2023), Paper No. 106121, 17 pp., doi:10.1016/j.cor.2022.106121.
3 194 0.965083352280 Henry Cohn, 2024.
3 195 0.965251036900 X. Lai, D. Yue, J.-K. Hao, F. Glover, and Z. Lü, Iterated dynamic neighborhood search for packing equal circles on a sphere, Comput. Oper. Res. 151 (2023), Paper No. 106121, 17 pp., doi:10.1016/j.cor.2022.106121.
3 196 0.965468021791 Henry Cohn, 2024.
3 197 0.965671400310 Henry Cohn, 2025.
3 198 0.965829315374 Henry Cohn, 2024.
3 199 0.965916172795 Henry Cohn, 2024.
3 200 0.965942044452 Henry Cohn, 2025.
3 201 0.966306900791 Henry Cohn, 2024.
3 202 0.966420952188 Henry Cohn, 2025.
3 203 0.966622724376 Henry Cohn, 2024.
3 204 0.966712897537 Henry Cohn, 2024.
3 205 0.966826978769 Henry Cohn, 2025.
3 206 0.967078415732 Henry Cohn, 2024.
3 207 0.967258049747 Henry Cohn, 2024.
3 208 0.967362842483 Henry Cohn, 2024.
3 209 0.967547223611 Henry Cohn, 2024.
3 210 0.967630597679 Henry Cohn, 2024.
3 211 0.967822897132 Henry Cohn, 2024.
3 212 0.967927157323 Henry Cohn, 2024.
3 213 0.968163116144 Henry Cohn, 2024.
3 214 0.968277360489 Henry Cohn, 2025.
3 215 0.968453681521 Henry Cohn, 2024.
3 216 0.968596893733 X. Lai, D. Yue, J.-K. Hao, F. Glover, and Z. Lü, Iterated dynamic neighborhood search for packing equal circles on a sphere, Comput. Oper. Res. 151 (2023), Paper No. 106121, 17 pp., doi:10.1016/j.cor.2022.106121.
3 217 0.968776493956 Henry Cohn, 2025.
3 218 0.968883394297 Henry Cohn, 2025.
3 219 0.969051617681 Henry Cohn, 2025.
3 220 0.969138855053 Henry Cohn, 2024.
3 221 0.969215831481 Henry Cohn, 2024.
3 222 0.969434787486 Henry Cohn, 2024.
3 223 0.969554841105 Henry Cohn, 2024.
3 224 0.969694397387 Henry Cohn, 2024.
3 225 0.969832486673 Henry Cohn, 2024.
3 226 0.969909293134 Henry Cohn, 2026.
3 227 0.970127376655 Henry Cohn, 2025.
3 228 0.970249147842 Henry Cohn, 2024.
3 229 0.970369120893 Henry Cohn, 2025.
3 230 0.970483445180 Henry Cohn, 2024.
3 231 0.970608829668 Henry Cohn, 2024.
3 232 0.970693980479 Henry Cohn, 2024.
3 233 0.970846696940 Henry Cohn, 2025.
3 234 0.970904333828 Henry Cohn, 2025.
3 235 0.971108669673 Henry Cohn, 2025.
3 236 0.971194820033 Henry Cohn, 2024.
3 237 0.971302463818 Henry Cohn, 2024.
3 238 0.971452268582 Henry Cohn, 2025.
3 239 0.971571256039 Henry Cohn, 2024.
3 240 0.971657594484 Henry Cohn, 2024.
3 241 0.971802213952 Henry Cohn, 2024.
3 242 0.971893361216 Henry Cohn, 2025.
3 243 0.971985441053 Henry Cohn, 2024.
3 244 0.972112111081 Henry Cohn, 2025.
3 245 0.972207255147 Henry Cohn, 2024.
3 246 0.972337795891 Henry Cohn, 2024.
3 247 0.972484516196 Henry Cohn, 2024.
3 248 0.972578579063 Henry Cohn, 2026.
3 249 0.972727698402 Henry Cohn, 2024.
3 250 0.972808023884 Henry Cohn, 2025.
3 251 0.972878488641 Henry Cohn, 2025.
3 252 0.973005270899 Henry Cohn, 2024.
3 253 0.973112111220 Henry Cohn, 2024.
3 254 0.973166303401 Henry Cohn, 2026.
3 255 0.973336098901 Henry Cohn, 2025.
3 256 0.973419418775 Henry Cohn, 2024.
3 257 0.973518713646 Henry Cohn, 2024.
3 258 0.973601287197 Henry Cohn, 2024.
3 259 0.973687576212 Henry Cohn, 2024.
3 260 0.973743009714 Henry Cohn, 2024.
3 261 0.973920735044 Henry Cohn, 2025.
3 262 0.974027125019 Henry Cohn, 2024.
3 263 0.974151459437 Henry Cohn, 2024.
3 264 0.974246953956 Henry Cohn, 2024.
3 265 0.974330655728 Henry Cohn, 2024.
3 266 0.974398321697 Henry Cohn, 2024.
3 267 0.974465984042 Henry Cohn, 2025.
3 268 0.974543890479 Henry Cohn, 2024.
3 269 0.974603593005 Henry Cohn, 2024.
3 270 0.974616849625 T. Tarnai and Zs. Gáspár, Multi-symmetric close packings of equal spheres on the spherical surface, Acta Cryst. Sect. A 43 (1987), 612–616, doi:10.1107/S0108767387098842.
Minimal polynomial listed in plain text data
3 271 0.974808781632 Henry Cohn, 2024.
3 272 0.974950342892 Henry Cohn, 2024.
3 273 0.975065447378 Henry Cohn, 2024.
3 274 0.975124578016 Henry Cohn, 2024.
3 275 0.975240636386 Henry Cohn, 2024.
3 276 0.975320045419 Henry Cohn, 2024.
3 277 0.975403410833 Henry Cohn, 2026.
3 278 0.975464347279 Henry Cohn, 2024.
3 279 0.975521244170 Henry Cohn, 2024.
3 280 0.975556159117 Henry Cohn, 2024.
3 281 0.975696078155 Henry Cohn, 2024.
3 282 0.975817103894 X. Lai, D. Yue, J.-K. Hao, F. Glover, and Z. Lü, Iterated dynamic neighborhood search for packing equal circles on a sphere, Comput. Oper. Res. 151 (2023), Paper No. 106121, 17 pp., doi:10.1016/j.cor.2022.106121.
3 283 0.975926949120 Henry Cohn, 2024.
3 284 0.976026277162 Henry Cohn, 2024.
3 285 0.976130656685 Henry Cohn, 2024.
3 286 0.976191323169 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
3 287 0.976292535597 Henry Cohn, 2024.
3 288 0.976363801867 Henry Cohn, 2026.
3 289 0.976439859800 Henry Cohn, 2024.
3 290 0.976500970455 Henry Cohn, 2024.
3 291 0.976554952830 Henry Cohn, 2024.
3 292 0.976605729892 Henry Cohn, 2024.
3 293 0.976711107353 Henry Cohn, 2024.
3 294 0.976800057925 Henry Cohn, 2024.
3 295 0.976890767574 Henry Cohn, 2024.
3 296 0.976945912178 Henry Cohn, 2024.
3 297 0.977073329897 Henry Cohn, 2024.
3 298 0.977138858781 Henry Cohn, 2026.
3 299 0.977212814333 Henry Cohn, 2026, needs more optimization.
3 300 0.977219217071 R. H. Hardin, N. J. A. Sloane, and W. D. Smith, Tables of spherical codes with icosahedral symmetry, 1994–2000.
Minimal polynomial listed in plain text data
3 301 0.977392313268 Henry Cohn, 2024.
3 302 0.977456955232 Henry Cohn, 2026.
3 303 0.977523371220 Henry Cohn, 2024.
3 304 0.977583884150 Henry Cohn, 2024.
3 305 0.977632490985 Henry Cohn, 2024.
3 306 0.977704022662 Henry Cohn, 2026, needs more optimization.
3 307 0.977813909097 Henry Cohn, 2026.
3 308 0.977892051736 Henry Cohn, 2024.
3 309 0.977961312021 Henry Cohn, 2024.
3 310 0.978013425289 Henry Cohn, 2024.
3 311 0.978090634292 Henry Cohn, 2024.
3 312 0.978120344725 Henry Cohn, 2026, needs more optimization.
3 313 0.978224715180 Henry Cohn, 2026, needs more optimization.
3 314 0.978264330414 Henry Cohn, 2026.
3 315 0.978359778769 Henry Cohn, 2024.
3 316 0.978410524035 Henry Cohn, 2026, needs more optimization.
3 317 0.978487475787 Henry Cohn, 2024.
3 318 0.978544321333 Henry Cohn, 2026.
3 319 0.978603060123 Henry Cohn, 2024.
3 320 0.978663267012 Henry Cohn, 2024.
3 321 0.978701173891 Henry Cohn, 2026, needs more optimization.
3 322 0.978822184431 Henry Cohn, 2026.
3 323 0.978911588007 Henry Cohn, 2024.
3 324 0.978994028886 Henry Cohn, 2026, needs more optimization.
3 325 0.979042391577 Henry Cohn, 2026, needs more optimization.
3 326 0.979095664122 Henry Cohn, 2026, needs more optimization.
3 327 0.979174283158 Henry Cohn, 2026.
3 328 0.979227007488 Henry Cohn, 2024.
3 329 0.979277635210 Henry Cohn, 2024.
3 330 0.979324628117 Henry Cohn, 2026, needs more optimization.
3 331 0.979372870264 Henry Cohn, 2026, needs more optimization.
3 332 0.979423824372 Henry Cohn, 2024.
3 333 0.979489586862 Henry Cohn, 2026, needs more optimization.
3 334 0.979582034493 Henry Cohn, 2024.
3 335 0.979642932989 Henry Cohn, 2024.
3 336 0.979686468464 Henry Cohn, 2026.
3 337 0.979751882491 Henry Cohn, 2026.
3 338 0.979838818714 Henry Cohn, 2024.
3 339 0.979904919491 Henry Cohn, 2024.
3 340 0.979943850373 Henry Cohn, 2026.
3 341 0.979999270037 Henry Cohn, 2026.
3 342 0.980044047715 Henry Cohn, 2024.
3 343 0.980089600940 Henry Cohn, 2026.
3 344 0.980135977822 Henry Cohn, 2024.
3 345 0.980197727452 Henry Cohn, 2026, needs more optimization.
3 346 0.980275208082 Henry Cohn, 2024.
3 347 0.980349152228 Henry Cohn, 2024.
3 348 0.980406993197 Henry Cohn, 2024.
3 349 0.980459797495 Henry Cohn, 2026.
3 350 0.980513222800 Henry Cohn, 2026, needs more optimization.
3 351 0.980569841643 Henry Cohn, 2026, needs more optimization.
3 352 0.980619398778 Henry Cohn, 2024.
3 353 0.980684289246 Henry Cohn, 2026, needs more optimization.
3 354 0.980732120240 Henry Cohn, 2026, needs more optimization.
3 355 0.980776958770 Henry Cohn, 2024.
3 356 0.980821413544 Henry Cohn, 2026, needs more optimization.
3 357 0.980865743540 Henry Cohn, 2026.
3 358 0.980900885582 Henry Cohn, 2026.
3 359 0.980938721612 Henry Cohn, 2024.
3 360 0.980946761337 T. Tarnai and Zs. Gáspár, Multi-symmetric close packings of equal spheres on the spherical surface, Acta Cryst. Sect. A 43 (1987), 612–616, doi:10.1107/S0108767387098842.
3 361 0.981091247737 Henry Cohn, 2026.
3 362 0.981168174853 Henry Cohn, 2026, needs more optimization.
3 363 0.981225268927 Henry Cohn, 2024.
3 364 0.981274673313 Henry Cohn, 2026, needs more optimization.
3 365 0.981316235560 Henry Cohn, 2026, needs more optimization.
3 366 0.981370227579 Henry Cohn, 2026.
3 367 0.981413141131 Henry Cohn, 2026.
3 368 0.981467030026 Henry Cohn, 2024.
3 369 0.981501369093 Henry Cohn, 2024.
3 370 0.981559453185 Henry Cohn, 2024.
3 371 0.981613640563 Henry Cohn, 2024.
3 372 0.981659202089 Henry Cohn, 2024.
3 373 0.981715627838 Henry Cohn, 2024.
3 374 0.981743695439 Henry Cohn, 2024.
3 375 0.981792889902 Henry Cohn, 2024.
3 376 0.981825598990 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
3 377 0.981891941481 Henry Cohn, 2024.
3 378 0.981926575478 Henry Cohn, 2024.
3 379 0.981950820416 Henry Cohn, 2026, needs more optimization.
3 380 0.981966079866 Henry Cohn, 2025.
3 381 0.982053259897 Henry Cohn, 2026.
3 382 0.982151506158 Henry Cohn, 2026.
3 383 0.982191165481 Henry Cohn, 2024.
3 384 0.982231012956 Henry Cohn, 2026.
3 385 0.982281435205 Henry Cohn, 2024.
3 386 0.982313990090 Henry Cohn, 2024.
3 387 0.982346497568 Henry Cohn, 2024.
3 388 0.982373183313 Henry Cohn, 2024.
3 389 0.982417056387 Henry Cohn, 2026.
3 390 0.982438912809 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
3 391 0.982527810044 Henry Cohn, 2026, needs more optimization.
3 392 0.982588475638 Henry Cohn, 2026.
3 393 0.982649357699 Henry Cohn, 2024.
3 394 0.982692375827 Henry Cohn, 2024.
3 395 0.982725448100 Henry Cohn, 2026.
3 396 0.982765123660 Henry Cohn, 2026, needs more optimization.
3 397 0.982798694889 Henry Cohn, 2026.
3 398 0.982818286825 Henry Cohn, 2026, needs more optimization.
3 399 0.982856003493 Henry Cohn, 2026.
3 400 0.982906066576 Henry Cohn, 2026.
3 401 0.982947111243 Henry Cohn, 2026.
3 402 0.982978704486 Henry Cohn, 2026.
3 403 0.983047226508 Henry Cohn, 2026, needs more optimization.
3 404 0.983109826036 Henry Cohn, 2026, needs more optimization.
3 405 0.983168565133 Henry Cohn, 2024.
3 406 0.983206265163 Henry Cohn, 2024.
3 407 0.983245189251 Henry Cohn, 2026.
3 408 0.983288123210 Henry Cohn, 2024.
3 409 0.983324857501 Henry Cohn, 2024.
3 410 0.983353344472 Henry Cohn, 2026.
3 411 0.983397760620 Henry Cohn, 2024.
3 412 0.983427715393 Henry Cohn, 2026.
3 413 0.983461427167 Henry Cohn, 2024.
3 414 0.983495155996 Henry Cohn, 2024.
3 415 0.983544996006 Henry Cohn, 2026, needs more optimization.
3 416 0.983572356049 Henry Cohn, 2024.
3 417 0.983606337391 Henry Cohn, 2026.
3 418 0.983668285529 Henry Cohn, 2024.
3 419 0.983706936316 Henry Cohn, 2026.
3 420 0.983735076323 Henry Cohn, 2026, needs more optimization.
3 421 0.983801876824 Henry Cohn, 2024.
3 422 0.983830218357 Henry Cohn, 2026, needs more optimization.
3 423 0.983874347222 Henry Cohn, 2026.
3 424 0.983899706345 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
3 425 0.983947724258 Henry Cohn, 2024.
3 426 0.983967656850 Henry Cohn, 2024.
3 427 0.984017759902 Henry Cohn, 2024.
3 428 0.984058613099 Henry Cohn, 2026.
3 429 0.984081497349 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
3 430 0.984130874521 Henry Cohn, 2026, needs more optimization.
3 431 0.984165514392 Henry Cohn, 2024.
3 432 0.984201636678 Henry Cohn, 2024.
3 433 0.984245053116 Henry Cohn, 2026, needs more optimization.
3 434 0.984271594586 Henry Cohn, 2026, needs more optimization.
3 435 0.984318874079 Henry Cohn, 2026.
3 436 0.984359381087 Henry Cohn, 2024.
3 437 0.984376596212 Henry Cohn, 2024.
3 438 0.984419779873 Henry Cohn, 2024.
3 439 0.984454579489 Henry Cohn, 2026, needs more optimization.
3 440 0.984472421765 Henry Cohn, 2024.
3 441 0.984527980944 Henry Cohn, 2024.
3 442 0.984558411966 Henry Cohn, 2026, needs more optimization.
3 443 0.984592266668 Henry Cohn, 2024.
3 444 0.984628415926 Henry Cohn, 2024.
3 445 0.984667372266 Henry Cohn, 2024.
3 446 0.984702068844 Henry Cohn, 2024.
3 447 0.984730509217 Henry Cohn, 2024.
3 448 0.984778913431 Henry Cohn, 2024.
3 449 0.984798090520 Henry Cohn, 2026, needs more optimization.
3 450 0.984846922701 Henry Cohn, 2024.
3 451 0.984869418821 Henry Cohn, 2026.
3 452 0.984911000119 Henry Cohn, 2024.
3 453 0.984942286924 Henry Cohn, 2024.
3 454 0.984966228755 Henry Cohn, 2026, needs more optimization.
3 455 0.984994478749 Henry Cohn, 2024.
3 456 0.985031017295 Henry Cohn, 2024.
3 457 0.985064695326 Henry Cohn, 2024.
3 458 0.985097884587 Henry Cohn, 2024.
3 459 0.985125472667 Henry Cohn, 2026, needs more optimization.
3 460 0.985147680862 Henry Cohn, 2026.
3 461 0.985183865100 Henry Cohn, 2026, needs more optimization.
3 462 0.985218304940 Henry Cohn, 2026.
3 463 0.985261069429 Henry Cohn, 2026.
3 464 0.985297019485 Henry Cohn, 2024.
3 465 0.985320807146 Henry Cohn, 2026.
3 466 0.985359575651 Henry Cohn, 2026, needs more optimization.
3 467 0.985386081788 Henry Cohn, 2024.
3 468 0.985411837325 Henry Cohn, 2024.
3 469 0.985444627723 Henry Cohn, 2024.
3 470 0.985482640963 Henry Cohn, 2024.
3 471 0.985509915678 Henry Cohn, 2024.
3 472 0.985523730012 Henry Cohn, 2026.
3 473 0.985558412595 Henry Cohn, 2024.
3 474 0.985602045775 Henry Cohn, 2026, needs more optimization.
3 475 0.985602451902 Henry Cohn, 2026, needs more optimization.
3 476 0.985629966650 Henry Cohn, 2026.
3 477 0.985650812703 Henry Cohn, 2026.
3 478 0.985679876222 Henry Cohn, 2026.
3 479 0.985700108040 Henry Cohn, 2026, needs more optimization.
3 480 0.985721861452 T. Tarnai and Zs. Gáspár, Multi-symmetric close packings of equal spheres on the spherical surface, Acta Cryst. Sect. A 43 (1987), 612–616, doi:10.1107/S0108767387098842.
3 481 0.985794622844 Henry Cohn, 2026.
3 482 0.985841177159 Henry Cohn, 2026, needs more optimization.
3 483 0.985869964684 Henry Cohn, 2026.
3 484 0.985899970950 Henry Cohn, 2026, needs more optimization.
3 485 0.985924698901 Henry Cohn, 2024.
3 486 0.985950768752 Henry Cohn, 2024.
3 487 0.985985004243 Henry Cohn, 2024.
3 488 0.986009149228 Henry Cohn, 2024.
3 489 0.986026483781 Henry Cohn, 2024.
3 490 0.986059626300 Henry Cohn, 2026, needs more optimization.
3 491 0.986099610800 Henry Cohn, 2024.
3 492 0.986121929372 Henry Cohn, 2024.
3 493 0.986156039294 Henry Cohn, 2026, needs more optimization.
3 494 0.986181802784 Henry Cohn, 2026, needs more optimization.
3 495 0.986212504789 Henry Cohn, 2026.
3 496 0.986246272307 Henry Cohn, 2024.
3 497 0.986267131233 Henry Cohn, 2024.
3 498 0.986298103712 Henry Cohn, 2024.
3 499 0.986323180888 Henry Cohn, 2024.
3 500 0.986348497971 Henry Cohn, 2026, needs more optimization.
3 501 0.986368725989 Henry Cohn, 2026.
3 502 0.986395118302 Henry Cohn, 2026, needs more optimization.
3 503 0.986428428291 Henry Cohn, 2024.
3 504 0.986455469484 Henry Cohn, 2024.
3 505 0.986479196655 Henry Cohn, 2024.
3 506 0.986501726579 Henry Cohn, 2026.
3 507 0.986527855040 Henry Cohn, 2024.
3 508 0.986549751783 Henry Cohn, 2026, needs more optimization.
3 509 0.986555665406 Henry Cohn, 2026, needs more optimization.
3 510 0.986562950498 Henry Cohn, 2025.
3 511 0.986616701042 Henry Cohn, 2026.
3 512 0.986666793363 Henry Cohn, 2026.
3 513 0.986700077118 Henry Cohn, 2024.
3 514 0.986720532797 Henry Cohn, 2024.
3 515 0.986749064827 Henry Cohn, 2024.
3 516 0.986772800882 Henry Cohn, 2026.
3 517 0.986799492641 Henry Cohn, 2024.
3 518 0.986819181629 Henry Cohn, 2026.
3 519 0.986843855828 Henry Cohn, 2026, needs more optimization.
3 520 0.986876145782 Henry Cohn, 2024.
3 521 0.986900278325 Henry Cohn, 2024.
3 522 0.986922042800 Henry Cohn, 2026, needs more optimization.
3 523 0.986949812576 Henry Cohn, 2026, needs more optimization.
3 524 0.986971259359 Henry Cohn, 2026, needs more optimization.
3 525 0.986995192288 Henry Cohn, 2026.
3 526 0.987019236077 Henry Cohn, 2024.
3 527 0.987045953386 Henry Cohn, 2026.
3 528 0.987069504316 Henry Cohn, 2024.
3 529 0.987089590281 Henry Cohn, 2024.
3 530 0.987121524163 Henry Cohn, 2024.
3 531 0.987141738237 Henry Cohn, 2024.
3 532 0.987165596115 Henry Cohn, 2024.
3 533 0.987185368627 Henry Cohn, 2024.
3 534 0.987215557894 Henry Cohn, 2024.
3 535 0.987233678537 Henry Cohn, 2026, needs more optimization.
3 536 0.987259191622 Henry Cohn, 2024.
3 537 0.987271183218 Henry Cohn, 2024.
3 538 0.987299580832 Henry Cohn, 2026.
3 539 0.987336486625 Henry Cohn, 2024.
3 540 0.987351430022 Henry Cohn, 2024.
3 541 0.987374329775 Henry Cohn, 2026.
3 542 0.987388996662 Henry Cohn, 2024.
3 543 0.987423671103 Henry Cohn, 2026.
3 544 0.987447704608 Henry Cohn, 2024.
3 545 0.987469058651 Henry Cohn, 2024.
3 546 0.987491594825 Henry Cohn, 2024.
3 547 0.987512470728 Henry Cohn, 2024.
3 548 0.987533400403 Henry Cohn, 2024.
3 549 0.987547178474 Henry Cohn, 2024.
3 550 0.987583651579 Henry Cohn, 2026.
3 551 0.987606449640 Henry Cohn, 2024.
3 552 0.987622107541 Henry Cohn, 2026, needs more optimization.
3 553 0.987648249263 Henry Cohn, 2024.
3 554 0.987670281304 Henry Cohn, 2024.
3 555 0.987693259384 Henry Cohn, 2024.
3 556 0.987718378190 Henry Cohn, 2024.
3 557 0.987733482064 Henry Cohn, 2026.
3 558 0.987758227820 Henry Cohn, 2026, needs more optimization.
3 559 0.987780703660 Henry Cohn, 2026.
3 560 0.987804065628 Henry Cohn, 2024.
3 561 0.987825037070 Henry Cohn, 2024.
3 562 0.987840456566 Henry Cohn, 2026.
3 563 0.987867088796 Henry Cohn, 2024.
3 564 0.987882106063 Henry Cohn, 2026, needs more optimization.
3 565 0.987909929449 Henry Cohn, 2026.
3 566 0.987930679295 Henry Cohn, 2024.
3 567 0.987952567335 Henry Cohn, 2024.
3 568 0.987974408939 Henry Cohn, 2024.
3 569 0.987994333054 Henry Cohn, 2024.
3 570 0.988009696089 Henry Cohn, 2026.
3 571 0.988036994032 Henry Cohn, 2024.
3 572 0.988045143812 Henry Cohn, 2025.
3 573 0.988071110674 Henry Cohn, 2026.
3 574 0.988099427052 Henry Cohn, 2024.
3 575 0.988116092887 Henry Cohn, 2024.
3 576 0.988134624929 Henry Cohn, 2024.
3 577 0.988155543378 Henry Cohn, 2024.
3 578 0.988175563350 Henry Cohn, 2024.
3 579 0.988199193100 Henry Cohn, 2024.
3 580 0.988214394071 Henry Cohn, 2024.
3 581 0.988236302808 Henry Cohn, 2024.
3 582 0.988258915209 Henry Cohn, 2024.
3 583 0.988278440743 Henry Cohn, 2024.
3 584 0.988296373611 Henry Cohn, 2024.
3 585 0.988316187693 Henry Cohn, 2024.
3 586 0.988336136398 Henry Cohn, 2024.
3 587 0.988354165587 Henry Cohn, 2024.
3 588 0.988367697736 Henry Cohn, 2026.
3 589 0.988390327285 Henry Cohn, 2024.
3 590 0.988413417033 Henry Cohn, 2024.
3 591 0.988426313006 Henry Cohn, 2026.
3 592 0.988448203051 Henry Cohn, 2026, needs more optimization.
3 593 0.988465092835 Henry Cohn, 2026, needs more optimization.
3 594 0.988487841215 Henry Cohn, 2026, needs more optimization.
3 595 0.988509243514 Henry Cohn, 2024.
3 596 0.988525644295 Henry Cohn, 2026.
3 597 0.988541943633 Henry Cohn, 2026.
3 598 0.988562584541 Henry Cohn, 2026.
3 599 0.988581647683 Henry Cohn, 2024.
3 600 0.988601034993 Henry Cohn, 2024.
3 601 0.988621946438 Henry Cohn, 2024.
3 602 0.988639847715 Henry Cohn, 2026, needs more optimization.
3 603 0.988656705182 Henry Cohn, 2026.
3 604 0.988675027867 Henry Cohn, 2024.
3 605 0.988698898761 Henry Cohn, 2026.
3 606 0.988712847782 Henry Cohn, 2024.
3 607 0.988726120936 Henry Cohn, 2026, needs more optimization.
3 608 0.988753049196 Henry Cohn, 2026, needs more optimization.
3 609 0.988760157529 Henry Cohn, 2024.
3 610 0.988786015398 Henry Cohn, 2026, needs more optimization.
3 611 0.988800912598 Henry Cohn, 2026, needs more optimization.
3 612 0.988821722164 Henry Cohn, 2026.
3 613 0.988842455232 Henry Cohn, 2024.
3 614 0.988857096430 Henry Cohn, 2024.
3 615 0.988873099629 Henry Cohn, 2026, needs more optimization.
3 616 0.988892714835 Henry Cohn, 2024.
3 617 0.988912783824 Henry Cohn, 2024.
3 618 0.988927807992 Henry Cohn, 2024.
3 619 0.988948201134 Henry Cohn, 2025.
3 620 0.988948235960 R. H. Hardin, N. J. A. Sloane, and W. D. Smith, Tables of spherical codes with icosahedral symmetry, 1994–2000.
3 621 0.988984109802 Henry Cohn, 2024.
3 622 0.989000035626 Henry Cohn, 2026.
3 623 0.989012818314 Henry Cohn, 2024.
3 624 0.989034528790 Henry Cohn, 2024.
3 625 0.989047039560 Henry Cohn, 2026.
3 626 0.989070144515 Henry Cohn, 2026.
3 627 0.989088135354 Henry Cohn, 2024.
3 628 0.989102260067 Henry Cohn, 2026, needs more optimization.
3 629 0.989121123248 Henry Cohn, 2024.
3 630 0.989134691942 Henry Cohn, 2024.
3 631 0.989155822068 Henry Cohn, 2024.
3 632 0.989172993109 Henry Cohn, 2024.
3 633 0.989188471837 Henry Cohn, 2024.
3 634 0.989201672529 Henry Cohn, 2026, needs more optimization.
3 635 0.989217714617 Henry Cohn, 2026.
3 636 0.989241817793 Henry Cohn, 2026, needs more optimization.
3 637 0.989258653000 Henry Cohn, 2026, needs more optimization.
3 638 0.989267204518 Henry Cohn, 2024.
3 639 0.989289999844 Henry Cohn, 2026.
3 640 0.989301986015 Henry Cohn, 2024.
3 641 0.989321411266 Henry Cohn, 2024.
3 642 0.989332573182 Henry Cohn, 2024.
3 643 0.989348424838 Henry Cohn, 2026.
3 644 0.989370321422 Henry Cohn, 2026, needs more optimization.
3 645 0.989382211173 Henry Cohn, 2026.
3 646 0.989398690989 Henry Cohn, 2024.
3 647 0.989412931660 Henry Cohn, 2026.
3 648 0.989432732690 Henry Cohn, 2026, needs more optimization.
3 649 0.989449788085 Henry Cohn, 2026, needs more optimization.
3 650 0.989461679845 Henry Cohn, 2026.
3 651 0.989485039605 Henry Cohn, 2024.
3 652 0.989499769599 Henry Cohn, 2026, needs more optimization.
3 653 0.989517659733 Henry Cohn, 2024.
3 654 0.989528389272 Henry Cohn, 2024.
3 655 0.989544914621 Henry Cohn, 2026.
3 656 0.989563787961 Henry Cohn, 2024.
3 657 0.989576352164 Henry Cohn, 2024.
3 658 0.989590441670 Henry Cohn, 2024.
3 659 0.989608602208 Henry Cohn, 2024.
3 660 0.989623972684 Henry Cohn, 2026, needs more optimization.
3 661 0.989637856948 Henry Cohn, 2026.
3 662 0.989658469367 Henry Cohn, 2024.
3 663 0.989668542979 Henry Cohn, 2024.
3 664 0.989679965913 Henry Cohn, 2026.
3 665 0.989692795388 Henry Cohn, 2026, needs more optimization.
3 666 0.989717351243 Henry Cohn, 2026.
3 667 0.989730982552 Henry Cohn, 2026.
3 668 0.989745107620 Henry Cohn, 2026, needs more optimization.
3 669 0.989759503187 Henry Cohn, 2026, needs more optimization.
3 670 0.989765777159 Henry Cohn, 2024.
3 671 0.989789044042 Henry Cohn, 2026.
3 672 0.989793192154 Henry Cohn, 2026.
3 673 0.989818330488 Henry Cohn, 2024.
3 674 0.989830195771 Henry Cohn, 2026.
3 675 0.989846916511 Henry Cohn, 2026, needs more optimization.
3 676 0.989861529212 Henry Cohn, 2024.
3 677 0.989873040790 Henry Cohn, 2026.
3 678 0.989879779829 Henry Cohn, 2024.
3 679 0.989905658846 Henry Cohn, 2026.
3 680 0.989918641442 Henry Cohn, 2026, needs more optimization.
3 681 0.989936920244 Henry Cohn, 2024.
3 682 0.989953273780 Henry Cohn, 2026.
3 683 0.989967898498 Henry Cohn, 2026, needs more optimization.
3 684 0.989976775468 Henry Cohn, 2026.
3 685 0.990001194691 Henry Cohn, 2026, needs more optimization.
3 686 0.990006418271 Henry Cohn, 2024.
3 687 0.990023877788 Henry Cohn, 2026, needs more optimization.
3 688 0.990037853003 Henry Cohn, 2024.
3 689 0.990050270939 Henry Cohn, 2026.
3 692 0.990060116362 R. H. Hardin, N. J. A. Sloane, and W. D. Smith, Tables of spherical codes with icosahedral symmetry, 1994–2000.
3 693 0.990078940124 Henry Cohn, 2026, needs more optimization.
3 694 0.990103743152 Henry Cohn, 2026, needs more optimization.
3 695 0.990114989762 Henry Cohn, 2026.
3 696 0.990138293016 Henry Cohn, 2026.
3 697 0.990163001875 Henry Cohn, 2026.
3 698 0.990178131415 Henry Cohn, 2024.
3 699 0.990191563570 Henry Cohn, 2026, needs more optimization.
3 700 0.990192254287 Henry Cohn, 2026.
3 701 0.990202423105 Henry Cohn, 2026, needs more optimization.
3 702 0.990207507930 Henry Cohn, 2025.
3 703 0.990226501892 Henry Cohn, 2026.
3 704 0.990247522690 Henry Cohn, 2026, needs more optimization.
3 705 0.990263988882 Henry Cohn, 2026, needs more optimization.
3 706 0.990280269273 Henry Cohn, 2026.
3 707 0.990307749113 Henry Cohn, 2024.
3 708 0.990308161383 Henry Cohn, 2026, needs more optimization.
3 709 0.990323405334 Henry Cohn, 2026.
3 710 0.990330662130 Henry Cohn, 2026.
3 711 0.990344030199 Henry Cohn, 2026.
3 712 0.990367295324 Henry Cohn, 2026.
3 713 0.990383183548 Henry Cohn, 2026, needs more optimization.
3 714 0.990387021148 Henry Cohn, 2026, needs more optimization.
3 715 0.990399232663 Henry Cohn, 2026, needs more optimization.
3 716 0.990424201178 Henry Cohn, 2024.
3 717 0.990435742039 Henry Cohn, 2026, needs more optimization.
3 718 0.990448237688 Henry Cohn, 2024.
3 719 0.990461529899 Henry Cohn, 2024.
3 720 0.990474919274 Henry Cohn, 2024.
3 721 0.990485931183 Henry Cohn, 2026.
3 722 0.990499809958 Henry Cohn, 2024.
3 723 0.990511130593 Henry Cohn, 2026, needs more optimization.
3 724 0.990532198847 Henry Cohn, 2024.
3 725 0.990534529638 Henry Cohn, 2024.
3 726 0.990551400390 Henry Cohn, 2026, needs more optimization.
3 727 0.990566965324 Henry Cohn, 2024.
3 728 0.990571170880 Henry Cohn, 2026, needs more optimization.
3 729 0.990582447225 Henry Cohn, 2026.
3 730 0.990603287439 Henry Cohn, 2024.
3 731 0.990612626443 Henry Cohn, 2024.
3 732 0.990621413211 Henry Cohn, 2025.
3 733 0.990635128011 Henry Cohn, 2026, needs more optimization.
3 734 0.990652693601 Henry Cohn, 2026, needs more optimization.
3 735 0.990665859867 Henry Cohn, 2026.
3 736 0.990680033860 Henry Cohn, 2026.
3 737 0.990695306177 Henry Cohn, 2024.
3 738 0.990704677084 Henry Cohn, 2024.
3 739 0.990712804529 Henry Cohn, 2026, needs more optimization.
3 740 0.990728865941 Henry Cohn, 2024.
3 741 0.990738820030 Henry Cohn, 2026.
3 742 0.990755361153 Henry Cohn, 2024.
3 743 0.990760199525 Henry Cohn, 2026.
3 744 0.990775592495 Henry Cohn, 2026.
3 745 0.990786255878 Henry Cohn, 2026, needs more optimization.
3 746 0.990800147942 Henry Cohn, 2026, needs more optimization.
3 747 0.990816878553 Henry Cohn, 2024.
3 748 0.990825554974 Henry Cohn, 2026, needs more optimization.
3 749 0.990837968357 Henry Cohn, 2026.
3 750 0.990847475915 X. Lai, D. Yue, J.-K. Hao, F. Glover, and Z. Lü, Iterated dynamic neighborhood search for packing equal circles on a sphere, Comput. Oper. Res. 151 (2023), Paper No. 106121, 17 pp., doi:10.1016/j.cor.2022.106121.
3 751 0.990857663690 Henry Cohn, 2024.
3 752 0.990870655114 Henry Cohn, 2026.
3 753 0.990883514545 Henry Cohn, 2024.
3 754 0.990896951324 Henry Cohn, 2026.
3 755 0.990899134620 Henry Cohn, 2026, needs more optimization.
3 756 0.990921466258 Henry Cohn, 2026, needs more optimization.
3 757 0.990937812953 Henry Cohn, 2024.
3 758 0.990946005792 Henry Cohn, 2024.
3 759 0.990954743746 Henry Cohn, 2024.
3 760 0.990970877087 Henry Cohn, 2024.
3 761 0.990975674468 Henry Cohn, 2026.
3 762 0.990993252010 Henry Cohn, 2024.
3 763 0.991002546962 Henry Cohn, 2024.
3 764 0.991020015136 Henry Cohn, 2026, needs more optimization.
3 765 0.991024981687 Henry Cohn, 2026.
3 766 0.991034226787 Henry Cohn, 2026.
3 767 0.991054850991 Henry Cohn, 2024.
3 768 0.991061683327 Henry Cohn, 2026.
3 769 0.991073054499 Henry Cohn, 2024.
3 770 0.991085755280 Henry Cohn, 2024.
3 771 0.991092703929 Henry Cohn, 2026, needs more optimization.
3 772 0.991107834438 Henry Cohn, 2024.
3 773 0.991119133097 Henry Cohn, 2026.
3 774 0.991132071939 Henry Cohn, 2024.
3 775 0.991142880919 Henry Cohn, 2026, needs more optimization.
3 776 0.991154326426 Henry Cohn, 2026, needs more optimization.
3 777 0.991161697853 Henry Cohn, 2024.
3 778 0.991176107049 Henry Cohn, 2026, needs more optimization.
3 779 0.991186101604 Henry Cohn, 2026.
3 780 0.991195467101 Henry Cohn, 2024.
3 781 0.991212495316 Henry Cohn, 2024.
3 782 0.991215177221 Henry Cohn, 2026, needs more optimization.
3 783 0.991224998811 Henry Cohn, 2026, needs more optimization.
3 784 0.991237581418 Henry Cohn, 2024.
3 785 0.991246020182 Henry Cohn, 2026, needs more optimization.
3 786 0.991261576581 Henry Cohn, 2026.
3 787 0.991274864071 Henry Cohn, 2026, needs more optimization.
3 788 0.991285577631 Henry Cohn, 2026.
3 789 0.991288796383 Henry Cohn, 2026, needs more optimization.
3 790 0.991311108786 Henry Cohn, 2024.
3 791 0.991319397658 Henry Cohn, 2024.
3 792 0.991327970122 Henry Cohn, 2024.
3 793 0.991336046932 Henry Cohn, 2026, needs more optimization.
3 794 0.991351979642 Henry Cohn, 2026, needs more optimization.
3 795 0.991358759051 Henry Cohn, 2026, needs more optimization.
3 796 0.991373620973 Henry Cohn, 2024.
3 797 0.991382382844 Henry Cohn, 2024.
3 798 0.991393707648 Henry Cohn, 2026.
3 799 0.991404670857 Henry Cohn, 2026, needs more optimization.
3 800 0.991414851715 Henry Cohn, 2024.
3 801 0.991423316027 Henry Cohn, 2026, needs more optimization.
3 802 0.991434093044 Henry Cohn, 2026, needs more optimization.
3 803 0.991449666567 Henry Cohn, 2026.
3 804 0.991459924550 Henry Cohn, 2024.
3 805 0.991468080347 Henry Cohn, 2024.
3 806 0.991477473610 Henry Cohn, 2026, needs more optimization.
3 807 0.991488929993 Henry Cohn, 2024.
3 808 0.991499113412 Henry Cohn, 2026.
3 809 0.991512054441 Henry Cohn, 2026, needs more optimization.
3 810 0.991520665687 Henry Cohn, 2024.
3 811 0.991528398760 Henry Cohn, 2026.
3 812 0.991540671325 Henry Cohn, 2026.
3 813 0.991547822510 Henry Cohn, 2024.
3 814 0.991561413238 Henry Cohn, 2026.
3 815 0.991566962007 Henry Cohn, 2026, needs more optimization.
3 816 0.991580342934 Henry Cohn, 2024.
3 817 0.991591011326 Henry Cohn, 2024.
3 818 0.991597091498 Henry Cohn, 2026, needs more optimization.
3 819 0.991609552901 Henry Cohn, 2026, needs more optimization.
3 820 0.991624044122 Henry Cohn, 2024.
3 821 0.991630142697 Henry Cohn, 2026, needs more optimization.
3 822 0.991639297576 Henry Cohn, 2026.
3 823 0.991650165081 Henry Cohn, 2024.
3 824 0.991660076581 Henry Cohn, 2024.
3 825 0.991668700784 Henry Cohn, 2026, needs more optimization.
3 826 0.991679203409 Henry Cohn, 2026, needs more optimization.
3 827 0.991687082167 Henry Cohn, 2026, needs more optimization.
3 828 0.991700756929 Henry Cohn, 2024.
3 829 0.991713398461 Henry Cohn, 2024.
3 830 0.991721621394 Henry Cohn, 2024.
3 831 0.991727034826 Henry Cohn, 2026.
3 832 0.991733957066 Henry Cohn, 2026.
3 833 0.991746497985 Henry Cohn, 2026, needs more optimization.
3 834 0.991758792862 Henry Cohn, 2026.
3 835 0.991760362693 Henry Cohn, 2026, needs more optimization.
3 836 0.991770171617 Henry Cohn, 2026, needs more optimization.
3 837 0.991780503947 Henry Cohn, 2026.
3 838 0.991796901496 Henry Cohn, 2026, needs more optimization.
3 839 0.991804758597 Henry Cohn, 2026, needs more optimization.
3 840 0.991804766960 Henry Cohn, 2026, needs more optimization.
3 841 0.991814443516 Henry Cohn, 2026, needs more optimization.
3 842 0.991823489583 Henry Cohn, 2026, needs more optimization.
3 843 0.991831838925 Henry Cohn, 2026, needs more optimization.
3 844 0.991847905567 Henry Cohn, 2026, needs more optimization.
3 845 0.991854773658 Henry Cohn, 2026.
3 846 0.991861925048 Henry Cohn, 2026, needs more optimization.
3 847 0.991869552615 Henry Cohn, 2026.
3 848 0.991876988506 Henry Cohn, 2026.
3 849 0.991884604711 Henry Cohn, 2026.
3 850 0.991891189264 Henry Cohn, 2026, needs more optimization.
3 851 0.991898113840 Henry Cohn, 2026.
3 852 0.991904249523 R. H. Hardin, N. J. A. Sloane, and W. D. Smith, Tables of spherical codes with icosahedral symmetry, 1994–2000.
3 853 0.991917993656 Henry Cohn, 2026, needs more optimization.
3 854 0.991934894060 Henry Cohn, 2026, needs more optimization.
3 855 0.991948423912 Henry Cohn, 2026.
3 856 0.991959732459 Henry Cohn, 2026, needs more optimization.
3 857 0.991976233079 Henry Cohn, 2026, needs more optimization.
3 858 0.991987713948 Henry Cohn, 2026.
3 859 0.991994871145 Henry Cohn, 2026, needs more optimization.
3 860 0.992000220754 Henry Cohn, 2026.
3 861 0.992009501248 Henry Cohn, 2026, needs more optimization.
3 862 0.992019498595 Henry Cohn, 2026, needs more optimization.
3 863 0.992030946047 Henry Cohn, 2026, needs more optimization.
3 864 0.992045910827 Henry Cohn, 2025.
3 865 0.992049202700 Henry Cohn, 2026.
3 866 0.992059688359 Henry Cohn, 2026.
3 867 0.992072381754 Henry Cohn, 2025.
3 868 0.992079945563 Henry Cohn, 2026, needs more optimization.
3 869 0.992081499989 Henry Cohn, 2026, needs more optimization.
3 870 0.992086777323 Henry Cohn, 2026.
3 871 0.992092487763 Henry Cohn, 2026.
3 872 0.992098850920 R. H. Hardin, N. J. A. Sloane, and W. D. Smith, Tables of spherical codes with icosahedral symmetry, 1994–2000.
3 873 0.992109762118 Henry Cohn, 2026.
3 874 0.992124799921 Henry Cohn, 2026, needs more optimization.
3 875 0.992137558500 Henry Cohn, 2026.
3 876 0.992144394016 Henry Cohn, 2026, needs more optimization.
3 877 0.992154329715 Henry Cohn, 2025.
3 878 0.992163497065 Henry Cohn, 2026, needs more optimization.
3 879 0.992169048805 Henry Cohn, 2026, needs more optimization.
3 880 0.992185909971 Henry Cohn, 2025.
3 881 0.992192486886 Henry Cohn, 2025.
3 882 0.992198371680 Henry Cohn, 2025.
3 883 0.992205243450 Henry Cohn, 2026, needs more optimization.
3 884 0.992213792229 Henry Cohn, 2026, needs more optimization.
3 885 0.992223430817 Henry Cohn, 2026, needs more optimization.
3 886 0.992236374298 Henry Cohn, 2026.
3 887 0.992242382220 Henry Cohn, 2025.
3 888 0.992254765797 Henry Cohn, 2026, needs more optimization.
3 889 0.992263158186 Henry Cohn, 2026, needs more optimization.
3 890 0.992270277564 Henry Cohn, 2026, needs more optimization.
3 891 0.992282228896 Henry Cohn, 2026, needs more optimization.
3 892 0.992285856055 Henry Cohn, 2026.
3 893 0.992295938617 Henry Cohn, 2026, needs more optimization.
3 894 0.992309459744 Henry Cohn, 2025.
3 895 0.992316358484 Henry Cohn, 2025.
3 896 0.992316827394 Henry Cohn, 2026.
3 897 0.992332110080 Henry Cohn, 2025.
3 898 0.992338696092 Henry Cohn, 2025.
3 899 0.992345607640 Henry Cohn, 2026.
3 900 0.992355674372 Henry Cohn, 2026.
3 901 0.992359380332 Henry Cohn, 2026, needs more optimization.
3 902 0.992371998120 Henry Cohn, 2026, needs more optimization.
3 903 0.992381167272 Henry Cohn, 2026, needs more optimization.
3 904 0.992389884610 Henry Cohn, 2026, needs more optimization.
3 905 0.992399600923 Henry Cohn, 2026, needs more optimization.
3 906 0.992403008027 Henry Cohn, 2026, needs more optimization.
3 907 0.992414671348 Henry Cohn, 2026, needs more optimization.
3 908 0.992421147752 Henry Cohn, 2026, needs more optimization.
3 909 0.992428356067 Henry Cohn, 2026, needs more optimization.
3 910 0.992437123795 Henry Cohn, 2025.
3 911 0.992442944074 Henry Cohn, 2026.
3 912 0.992454600852 Henry Cohn, 2025.
3 913 0.992469409936 Henry Cohn, 2026, needs more optimization.
3 914 0.992471207708 Henry Cohn, 2025.
3 915 0.992480688576 Henry Cohn, 2026.
3 916 0.992487103876 Henry Cohn, 2026.
3 917 0.992497063301 Henry Cohn, 2026.
3 918 0.992505586908 Henry Cohn, 2026, needs more optimization.
3 919 0.992512397512 Henry Cohn, 2026.
3 920 0.992517498611 Henry Cohn, 2026.
3 921 0.992531088356 Henry Cohn, 2026, needs more optimization.
3 922 0.992534994238 Henry Cohn, 2026, needs more optimization.
3 923 0.992545962026 Henry Cohn, 2026.
3 924 0.992553990146 Henry Cohn, 2025.
3 925 0.992561907552 Henry Cohn, 2026.
3 926 0.992564856890 Henry Cohn, 2026.
3 927 0.992576722563 Henry Cohn, 2026, needs more optimization.
3 928 0.992580182120 Henry Cohn, 2026.
3 929 0.992588276926 Henry Cohn, 2026.
3 930 0.992594659009 Henry Cohn, 2026.
3 931 0.992603050921 Henry Cohn, 2026.
3 932 0.992611564654 Henry Cohn, 2026, needs more optimization.
3 933 0.992624602034 Henry Cohn, 2025.
3 934 0.992625562478 Henry Cohn, 2026, needs more optimization.
3 935 0.992636962822 Henry Cohn, 2026, needs more optimization.
3 936 0.992645528874 Henry Cohn, 2026, needs more optimization.
3 937 0.992652128678 Henry Cohn, 2026, needs more optimization.
3 938 0.992665682904 Henry Cohn, 2025.
3 939 0.992672947443 Henry Cohn, 2025.
3 940 0.992677472433 Henry Cohn, 2026.
3 941 0.992684585898 Henry Cohn, 2026.
3 942 0.992696579115 Henry Cohn, 2025.
3 943 0.992698785176 Henry Cohn, 2026, needs more optimization.
3 944 0.992710970106 Henry Cohn, 2026, needs more optimization.
3 945 0.992717631580 Henry Cohn, 2025.
3 946 0.992721619544 Henry Cohn, 2026, needs more optimization.
3 947 0.992726855397 Henry Cohn, 2026.
3 948 0.992731848428 Henry Cohn, 2026, needs more optimization.
3 949 0.992751074856 Henry Cohn, 2026.
3 950 0.992751415901 Henry Cohn, 2026, needs more optimization.
3 951 0.992759834272 Henry Cohn, 2026.
3 952 0.992771438024 Henry Cohn, 2025.
3 953 0.992777286390 Henry Cohn, 2026, needs more optimization.
3 954 0.992782542839 Henry Cohn, 2026, needs more optimization.
3 955 0.992790113965 Henry Cohn, 2026, needs more optimization.
3 956 0.992801093482 Henry Cohn, 2025.
3 957 0.992810004476 Henry Cohn, 2025.
3 958 0.992816897919 Henry Cohn, 2026, needs more optimization.
3 959 0.992823549807 Henry Cohn, 2026.
3 960 0.992829048036 Henry Cohn, 2026, needs more optimization.
3 961 0.992838773549 Henry Cohn, 2025.
3 962 0.992842996151 Henry Cohn, 2026.
3 963 0.992851430685 Henry Cohn, 2026.
3 964 0.992860398135 Henry Cohn, 2025.
3 965 0.992867450055 Henry Cohn, 2026, needs more optimization.
3 966 0.992873726071 Henry Cohn, 2026.
3 967 0.992879664516 Henry Cohn, 2026.
3 968 0.992886923604 Henry Cohn, 2025.
3 969 0.992894684947 Henry Cohn, 2026.
3 970 0.992900101770 Henry Cohn, 2026, needs more optimization.
3 971 0.992910234827 Henry Cohn, 2025.
3 972 0.992915598654 Henry Cohn, 2025.
3 973 0.992916191307 Henry Cohn, 2026, needs more optimization.
3 974 0.992924646469 Henry Cohn, 2026.
3 975 0.992931434432 Henry Cohn, 2026.
3 976 0.992939135834 Henry Cohn, 2026, needs more optimization.
3 977 0.992953433939 Henry Cohn, 2025.
3 978 0.992956414996 Henry Cohn, 2026, needs more optimization.
3 979 0.992964322394 Henry Cohn, 2026.
3 980 0.992974636259 Henry Cohn, 2024.
3 981 0.992980975086 Henry Cohn, 2026, needs more optimization.
3 982 0.992986020491 Henry Cohn, 2026.
3 983 0.992998353831 Henry Cohn, 2025.
3 984 0.993003417762 Henry Cohn, 2025.
3 985 0.993011691492 Henry Cohn, 2025.
3 986 0.993014102217 Henry Cohn, 2026.
3 987 0.993015794704 Henry Cohn, 2026, needs more optimization.
3 988 0.993022620792 Henry Cohn, 2026.
3 989 0.993037184620 Henry Cohn, 2025.
3 990 0.993045751650 Henry Cohn, 2025.
3 991 0.993048484035 Henry Cohn, 2026, needs more optimization.
3 992 0.993056523152 Henry Cohn, 2026, needs more optimization.
3 993 0.993060184436 Henry Cohn, 2026, needs more optimization.
3 994 0.993068317141 Henry Cohn, 2026.
3 995 0.993077408987 Henry Cohn, 2026.
3 996 0.993082348997 Henry Cohn, 2026, needs more optimization.
3 997 0.993095076600 Henry Cohn, 2026, needs more optimization.
3 998 0.993095697499 Henry Cohn, 2026, needs more optimization.
3 999 0.993104406489 Henry Cohn, 2026, needs more optimization.
3 1000 0.993108149353 Henry Cohn, 2026.
3 1001 0.993116770143 Henry Cohn, 2026.
3 1002 0.993125357511 Henry Cohn, 2026.
3 1003 0.993132170420 Henry Cohn, 2025.
3 1004 0.993135721387 Henry Cohn, 2026, needs more optimization.
3 1005 0.993147564003 Henry Cohn, 2026.
3 1006 0.993151568176 Henry Cohn, 2026.
3 1007 0.993154938662 Henry Cohn, 2026.
3 1008 0.993159005478 Henry Cohn, 2025.
3 1009 0.993168698943 Henry Cohn, 2026, needs more optimization.
3 1010 0.993175003357 Henry Cohn, 2026, needs more optimization.
3 1011 0.993182202668 Henry Cohn, 2026, needs more optimization.
3 1012 0.993189191930 Henry Cohn, 2026, needs more optimization.
3 1013 0.993196507117 Henry Cohn, 2026, needs more optimization.
3 1014 0.993201606413 Henry Cohn, 2026, needs more optimization.
3 1015 0.993208460986 Henry Cohn, 2026, needs more optimization.
3 1016 0.993214865526 Henry Cohn, 2026, needs more optimization.
3 1017 0.993221389003 Henry Cohn, 2026, needs more optimization.
3 1018 0.993228968640 Henry Cohn, 2026, needs more optimization.
3 1019 0.993235373182 Henry Cohn, 2026.
3 1020 0.993235373238 R. H. Hardin, N. J. A. Sloane, and W. D. Smith, Tables of spherical codes with icosahedral symmetry, 1994–2000.
3 1021 0.993243005702 Henry Cohn, 2026, needs more optimization.
3 1022 0.993250016189 Henry Cohn, 2026, needs more optimization.
3 1023 0.993256159915 Henry Cohn, 2026, needs more optimization.
3 1024 0.993262743306 Henry Cohn, 2026, needs more optimization.
4 9 0.162015199612 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996; K. J. Nurmela, Constructing spherical codes by global optimization methods, Research Report A32, Digital Systems Laboratory, Helsinki University of Technology, 1995, https://research.ics.aalto.fi/publications/info/bibdb.HUT-TCS-A32.shtml.
16⁢x3−16⁢x2−4⁢x+1
4 10* 0.166666666667 A. L. Mackay, The packing of three-dimensional spheres on the surface of a four-dimensional hypersphere, J. Phys. A 13 (1980), 3373–3379, doi:10.1088/0305-4470/13/11/011; C. Bachoc and F. Vallentin, Optimality and uniqueness of the (4,10,1/6) spherical code, J. Combin. Theory Ser. A 116 (2009), 195–204, doi:10.1016/j.jcta.2008.05.001.
6⁢x−1
4 11 0.230405563595 L. T. Wille, Close packing in curved space by simulated annealing, Journal of Physics A: Mathematical and General 20 (1987), L1211–L1218, doi:10.1088/0305-4470/20/17/014.
8⁢x3−12⁢x2−2⁢x+1
4 12 0.25 A. L. Mackay, The packing of three-dimensional spheres on the surface of a four-dimensional hypersphere, J. Phys. A 13 (1980), 3373–3379, doi:10.1088/0305-4470/13/11/011.
4⁢x−1
4 13 0.307295653982 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996; K. J. Nurmela, Constructing spherical codes by global optimization methods, Research Report A32, Digital Systems Laboratory, Helsinki University of Technology, 1995, https://research.ics.aalto.fi/publications/info/bibdb.HUT-TCS-A32.shtml.
5632⁢x9+9472⁢x8−3072⁢x7−5888⁢x6+544⁢x5+944⁢x4+152⁢x3−44⁢x2−14⁢x−1
4 14 0.319518594213 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996; K. J. Nurmela, Constructing spherical codes by global optimization methods, Research Report A32, Digital Systems Laboratory, Helsinki University of Technology, 1995, https://research.ics.aalto.fi/publications/info/bibdb.HUT-TCS-A32.shtml.
58⁢x7+174⁢x6+140⁢x5−16⁢x4−54⁢x3−10⁢x2+4⁢x+1
4 15 0.350992175946 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996; K. J. Nurmela, Constructing spherical codes by global optimization methods, Research Report A32, Digital Systems Laboratory, Helsinki University of Technology, 1995, https://research.ics.aalto.fi/publications/info/bibdb.HUT-TCS-A32.shtml.
36⁢x4−18⁢x3+10⁢x2−1
4 16 0.387628177123 A. L. Mackay, The packing of three-dimensional spheres on the surface of a four-dimensional hypersphere, J. Phys. A 13 (1980), 3373–3379, doi:10.1088/0305-4470/13/11/011.
256⁢x10+1024⁢x9+256⁢x8−1152⁢x7+160⁢x6+176⁢x5−144⁢x4+36⁢x3+37⁢x2−6⁢x−3
4 17 0.412259362694 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996; K. J. Nurmela, Constructing spherical codes by global optimization methods, Research Report A32, Digital Systems Laboratory, Helsinki University of Technology, 1995, https://research.ics.aalto.fi/publications/info/bibdb.HUT-TCS-A32.shtml.
4 18 0.422819414074 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996; K. J. Nurmela, Constructing spherical codes by global optimization methods, Research Report A32, Digital Systems Laboratory, Helsinki University of Technology, 1995, https://research.ics.aalto.fi/publications/info/bibdb.HUT-TCS-A32.shtml.
Minimal polynomial listed in plain text data
4 19 0.434258545911 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996; K. J. Nurmela, Constructing spherical codes by global optimization methods, Research Report A32, Digital Systems Laboratory, Helsinki University of Technology, 1995, https://research.ics.aalto.fi/publications/info/bibdb.HUT-TCS-A32.shtml.
3⁢x2+x−1
4 20 0.434258545911 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996; K. J. Nurmela, Constructing spherical codes by global optimization methods, Research Report A32, Digital Systems Laboratory, Helsinki University of Technology, 1995, https://research.ics.aalto.fi/publications/info/bibdb.HUT-TCS-A32.shtml.
3⁢x2+x−1
4 21 0.471380858508 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996; K. J. Nurmela, Constructing spherical codes by global optimization methods, Research Report A32, Digital Systems Laboratory, Helsinki University of Technology, 1995, https://research.ics.aalto.fi/publications/info/bibdb.HUT-TCS-A32.shtml.
16⁢x8−128⁢x7−64⁢x6+32⁢x5+72⁢x4+32⁢x3−16⁢x2−8⁢x+1
4 22 0.497884130844 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996; K. J. Nurmela, Constructing spherical codes by global optimization methods, Research Report A32, Digital Systems Laboratory, Helsinki University of Technology, 1995, https://research.ics.aalto.fi/publications/info/bibdb.HUT-TCS-A32.shtml.
4 23 0.5 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996; K. J. Nurmela, Constructing spherical codes by global optimization methods, Research Report A32, Digital Systems Laboratory, Helsinki University of Technology, 1995, https://research.ics.aalto.fi/publications/info/bibdb.HUT-TCS-A32.shtml.
2⁢x−1
4 24* 0.5 L. Schläfli, Theorie der vielfachen Kontinuität [1852], Denkschriften der Schweizerischen naturforschenden Gesellschaft, vol. 38, J. H. Graf, Bern, 1901; D. de Laat, N. Leijenhorst, and W. H. H. de Muinck Keizer, Optimality and uniqueness of the D4 root system, preprint, 2024, arXiv:2404.18794.
2⁢x−1
4 25 0.537316056656 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996; K. J. Nurmela, Constructing spherical codes by global optimization methods, Research Report A32, Digital Systems Laboratory, Helsinki University of Technology, 1995, https://research.ics.aalto.fi/publications/info/bibdb.HUT-TCS-A32.shtml.
4 26 0.540789617698 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996; K. J. Nurmela, Constructing spherical codes by global optimization methods, Research Report A32, Digital Systems Laboratory, Helsinki University of Technology, 1995, https://research.ics.aalto.fi/publications/info/bibdb.HUT-TCS-A32.shtml.
3392⁢x6+2112⁢x5−496⁢x4−656⁢x3−132⁢x2+6⁢x−1
4 27 0.557591351181 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
794⁢x5+393⁢x4−344⁢x3−82⁢x2+6⁢x+1
4 28 0.567338804075 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996; K. J. Nurmela, Constructing spherical codes by global optimization methods, Research Report A32, Digital Systems Laboratory, Helsinki University of Technology, 1995, https://research.ics.aalto.fi/publications/info/bibdb.HUT-TCS-A32.shtml.
4 29 0.573148530449 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
Minimal polynomial listed in plain text data
4 30 0.584232813931 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
4 31 0.590765838581 H. Cohn, Small spherical and projective codes, data set, updated 2024, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
4 32 0.595720149236 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996; K. J. Nurmela, Constructing spherical codes by global optimization methods, Research Report A32, Digital Systems Laboratory, Helsinki University of Technology, 1995, https://research.ics.aalto.fi/publications/info/bibdb.HUT-TCS-A32.shtml.
4 33 0.600755407756 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
4 34 0.610128556790 Henry Cohn, 2024.
4 35 0.621523986641 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
4 36 0.628309089475 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
4 37 0.630368722499 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996; K. J. Nurmela, Constructing spherical codes by global optimization methods, Research Report A32, Digital Systems Laboratory, Helsinki University of Technology, 1995, https://research.ics.aalto.fi/publications/info/bibdb.HUT-TCS-A32.shtml.
4 38 0.640732732793 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
4 39 0.646928247960 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996; K. J. Nurmela, Constructing spherical codes by global optimization methods, Research Report A32, Digital Systems Laboratory, Helsinki University of Technology, 1995, https://research.ics.aalto.fi/publications/info/bibdb.HUT-TCS-A32.shtml.
4 40 0.650497801063 J. Wang, Finding and investigating exact spherical codes, Experiment. Math. 18 (2009), 249–256, https://projecteuclid.org/euclid.em/1259158434.
4 41 0.655274051124 Henry Cohn, 2024.
4 42 0.658420878517 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
4 43 0.662667198430 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996; K. J. Nurmela, Constructing spherical codes by global optimization methods, Research Report A32, Digital Systems Laboratory, Helsinki University of Technology, 1995, https://research.ics.aalto.fi/publications/info/bibdb.HUT-TCS-A32.shtml.
4 44 0.668804906276 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
36⁢x8−60⁢x7+481⁢x6+166⁢x5−205⁢x4−116⁢x3+11⁢x2+10⁢x+1
4 45 0.676924957837 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
4 46 0.682325866078 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
4 47 0.685400852293 Henry Cohn, 2025.
4 48 0.689831186714 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
4 49 0.693413660571 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
4 50 0.693726127145 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996; K. J. Nurmela, Constructing spherical codes by global optimization methods, Research Report A32, Digital Systems Laboratory, Helsinki University of Technology, 1995, https://research.ics.aalto.fi/publications/info/bibdb.HUT-TCS-A32.shtml.
Minimal polynomial listed in plain text data
4 51 0.701375493264 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
4 52 0.703627792371 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
4 53 0.707671488219 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
4 54 0.709714380727 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
4 55 0.715661893754 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
4 56 0.719201427062 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
4 57 0.722366203194 Henry Cohn, 2025.
4 58 0.724963759986 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
4 59 0.726684594037 Henry Cohn, 2025.
4 60 0.728768479335 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
4 61 0.731517689032 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
4 62 0.733882910506 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
4 63 0.738725371284 Henry Cohn, 2025.
4 64 0.739558032728 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
4 65 0.742483255369 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
4 66 0.745996162085 Henry Cohn, 2025.
4 67 0.748966563154 Henry Cohn, 2025.
4 68 0.751044149551 Henry Cohn, 2025.
4 69 0.752628993819 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
4 70 0.753734038368 Henry Cohn, 2025.
4 71 0.756373364760 Henry Cohn, 2025.
4 72 0.758022144348 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
4 73 0.759191014470 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
4 74 0.759545691353 Henry Cohn, 2025.
4 75 0.760558878464 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
4 76 0.761064664765 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
Minimal polynomial listed in plain text data
4 77 0.765202546890 Henry Cohn, 2025.
4 78 0.768765601292 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
4 79 0.773060404397 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
4 80 0.775691894892 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
4 81 0.777799033764 Henry Cohn, 2025.
4 82 0.779753559198 Henry Cohn, 2025.
4 83 0.781053544402 Henry Cohn, 2025.
4 84 0.782373204314 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
4 85 0.783715044186 Henry Cohn, 2024.
4 86 0.784899018852 Henry Cohn, 2025.
4 87 0.785487328991 Henry Cohn, 2025.
4 88 0.785927649195 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
4 89 0.788520093069 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
4 90 0.790391197000 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
4 91 0.791393154383 Henry Cohn, 2025.
4 92 0.792211293351 Henry Cohn, 2025.
4 93 0.793047017514 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
4 94 0.793553793569 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
4 95 0.796982807052 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
4 96 0.797980534415 Henry Cohn, 2025.
4 97 0.799480375605 Henry Cohn, 2023.
4 98 0.800765983579 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
4 99 0.801793100994 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
4 100 0.803178722499 Henry Cohn, 2025.
4 101 0.803884649087 Henry Cohn, 2025.
4 102 0.804699654814 Henry Cohn, 2025.
4 103 0.805093331367 Henry Cohn, 2025.
4 104 0.806308735044 Henry Cohn, 2025.
4 105 0.807104890332 Henry Cohn, 2025.
4 106 0.807600771583 Henry Cohn, 2025.
4 107 0.808031793624 Henry Cohn, 2025.
4 108 0.808488610194 Henry Cohn, 2025.
4 109 0.808687291189 Henry Cohn, 2025.
4 110 0.808927278480 Henry Cohn, 2025.
4 111 0.808991157916 Henry Cohn, 2025.
4 112 0.809016055614 Henry Cohn, 2025.
4 113 0.809016994375 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
4⁢x2−2⁢x−1
4 114 0.809016994375 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
4⁢x2−2⁢x−1
4 115 0.809016994375 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
4⁢x2−2⁢x−1
4 116 0.809016994375 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
4⁢x2−2⁢x−1
4 117 0.809016994375 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
4⁢x2−2⁢x−1
4 118 0.809016994375 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
4⁢x2−2⁢x−1
4 119 0.809016994375 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
4⁢x2−2⁢x−1
4 120* 0.809016994375 L. Schläfli, Theorie der vielfachen Kontinuität [1852], Denkschriften der Schweizerischen naturforschenden Gesellschaft, vol. 38, J. H. Graf, Bern, 1901; K. Böröczky, Packing of spheres in spaces of constant curvature, Acta Mathematica Academiae Scientiarum Hungarica 32 (1978), 243–261, doi:10.1007/BF01902361.
4⁢x2−2⁢x−1
4 121 0.824638011670 Henry Cohn, 2025.
4 122 0.826371365501 Henry Cohn, 2025.
4 123 0.827331732524 Henry Cohn, 2025.
4 124 0.829076814196 Henry Cohn, 2025.
4 125 0.830275122838 Henry Cohn, 2025.
4 126 0.831265978577 Henry Cohn, 2025.
4 127 0.832258295757 Henry Cohn, 2025.
4 128 0.833179391366 Henry Cohn, 2025.
4 129 0.833853106202 Henry Cohn, 2025.
4 130 0.834729130389 Henry Cohn, 2025.
4 131 0.835454616797 Henry Cohn, 2025.
4 132 0.835826242592 Henry Cohn, 2025.
4 133 0.836970287069 Henry Cohn, 2025.
4 134 0.837549857120 Henry Cohn, 2025.
4 135 0.838174290974 Henry Cohn, 2025.
4 136 0.838408035762 Henry Cohn, 2025.
4 137 0.838792717376 Henry Cohn, 2025.
4 138 0.839094608099 Henry Cohn, 2025.
4 139 0.839507413737 Henry Cohn, 2024.
4 140 0.839796230234 Henry Cohn, 2025.
4 141 0.840152855333 Henry Cohn, 2024.
4 142 0.840928789319 Henry Cohn, 2025.
4 143 0.842625863066 Henry Cohn, 2025.
4 144 0.843226230314 Henry Cohn, 2026.
4 145 0.845004703395 Henry Cohn, 2025.
4 146 0.846045189902 Henry Cohn, 2024.
4 147 0.846906008500 Henry Cohn, 2025.
4 148 0.847320837337 Henry Cohn, 2025.
4 149 0.847701351395 Henry Cohn, 2025.
4 150 0.848008139501 Henry Cohn, 2025.
4 151 0.848395999617 Henry Cohn, 2025.
4 152 0.848746833410 Henry Cohn, 2024.
4 153 0.849106783811 Henry Cohn, 2025.
4 154 0.849448181031 Henry Cohn, 2024.
4 155 0.850528693851 Henry Cohn, 2025.
4 156 0.852364181174 Henry Cohn, 2025.
4 157 0.853098036527 Henry Cohn, 2025.
4 158 0.853541001367 Henry Cohn, 2025.
4 159 0.853851387665 Henry Cohn, 2025.
4 160 0.854015402705 Henry Cohn, 2025.
4 161 0.855036011488 Henry Cohn, 2025.
4 162 0.856011990176 Henry Cohn, 2025.
4 163 0.856495635329 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
4 164 0.856668082967 Henry Cohn, 2025.
4 165 0.856908324217 Henry Cohn, 2024.
4 166 0.857225219240 Henry Cohn, 2025.
4 167 0.857623781724 Henry Cohn, 2025.
4 168 0.859313343133 Henry Cohn, 2025.
4 169 0.860417510162 Henry Cohn, 2025.
4 170 0.861218036143 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
4 171 0.861877205800 Henry Cohn, 2025.
4 172 0.862347282110 Henry Cohn, 2026, needs more optimization.
4 173 0.862725307388 Henry Cohn, 2025.
4 174 0.863170417348 Henry Cohn, 2026.
4 175 0.863367463185 Henry Cohn, 2025.
4 176 0.863624102971 Henry Cohn, 2025.
4 177 0.863764381494 Henry Cohn, 2025.
4 178 0.863928834672 Henry Cohn, 2025.
4 179 0.864723195011 Henry Cohn, 2025.
4 180 0.865782670861 Henry Cohn, 2025.
4 181 0.866598382577 Henry Cohn, 2025.
4 182 0.867102135062 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
4 183 0.867335807322 Henry Cohn, 2025.
4 184 0.867763055785 Henry Cohn, 2025.
4 185 0.868215850425 Henry Cohn, 2026.
4 186 0.868514858637 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
4 187 0.868813031570 Henry Cohn, 2026, needs more optimization.
4 188 0.869207825431 Henry Cohn, 2025.
4 189 0.869491543071 Henry Cohn, 2025.
4 190 0.870050972636 Henry Cohn, 2025.
4 191 0.870814241870 Henry Cohn, 2025.
4 192 0.871340639696 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
4 193 0.871545546243 Henry Cohn, 2025.
4 194 0.871792013221 Henry Cohn, 2025.
4 195 0.872105415403 Henry Cohn, 2026, needs more optimization.
4 196 0.872623379660 Henry Cohn, 2026.
4 197 0.873487426793 Henry Cohn, 2025.
4 198 0.874156501901 Henry Cohn, 2025.
4 199 0.875066499628 Henry Cohn, 2026.
4 200 0.875667629554 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
4 201 0.876122588406 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
4 202 0.876522635298 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
4 203 0.876807613055 Henry Cohn, 2026.
4 204 0.877193219688 Henry Cohn, 2026.
4 205 0.877534211883 Henry Cohn, 2025.
4 206 0.877773524417 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
4 207 0.877983074153 Henry Cohn, 2026.
4 208 0.878215104089 Henry Cohn, 2025.
4 209 0.878614728692 Henry Cohn, 2026.
4 210 0.879213799752 Henry Cohn, 2025.
4 211 0.879527571942 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
4 212 0.879653371881 Henry Cohn, 2026.
4 213 0.879816584432 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
4 214 0.879945724274 Henry Cohn, 2025.
4 215 0.880272662054 Henry Cohn, 2025.
4 216 0.880902709084 Henry Cohn, 2026.
4 217 0.881489373180 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
4 218 0.881821797282 Henry Cohn, 2026, needs more optimization.
4 219 0.881957670465 Henry Cohn, 2025.
4 220 0.882547029792 Henry Cohn, 2025.
4 221 0.883034324004 Henry Cohn, 2026.
4 222 0.883456069925 Henry Cohn, 2025.
4 223 0.884138189446 Henry Cohn, 2025.
4 224 0.884684734191 Henry Cohn, 2025.
4 225 0.885119168015 Henry Cohn, 2026.
4 226 0.885320859080 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
4 227 0.885541386047 Henry Cohn, 2025.
4 228 0.885824040293 Henry Cohn, 2025.
4 229 0.886054621852 Henry Cohn, 2026, needs more optimization.
4 230 0.886372063295 Henry Cohn, 2025.
4 231 0.886803796459 Henry Cohn, 2026, needs more optimization.
4 232 0.887100396043 Henry Cohn, 2026.
4 233 0.887339463629 Henry Cohn, 2025.
4 234 0.887586535331 Henry Cohn, 2025.
4 235 0.887912344037 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
4 236 0.888076450831 Henry Cohn, 2025.
4 237 0.888444553045 Henry Cohn, 2025.
4 238 0.888895172867 Henry Cohn, 2025.
4 239 0.889105362853 Henry Cohn, 2026.
4 240 0.889490760287 Henry Cohn, 2026, needs more optimization.
4 241 0.889868276226 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
4 242 0.890164712924 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
4 243 0.890327494714 Henry Cohn, 2025.
4 244 0.890724603786 Henry Cohn, 2026.
4 245 0.890944532473 Henry Cohn, 2026, needs more optimization.
4 246 0.891230987587 Henry Cohn, 2025.
4 247 0.891664123274 Henry Cohn, 2026.
4 248 0.891998665833 Henry Cohn, 2026, needs more optimization.
4 249 0.892287393255 Henry Cohn, 2026, needs more optimization.
4 250 0.892630822839 Henry Cohn, 2026, needs more optimization.
4 251 0.892992054634 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
4 252 0.893212813065 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
4 253 0.893448665997 Henry Cohn, 2026, needs more optimization.
4 254 0.893722953701 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
4 255 0.893997549375 Henry Cohn, 2026.
4 256 0.894519020596 Henry Cohn, 2026, needs more optimization.
4 257 0.894704108549 Henry Cohn, 2026.
4 258 0.894983025797 Henry Cohn, 2026, needs more optimization.
4 259 0.895408555760 Henry Cohn, 2026, needs more optimization.
4 260 0.895581669593 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
4 261 0.895841213806 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
4 262 0.896169452605 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
4 263 0.896400276225 Henry Cohn, 2026, needs more optimization.
4 264 0.896612885654 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
4 265 0.896785136781 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
4 266 0.896962517936 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
4 267 0.897216331693 Henry Cohn, 2026, needs more optimization.
4 268 0.897341443704 Henry Cohn, 2026, needs more optimization.
4 269 0.897584249844 Henry Cohn, 2026, needs more optimization.
4 270 0.897722405122 Henry Cohn, 2026, needs more optimization.
4 271 0.897984717497 Henry Cohn, 2026, needs more optimization.
4 272 0.898196108609 Henry Cohn, 2026, needs more optimization.
4 273 0.898338831510 Henry Cohn, 2026, needs more optimization.
4 274 0.898507453079 Henry Cohn, 2026, needs more optimization.
4 275 0.898703285489 Henry Cohn, 2026, needs more optimization.
4 276 0.898990509891 Henry Cohn, 2026, needs more optimization.
4 277 0.899257716082 Henry Cohn, 2026, needs more optimization.
4 278 0.899399764294 Henry Cohn, 2026, needs more optimization.
4 279 0.899551098551 Henry Cohn, 2026, needs more optimization.
4 280 0.899640975210 Henry Cohn, 2026, needs more optimization.
4 281 0.900127314981 Henry Cohn, 2026.
4 282 0.900628397128 Henry Cohn, 2026, needs more optimization.
4 283 0.900999811191 Henry Cohn, 2026, needs more optimization.
4 284 0.901162008148 Henry Cohn, 2026, needs more optimization.
4 285 0.901208850582 Henry Cohn, 2026, needs more optimization.
4 286 0.901352037990 Henry Cohn, 2026, needs more optimization.
4 287 0.901408241003 Henry Cohn, 2026, needs more optimization.
4 288 0.901415628426 Henry Cohn, 2026, needs more optimization.
4 289 0.902147462122 Henry Cohn, 2026, needs more optimization.
4 290 0.902668032652 Henry Cohn, 2026, needs more optimization.
4 291 0.903108218652 Henry Cohn, 2026, needs more optimization.
4 292 0.903479788245 Henry Cohn, 2026, needs more optimization.
4 293 0.903762089966 Henry Cohn, 2026, needs more optimization.
4 294 0.903947280983 Henry Cohn, 2026, needs more optimization.
4 295 0.904226222560 Henry Cohn, 2026, needs more optimization.
4 296 0.904541783579 Henry Cohn, 2026, needs more optimization.
4 297 0.904746060747 Henry Cohn, 2026, needs more optimization.
4 298 0.904877270133 Henry Cohn, 2026, needs more optimization.
4 299 0.905146611996 Henry Cohn, 2026, needs more optimization.
4 300 0.905313494754 Henry Cohn, 2026, needs more optimization.
4 301 0.905597318680 Henry Cohn, 2026, needs more optimization.
4 302 0.905742463135 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
4 303 0.906066938468 Henry Cohn, 2026, needs more optimization.
4 304 0.906254637567 Henry Cohn, 2026, needs more optimization.
4 305 0.906320387023 Henry Cohn, 2026, needs more optimization.
4 306 0.906511544495 Henry Cohn, 2026, needs more optimization.
4 307 0.906769020187 Henry Cohn, 2026, needs more optimization.
4 308 0.906981079246 Henry Cohn, 2026, needs more optimization.
4 309 0.907297386610 Henry Cohn, 2026, needs more optimization.
4 310 0.907345163074 Henry Cohn, 2026, needs more optimization.
4 311 0.907479010087 Henry Cohn, 2026, needs more optimization.
4 312 0.907797918050 Henry Cohn, 2026, needs more optimization.
4 313 0.907999397269 Henry Cohn, 2026, needs more optimization.
4 314 0.908137005840 Henry Cohn, 2026, needs more optimization.
4 315 0.908334408866 Henry Cohn, 2026, needs more optimization.
4 316 0.908439132055 Henry Cohn, 2026, needs more optimization.
4 317 0.908713928386 Henry Cohn, 2026, needs more optimization.
4 318 0.908941299492 Henry Cohn, 2026, needs more optimization.
4 319 0.909145405307 Henry Cohn, 2026, needs more optimization.
4 320 0.909320854901 Henry Cohn, 2026, needs more optimization.
4 321 0.909491369498 Henry Cohn, 2026, needs more optimization.
4 322 0.909572924191 Henry Cohn, 2026, needs more optimization.
4 323 0.909664277020 Henry Cohn, 2026, needs more optimization.
4 324 0.909833171539 Henry Cohn, 2026, needs more optimization.
4 325 0.910040662440 Henry Cohn, 2026, needs more optimization.
4 326 0.910201960133 Henry Cohn, 2026, needs more optimization.
4 327 0.910288142665 Henry Cohn, 2026, needs more optimization.
4 328 0.910395023215 Henry Cohn, 2026, needs more optimization.
4 329 0.910665712623 Henry Cohn, 2026, needs more optimization.
4 330 0.910911540300 Henry Cohn, 2026, needs more optimization.
4 331 0.911137010713 Henry Cohn, 2026, needs more optimization.
4 332 0.911288710603 Henry Cohn, 2026, needs more optimization.
4 333 0.911520999341 Henry Cohn, 2026, needs more optimization.
4 334 0.911635352404 Henry Cohn, 2026, needs more optimization.
4 335 0.911928209819 Henry Cohn, 2026, needs more optimization.
4 336 0.912142693612 Henry Cohn, 2026, needs more optimization.
4 337 0.912392283319 Henry Cohn, 2026, needs more optimization.
4 338 0.912622753554 Henry Cohn, 2026, needs more optimization.
4 339 0.912849496394 Henry Cohn, 2026, needs more optimization.
4 340 0.913082210088 Henry Cohn, 2026, needs more optimization.
4 341 0.913350204421 Henry Cohn, 2026, needs more optimization.
4 342 0.913448740922 Henry Cohn, 2026, needs more optimization.
4 343 0.913632488568 Henry Cohn, 2026, needs more optimization.
4 344 0.913824325681 Henry Cohn, 2026, needs more optimization.
4 345 0.914105247595 Henry Cohn, 2026, needs more optimization.
4 346 0.914199615014 Henry Cohn, 2026, needs more optimization.
4 347 0.914370745668 Henry Cohn, 2026, needs more optimization.
4 348 0.914597659316 Henry Cohn, 2026, needs more optimization.
4 349 0.914787147751 Henry Cohn, 2026, needs more optimization.
4 350 0.914826499941 Henry Cohn, 2026, needs more optimization.
4 351 0.915003300656 Henry Cohn, 2026, needs more optimization.
4 352 0.915195438247 Henry Cohn, 2026, needs more optimization.
4 353 0.915241483582 Henry Cohn, 2026, needs more optimization.
4 354 0.915422024189 Henry Cohn, 2026, needs more optimization.
4 355 0.915510186992 Henry Cohn, 2026, needs more optimization.
4 356 0.915645206942 Henry Cohn, 2026, needs more optimization.
4 357 0.915773139125 Henry Cohn, 2026, needs more optimization.
4 358 0.915932571848 Henry Cohn, 2026, needs more optimization.
4 359 0.916064146263 Henry Cohn, 2026, needs more optimization.
4 360 0.916227016893 Henry Cohn, 2026, needs more optimization.
4 361 0.916275616951 Henry Cohn, 2026, needs more optimization.
4 362 0.916284241069 Henry Cohn, 2026, needs more optimization.
4 363 0.916449857138 Henry Cohn, 2026, needs more optimization.
4 364 0.916566270835 Henry Cohn, 2026, needs more optimization.
4 365 0.916732127641 Henry Cohn, 2026, needs more optimization.
4 366 0.916828437041 Henry Cohn, 2026, needs more optimization.
4 367 0.917138975218 Henry Cohn, 2026, needs more optimization.
4 368 0.917194982988 Henry Cohn, 2026, needs more optimization.
4 369 0.917249817356 Henry Cohn, 2026, needs more optimization.
4 370 0.917312758518 Henry Cohn, 2026, needs more optimization.
4 371 0.917449371611 Henry Cohn, 2026, needs more optimization.
4 372 0.917595341351 Henry Cohn, 2026, needs more optimization.
4 373 0.917877174623 Henry Cohn, 2026, needs more optimization.
4 374 0.918147785233 Henry Cohn, 2026, needs more optimization.
4 375 0.918338724046 Henry Cohn, 2026, needs more optimization.
4 376 0.918496193596 Henry Cohn, 2026, needs more optimization.
4 377 0.918569680183 Henry Cohn, 2026, needs more optimization.
4 378 0.918649548034 Henry Cohn, 2026, needs more optimization.
4 379 0.918855228427 Henry Cohn, 2026, needs more optimization.
4 380 0.918968688895 Henry Cohn, 2026, needs more optimization.
4 381 0.919137746629 Henry Cohn, 2026, needs more optimization.
4 382 0.919183440988 Henry Cohn, 2026, needs more optimization.
4 383 0.919269387804 Henry Cohn, 2026, needs more optimization.
4 384 0.919332504152 Henry Cohn, 2026, needs more optimization.
4 385 0.919374373395 Henry Cohn, 2026, needs more optimization.
4 386 0.919462080655 Henry Cohn, 2026, needs more optimization.
4 387 0.919485767372 Henry Cohn, 2026, needs more optimization.
4 388 0.919680409497 Henry Cohn, 2026, needs more optimization.
4 389 0.919722706966 Henry Cohn, 2026, needs more optimization.
4 390 0.919936179660 Henry Cohn, 2026, needs more optimization.
4 391 0.920140555756 Henry Cohn, 2026, needs more optimization.
4 392 0.920311946197 Henry Cohn, 2026, needs more optimization.
4 393 0.920430103140 Henry Cohn, 2026, needs more optimization.
4 394 0.920471448895 Henry Cohn, 2026, needs more optimization.
4 395 0.920571069762 Henry Cohn, 2026, needs more optimization.
4 396 0.920783591868 Henry Cohn, 2026, needs more optimization.
4 397 0.921004408625 Henry Cohn, 2026, needs more optimization.
4 398 0.921112962607 Henry Cohn, 2026, needs more optimization.
4 399 0.921184373600 Henry Cohn, 2026, needs more optimization.
4 400 0.921353549198 Henry Cohn, 2026, needs more optimization.
4 401 0.921449432364 Henry Cohn, 2026, needs more optimization.
4 402 0.921691128153 Henry Cohn, 2026, needs more optimization.
4 403 0.921777133855 Henry Cohn, 2026, needs more optimization.
4 404 0.921826297598 Henry Cohn, 2026, needs more optimization.
4 405 0.921860539955 Henry Cohn, 2026, needs more optimization.
4 406 0.921891687192 Henry Cohn, 2026, needs more optimization.
4 407 0.921971401665 Henry Cohn, 2026, needs more optimization.
4 408 0.921997660815 Henry Cohn, 2026, needs more optimization.
4 409 0.922339066157 Henry Cohn, 2026, needs more optimization.
4 410 0.922637784830 Henry Cohn, 2026, needs more optimization.
4 411 0.922708081549 Henry Cohn, 2026, needs more optimization.
4 412 0.922993794176 Henry Cohn, 2026, needs more optimization.
4 413 0.923215104838 Henry Cohn, 2026, needs more optimization.
4 414 0.923243303012 Henry Cohn, 2026, needs more optimization.
4 415 0.923432188322 Henry Cohn, 2026, needs more optimization.
4 416 0.923453699868 Henry Cohn, 2026, needs more optimization.
4 417 0.923513439158 Henry Cohn, 2026, needs more optimization.
4 418 0.923595435844 Henry Cohn, 2026, needs more optimization.
4 419 0.923725698350 Henry Cohn, 2026, needs more optimization.
4 420 0.923894048591 Henry Cohn, 2026, needs more optimization.
4 421 0.923980593106 Henry Cohn, 2026, needs more optimization.
4 422 0.924134530060 Henry Cohn, 2026, needs more optimization.
4 423 0.924286175725 Henry Cohn, 2026, needs more optimization.
4 424 0.924500348082 Henry Cohn, 2026, needs more optimization.
4 425 0.924700614054 Henry Cohn, 2026, needs more optimization.
4 426 0.924907486541 Henry Cohn, 2026, needs more optimization.
4 427 0.925096734289 Henry Cohn, 2026, needs more optimization.
4 428 0.925214426385 Henry Cohn, 2026, needs more optimization.
4 429 0.925413131787 Henry Cohn, 2026, needs more optimization.
4 430 0.925532810634 Henry Cohn, 2026, needs more optimization.
4 431 0.925691510827 Henry Cohn, 2026, needs more optimization.
4 432 0.925804465285 Henry Cohn, 2026, needs more optimization.
4 433 0.925930539663 Henry Cohn, 2026, needs more optimization.
4 434 0.925998197102 Henry Cohn, 2026, needs more optimization.
4 435 0.926183308535 Henry Cohn, 2026, needs more optimization.
4 436 0.926256081358 Henry Cohn, 2026, needs more optimization.
4 437 0.926442603154 Henry Cohn, 2026, needs more optimization.
4 438 0.926608240701 Henry Cohn, 2026, needs more optimization.
4 439 0.926759637027 Henry Cohn, 2026, needs more optimization.
4 440 0.926887365155 Henry Cohn, 2026, needs more optimization.
4 441 0.927036892630 Henry Cohn, 2026, needs more optimization.
4 442 0.927161288181 Henry Cohn, 2026, needs more optimization.
4 443 0.927211478016 Henry Cohn, 2026, needs more optimization.
4 444 0.927332275626 Henry Cohn, 2026, needs more optimization.
4 445 0.927430179902 Henry Cohn, 2026, needs more optimization.
4 446 0.927512259568 Henry Cohn, 2026, needs more optimization.
4 447 0.927594443776 Henry Cohn, 2026, needs more optimization.
4 448 0.927691710837 Henry Cohn, 2026, needs more optimization.
4 449 0.927843987913 Henry Cohn, 2026, needs more optimization.
4 450 0.928010204812 Henry Cohn, 2026, needs more optimization.
4 451 0.928081665169 Henry Cohn, 2026, needs more optimization.
4 452 0.928144362779 Henry Cohn, 2026, needs more optimization.
4 453 0.928186977030 Henry Cohn, 2026, needs more optimization.
4 454 0.928308531512 Henry Cohn, 2026, needs more optimization.
4 455 0.928327645700 Henry Cohn, 2026, needs more optimization.
4 456 0.928426727334 Henry Cohn, 2026, needs more optimization.
4 457 0.928541688922 Henry Cohn, 2026, needs more optimization.
4 458 0.928587629933 Henry Cohn, 2026, needs more optimization.
4 459 0.928668383431 Henry Cohn, 2026, needs more optimization.
4 460 0.928755859680 Henry Cohn, 2026, needs more optimization.
4 461 0.928916303242 Henry Cohn, 2026, needs more optimization.
4 462 0.929026761128 Henry Cohn, 2026, needs more optimization.
4 463 0.929124192900 Henry Cohn, 2026, needs more optimization.
4 464 0.929225837018 Henry Cohn, 2026, needs more optimization.
4 465 0.929338086871 Henry Cohn, 2026, needs more optimization.
4 466 0.929493611202 Henry Cohn, 2026, needs more optimization.
4 467 0.929652460745 Henry Cohn, 2026, needs more optimization.
4 468 0.929731607409 Henry Cohn, 2026, needs more optimization.
4 469 0.929858667670 Henry Cohn, 2026, needs more optimization.
4 470 0.929964722242 Henry Cohn, 2026, needs more optimization.
4 471 0.930087402486 Henry Cohn, 2026, needs more optimization.
4 472 0.930284440643 Henry Cohn, 2026, needs more optimization.
4 473 0.930409696786 Henry Cohn, 2026, needs more optimization.
4 474 0.930540845163 Henry Cohn, 2026, needs more optimization.
4 475 0.930658845161 Henry Cohn, 2026, needs more optimization.
4 476 0.930696686791 Henry Cohn, 2026, needs more optimization.
4 477 0.930791534273 Henry Cohn, 2026, needs more optimization.
4 478 0.930948232259 Henry Cohn, 2026, needs more optimization.
4 479 0.930994386934 Henry Cohn, 2026, needs more optimization.
4 480 0.931045112948 Henry Cohn, 2026, needs more optimization.
4 481 0.931140491211 Henry Cohn, 2026, needs more optimization.
4 482 0.931247547162 Henry Cohn, 2026, needs more optimization.
4 483 0.931360305402 Henry Cohn, 2026, needs more optimization.
4 484 0.931463358810 Henry Cohn, 2026, needs more optimization.
4 485 0.931577737344 Henry Cohn, 2026, needs more optimization.
4 486 0.931621017509 Henry Cohn, 2026, needs more optimization.
4 487 0.931675713173 Henry Cohn, 2026, needs more optimization.
4 488 0.931783092912 Henry Cohn, 2026, needs more optimization.
4 489 0.931863767270 Henry Cohn, 2026, needs more optimization.
4 490 0.931967844529 Henry Cohn, 2026, needs more optimization.
4 491 0.932017412115 Henry Cohn, 2026, needs more optimization.
4 492 0.932072621558 Henry Cohn, 2026, needs more optimization.
4 493 0.932141798752 Henry Cohn, 2026, needs more optimization.
4 494 0.932206145008 Henry Cohn, 2026, needs more optimization.
4 495 0.932282644994 Henry Cohn, 2026, needs more optimization.
4 496 0.932380050469 Henry Cohn, 2026, needs more optimization.
4 497 0.932486122371 Henry Cohn, 2026, needs more optimization.
4 498 0.932566496857 Henry Cohn, 2026, needs more optimization.
4 499 0.932634491005 Henry Cohn, 2026, needs more optimization.
4 500 0.932698594062 Henry Cohn, 2026, needs more optimization.
4 501 0.932738996207 Henry Cohn, 2026, needs more optimization.
4 502 0.932845323970 Henry Cohn, 2026, needs more optimization.
4 503 0.932924437333 Henry Cohn, 2026, needs more optimization.
4 504 0.933024669559 Henry Cohn, 2026, needs more optimization.
4 505 0.933093459762 Henry Cohn, 2026, needs more optimization.
4 506 0.933166070470 Henry Cohn, 2026, needs more optimization.
4 507 0.933261671104 Henry Cohn, 2026, needs more optimization.
4 508 0.933350520591 Henry Cohn, 2026, needs more optimization.
4 509 0.933456439500 Henry Cohn, 2026, needs more optimization.
4 510 0.933530697443 Henry Cohn, 2026, needs more optimization.
4 511 0.933642077565 Henry Cohn, 2026, needs more optimization.
4 512 0.933740816341 Henry Cohn, 2026, needs more optimization.
4 513 0.933891024620 Henry Cohn, 2026, needs more optimization.
4 514 0.933943028256 Henry Cohn, 2026, needs more optimization.
4 515 0.934029685643 Henry Cohn, 2026, needs more optimization.
4 516 0.934175399142 Henry Cohn, 2026, needs more optimization.
4 517 0.934193620696 Henry Cohn, 2026, needs more optimization.
4 518 0.934305876211 Henry Cohn, 2026, needs more optimization.
4 519 0.934446704656 Henry Cohn, 2026, needs more optimization.
4 520 0.934503800337 Henry Cohn, 2026, needs more optimization.
4 521 0.934587988035 Henry Cohn, 2026, needs more optimization.
4 522 0.934731876858 Henry Cohn, 2026, needs more optimization.
4 523 0.934786346012 Henry Cohn, 2026, needs more optimization.
4 524 0.934876190131 Henry Cohn, 2026, needs more optimization.
4 525 0.934988351825 Henry Cohn, 2026, needs more optimization.
4 526 0.935084865551 Henry Cohn, 2026, needs more optimization.
4 527 0.935178432944 Henry Cohn, 2026, needs more optimization.
4 528 0.935245846539 Henry Cohn, 2026, needs more optimization.
4 529 0.935293054321 Henry Cohn, 2026, needs more optimization.
4 530 0.935327093948 Henry Cohn, 2026, needs more optimization.
4 531 0.935457813866 Henry Cohn, 2026, needs more optimization.
4 532 0.935522953512 Henry Cohn, 2026, needs more optimization.
4 533 0.935592679913 Henry Cohn, 2026, needs more optimization.
4 534 0.935715440732 Henry Cohn, 2026, needs more optimization.
4 535 0.935747983892 Henry Cohn, 2026, needs more optimization.
4 536 0.935764712370 Henry Cohn, 2026, needs more optimization.
4 537 0.935851827637 Henry Cohn, 2026, needs more optimization.
4 538 0.936004672466 Henry Cohn, 2026, needs more optimization.
4 539 0.936070025277 Henry Cohn, 2026, needs more optimization.
4 540 0.936168399322 Henry Cohn, 2026, needs more optimization.
4 541 0.936204654771 Henry Cohn, 2026, needs more optimization.
4 542 0.936272956077 Henry Cohn, 2026, needs more optimization.
4 543 0.936387377450 Henry Cohn, 2026, needs more optimization.
4 544 0.936452956991 Henry Cohn, 2026, needs more optimization.
4 545 0.936524512250 Henry Cohn, 2026, needs more optimization.
4 546 0.936527304089 Henry Cohn, 2026, needs more optimization.
4 547 0.936600720841 Henry Cohn, 2026, needs more optimization.
4 548 0.936670541912 Henry Cohn, 2026, needs more optimization.
4 549 0.936739800041 Henry Cohn, 2026, needs more optimization.
4 550 0.936830691034 Henry Cohn, 2026, needs more optimization.
4 551 0.936860348618 Henry Cohn, 2026, needs more optimization.
4 552 0.936982415329 Henry Cohn, 2026, needs more optimization.
4 553 0.937066764746 Henry Cohn, 2026, needs more optimization.
4 554 0.937186204064 Henry Cohn, 2026, needs more optimization.
4 555 0.937288038089 Henry Cohn, 2026, needs more optimization.
4 556 0.937342624323 Henry Cohn, 2026, needs more optimization.
4 557 0.937410521847 Henry Cohn, 2026, needs more optimization.
4 558 0.937462551951 Henry Cohn, 2026, needs more optimization.
4 559 0.937608425869 Henry Cohn, 2026, needs more optimization.
4 560 0.937687909331 Henry Cohn, 2026, needs more optimization.
4 561 0.937741390008 Henry Cohn, 2026, needs more optimization.
4 562 0.937800135929 Henry Cohn, 2026, needs more optimization.
4 563 0.937854616216 Henry Cohn, 2026, needs more optimization.
4 564 0.937946958280 Henry Cohn, 2026, needs more optimization.
4 565 0.938001484234 Henry Cohn, 2026, needs more optimization.
4 566 0.938108773196 Henry Cohn, 2026, needs more optimization.
4 567 0.938170296793 Henry Cohn, 2026, needs more optimization.
4 568 0.938268908027 Henry Cohn, 2026, needs more optimization.
4 569 0.938344588548 Henry Cohn, 2026, needs more optimization.
4 570 0.938349141920 Henry Cohn, 2026, needs more optimization.
4 571 0.938420308040 Henry Cohn, 2026, needs more optimization.
4 572 0.938479558933 Henry Cohn, 2026, needs more optimization.
4 573 0.938551975281 Henry Cohn, 2026, needs more optimization.
4 574 0.938608701133 Henry Cohn, 2026, needs more optimization.
4 575 0.938717380795 Henry Cohn, 2026, needs more optimization.
4 576 0.938784833589 Henry Cohn, 2026, needs more optimization.
4 577 0.938907343673 Henry Cohn, 2026, needs more optimization.
4 578 0.938953322082 Henry Cohn, 2026, needs more optimization.
4 579 0.939048499509 Henry Cohn, 2026, needs more optimization.
4 580 0.939141179227 Henry Cohn, 2026, needs more optimization.
4 581 0.939204108810 Henry Cohn, 2026, needs more optimization.
4 582 0.939262537386 Henry Cohn, 2026, needs more optimization.
4 583 0.939307111089 Henry Cohn, 2026, needs more optimization.
4 584 0.939329798612 Henry Cohn, 2026, needs more optimization.
4 585 0.939432773359 Henry Cohn, 2026, needs more optimization.
4 586 0.939487297605 Henry Cohn, 2026, needs more optimization.
4 587 0.939550383261 Henry Cohn, 2026, needs more optimization.
4 588 0.939559793000 Henry Cohn, 2026, needs more optimization.
4 589 0.939637566969 Henry Cohn, 2026, needs more optimization.
4 590 0.939651040423 Henry Cohn, 2026, needs more optimization.
4 591 0.939776027077 Henry Cohn, 2026, needs more optimization.
4 592 0.939828349564 Henry Cohn, 2026, needs more optimization.
4 593 0.939829380710 Henry Cohn, 2026, needs more optimization.
4 594 0.939848575178 Henry Cohn, 2026, needs more optimization.
4 595 0.939917387324 Henry Cohn, 2026, needs more optimization.
4 596 0.939973475439 Henry Cohn, 2026, needs more optimization.
4 597 0.939992326265 Henry Cohn, 2026, needs more optimization.
4 598 0.940086160207 Henry Cohn, 2026, needs more optimization.
4 599 0.940160067480 Henry Cohn, 2026, needs more optimization.
4 600 0.940184611885 Henry Cohn, 2026, needs more optimization.
4 601 0.940232544017 Henry Cohn, 2026, needs more optimization.
4 602 0.940339273728 Henry Cohn, 2026, needs more optimization.
4 603 0.940407811131 Henry Cohn, 2026, needs more optimization.
4 604 0.940530243335 Henry Cohn, 2026, needs more optimization.
4 605 0.940595897672 Henry Cohn, 2026, needs more optimization.
4 606 0.940629332993 Henry Cohn, 2026, needs more optimization.
4 607 0.940690407187 Henry Cohn, 2026, needs more optimization.
4 608 0.940763737888 Henry Cohn, 2026, needs more optimization.
4 609 0.940823032137 Henry Cohn, 2026, needs more optimization.
4 610 0.940912709564 Henry Cohn, 2026, needs more optimization.
4 611 0.940947295787 Henry Cohn, 2026, needs more optimization.
4 612 0.940999234162 Henry Cohn, 2026, needs more optimization.
4 613 0.941058479695 Henry Cohn, 2026, needs more optimization.
4 614 0.941160930995 Henry Cohn, 2026, needs more optimization.
4 615 0.941237606521 Henry Cohn, 2026, needs more optimization.
4 616 0.941276608542 Henry Cohn, 2026, needs more optimization.
4 617 0.941339328104 Henry Cohn, 2026, needs more optimization.
4 618 0.941401968416 Henry Cohn, 2026, needs more optimization.
4 619 0.941445542755 Henry Cohn, 2026, needs more optimization.
4 620 0.941512427051 Henry Cohn, 2026, needs more optimization.
4 621 0.941548194183 Henry Cohn, 2026, needs more optimization.
4 622 0.941656526092 Henry Cohn, 2026, needs more optimization.
4 623 0.941696457719 Henry Cohn, 2026, needs more optimization.
4 624 0.941766559592 Henry Cohn, 2026, needs more optimization.
4 625 0.941838431002 Henry Cohn, 2026, needs more optimization.
4 626 0.941955443279 Henry Cohn, 2026, needs more optimization.
4 627 0.941998018942 Henry Cohn, 2026, needs more optimization.
4 628 0.942077697649 Henry Cohn, 2026, needs more optimization.
4 629 0.942133201968 Henry Cohn, 2026, needs more optimization.
4 630 0.942218535915 Henry Cohn, 2026, needs more optimization.
4 631 0.942289209513 Henry Cohn, 2026, needs more optimization.
4 632 0.942316211327 Henry Cohn, 2026, needs more optimization.
4 633 0.942417363986 Henry Cohn, 2026, needs more optimization.
4 634 0.942493383645 Henry Cohn, 2026, needs more optimization.
4 635 0.942529575089 Henry Cohn, 2026, needs more optimization.
4 636 0.942596119081 Henry Cohn, 2026, needs more optimization.
4 637 0.942614444546 Henry Cohn, 2026, needs more optimization.
4 638 0.942691700756 Henry Cohn, 2026, needs more optimization.
4 639 0.942756347541 Henry Cohn, 2026, needs more optimization.
4 640 0.942772999882 Henry Cohn, 2026, needs more optimization.
4 641 0.942876039843 Henry Cohn, 2026, needs more optimization.
4 642 0.942969051020 Henry Cohn, 2026, needs more optimization.
4 643 0.943068391833 Henry Cohn, 2026, needs more optimization.
4 644 0.943073892703 Henry Cohn, 2026, needs more optimization.
4 645 0.943118989496 Henry Cohn, 2026, needs more optimization.
4 646 0.943159621002 Henry Cohn, 2026, needs more optimization.
4 647 0.943207668875 Henry Cohn, 2026, needs more optimization.
4 648 0.943218851964 Henry Cohn, 2026, needs more optimization.
4 649 0.943257780687 Henry Cohn, 2026, needs more optimization.
4 650 0.943274345246 Henry Cohn, 2026, needs more optimization.
4 651 0.943339245664 Henry Cohn, 2026, needs more optimization.
4 652 0.943364587933 Henry Cohn, 2026, needs more optimization.
4 653 0.943379121445 Henry Cohn, 2026, needs more optimization.
4 654 0.943389655961 Henry Cohn, 2026, needs more optimization.
4 655 0.943451720020 Henry Cohn, 2026, needs more optimization.
4 656 0.943484447577 Henry Cohn, 2026, needs more optimization.
4 657 0.943546241712 Henry Cohn, 2026, needs more optimization.
4 658 0.943547354188 Henry Cohn, 2026, needs more optimization.
4 659 0.943561735522 Henry Cohn, 2026, needs more optimization.
4 660 0.943594661847 Henry Cohn, 2026, needs more optimization.
4 661 0.943623943567 Henry Cohn, 2026, needs more optimization.
4 662 0.943665038239 Henry Cohn, 2026, needs more optimization.
4 663 0.943709855467 Henry Cohn, 2026, needs more optimization.
4 664 0.943744033307 Henry Cohn, 2026, needs more optimization.
4 665 0.943779039775 Henry Cohn, 2026, needs more optimization.
4 666 0.943797504575 Henry Cohn, 2026, needs more optimization.
4 667 0.943828183852 Henry Cohn, 2026, needs more optimization.
4 668 0.943865438647 Henry Cohn, 2026, needs more optimization.
4 669 0.943891706519 Henry Cohn, 2026, needs more optimization.
4 670 0.943960439578 Henry Cohn, 2026, needs more optimization.
4 671 0.943997210820 Henry Cohn, 2026, needs more optimization.
4 672 0.944039779123 Henry Cohn, 2026, needs more optimization.
4 673 0.944115095092 Henry Cohn, 2026, needs more optimization.
4 674 0.944214356306 Henry Cohn, 2026, needs more optimization.
4 675 0.944323146535 Henry Cohn, 2026, needs more optimization.
4 676 0.944350962751 Henry Cohn, 2026, needs more optimization.
4 677 0.944399984729 Henry Cohn, 2026, needs more optimization.
4 678 0.944513116444 Henry Cohn, 2026, needs more optimization.
4 679 0.944589356043 Henry Cohn, 2026, needs more optimization.
4 680 0.944648718475 Henry Cohn, 2026, needs more optimization.
4 681 0.944719250904 Henry Cohn, 2026, needs more optimization.
4 682 0.944803667014 Henry Cohn, 2026, needs more optimization.
4 683 0.944832790327 Henry Cohn, 2026, needs more optimization.
4 684 0.944916555327 Henry Cohn, 2026, needs more optimization.
4 685 0.944976313583 Henry Cohn, 2026, needs more optimization.
4 686 0.945013618972 Henry Cohn, 2026, needs more optimization.
4 687 0.945149581530 Henry Cohn, 2026, needs more optimization.
4 688 0.945215918865 Henry Cohn, 2026, needs more optimization.
4 689 0.945292022564 Henry Cohn, 2026, needs more optimization.
4 690 0.945359225444 Henry Cohn, 2026, needs more optimization.
4 691 0.945455645291 Henry Cohn, 2026, needs more optimization.
4 692 0.945502815449 Henry Cohn, 2026, needs more optimization.
4 693 0.945612640744 Henry Cohn, 2026, needs more optimization.
4 694 0.945656651681 Henry Cohn, 2026, needs more optimization.
4 695 0.945721201559 Henry Cohn, 2026, needs more optimization.
4 696 0.945812268570 Henry Cohn, 2026, needs more optimization.
4 697 0.945831918935 Henry Cohn, 2026, needs more optimization.
4 698 0.945878915234 Henry Cohn, 2026, needs more optimization.
4 699 0.945995802950 Henry Cohn, 2026, needs more optimization.
4 700 0.946035096171 Henry Cohn, 2026, needs more optimization.
4 701 0.946101841884 Henry Cohn, 2026, needs more optimization.
4 702 0.946186074127 Henry Cohn, 2026, needs more optimization.
4 703 0.946201979994 Henry Cohn, 2026, needs more optimization.
4 704 0.946305095175 Henry Cohn, 2026, needs more optimization.
4 705 0.946324753546 Henry Cohn, 2026, needs more optimization.
4 706 0.946379355957 Henry Cohn, 2026, needs more optimization.
4 707 0.946432730609 Henry Cohn, 2026, needs more optimization.
4 708 0.946486897981 Henry Cohn, 2026, needs more optimization.
4 709 0.946515983215 Henry Cohn, 2026, needs more optimization.
4 710 0.946555332286 Henry Cohn, 2026, needs more optimization.
4 711 0.946597907309 Henry Cohn, 2026, needs more optimization.
4 712 0.946659590171 Henry Cohn, 2026, needs more optimization.
4 713 0.946723980784 Henry Cohn, 2026, needs more optimization.
4 714 0.946788543187 Henry Cohn, 2026, needs more optimization.
4 715 0.946814487460 Henry Cohn, 2026, needs more optimization.
4 716 0.946822220619 Henry Cohn, 2026, needs more optimization.
4 717 0.946896917788 Henry Cohn, 2026, needs more optimization.
4 718 0.946925379119 Henry Cohn, 2026, needs more optimization.
4 719 0.946958238862 Henry Cohn, 2026, needs more optimization.
4 720 0.947002376751 Henry Cohn, 2026, needs more optimization.
4 721 0.947056821065 Henry Cohn, 2026, needs more optimization.
4 722 0.947101547618 Henry Cohn, 2026, needs more optimization.
4 723 0.947125051685 Henry Cohn, 2026, needs more optimization.
4 724 0.947177898860 Henry Cohn, 2026, needs more optimization.
4 725 0.947192105518 Henry Cohn, 2026, needs more optimization.
4 726 0.947204824714 Henry Cohn, 2026, needs more optimization.
4 727 0.947252653863 Henry Cohn, 2026, needs more optimization.
4 728 0.947309211212 Henry Cohn, 2026, needs more optimization.
4 729 0.947341100381 Henry Cohn, 2026, needs more optimization.
4 730 0.947425281913 Henry Cohn, 2026, needs more optimization.
4 731 0.947460344003 Henry Cohn, 2026, needs more optimization.
4 732 0.947505682538 Henry Cohn, 2026, needs more optimization.
4 733 0.947547537480 Henry Cohn, 2026, needs more optimization.
4 734 0.947552094365 Henry Cohn, 2026, needs more optimization.
4 735 0.947575524392 Henry Cohn, 2026, needs more optimization.
4 736 0.947610887612 Henry Cohn, 2026, needs more optimization.
4 737 0.947663870175 Henry Cohn, 2026, needs more optimization.
4 738 0.947676706000 Henry Cohn, 2026, needs more optimization.
4 739 0.947707474168 Henry Cohn, 2026, needs more optimization.
4 740 0.947738131287 Henry Cohn, 2026, needs more optimization.
4 741 0.947822685297 Henry Cohn, 2026, needs more optimization.
4 742 0.947838577178 Henry Cohn, 2026, needs more optimization.
4 743 0.947863885928 Henry Cohn, 2026, needs more optimization.
4 744 0.947943071994 Henry Cohn, 2026, needs more optimization.
4 745 0.947997727674 Henry Cohn, 2026, needs more optimization.
4 746 0.948055031823 Henry Cohn, 2026, needs more optimization.
4 747 0.948098704012 Henry Cohn, 2026, needs more optimization.
4 748 0.948118892737 Henry Cohn, 2026, needs more optimization.
4 749 0.948180885101 Henry Cohn, 2026, needs more optimization.
4 750 0.948240856020 Henry Cohn, 2026, needs more optimization.
4 751 0.948281404659 Henry Cohn, 2026, needs more optimization.
4 752 0.948317587811 Henry Cohn, 2026, needs more optimization.
4 753 0.948343890897 Henry Cohn, 2026, needs more optimization.
4 754 0.948359329966 Henry Cohn, 2026, needs more optimization.
4 755 0.948384190179 Henry Cohn, 2026, needs more optimization.
4 756 0.948420326896 Henry Cohn, 2026, needs more optimization.
4 757 0.948469628121 Henry Cohn, 2026, needs more optimization.
4 758 0.948528431153 Henry Cohn, 2026, needs more optimization.
4 759 0.948556622265 Henry Cohn, 2026, needs more optimization.
4 760 0.948640911164 Henry Cohn, 2026, needs more optimization.
4 761 0.948682833839 Henry Cohn, 2026, needs more optimization.
4 762 0.948762048366 Henry Cohn, 2026, needs more optimization.
4 763 0.948802168315 Henry Cohn, 2026, needs more optimization.
4 764 0.948840737744 Henry Cohn, 2026, needs more optimization.
4 765 0.948849334885 Henry Cohn, 2026, needs more optimization.
4 766 0.948910026012 Henry Cohn, 2026, needs more optimization.
4 767 0.948941771118 Henry Cohn, 2026, needs more optimization.
4 768 0.948970708524 Henry Cohn, 2026, needs more optimization.
4 769 0.949050202954 Henry Cohn, 2026, needs more optimization.
4 770 0.949098906560 Henry Cohn, 2026, needs more optimization.
4 771 0.949104948719 Henry Cohn, 2026, needs more optimization.
4 772 0.949147699629 Henry Cohn, 2026, needs more optimization.
4 773 0.949228913632 Henry Cohn, 2026, needs more optimization.
4 774 0.949298593935 Henry Cohn, 2026, needs more optimization.
4 775 0.949335160224 Henry Cohn, 2026, needs more optimization.
4 776 0.949366078418 Henry Cohn, 2026, needs more optimization.
4 777 0.949404673333 Henry Cohn, 2026, needs more optimization.
4 778 0.949415759420 Henry Cohn, 2026, needs more optimization.
4 779 0.949499055777 Henry Cohn, 2026, needs more optimization.
4 780 0.949516477888 Henry Cohn, 2026, needs more optimization.
4 781 0.949534403975 Henry Cohn, 2026, needs more optimization.
4 782 0.949545767956 Henry Cohn, 2026, needs more optimization.
4 783 0.949603080321 Henry Cohn, 2026, needs more optimization.
4 784 0.949656855516 Henry Cohn, 2026, needs more optimization.
4 785 0.949673315235 Henry Cohn, 2026, needs more optimization.
4 786 0.949734411157 Henry Cohn, 2026, needs more optimization.
4 787 0.949764074703 Henry Cohn, 2026, needs more optimization.
4 788 0.949807330057 Henry Cohn, 2026, needs more optimization.
4 789 0.949821936952 Henry Cohn, 2026, needs more optimization.
4 790 0.949865413790 Henry Cohn, 2026, needs more optimization.
4 791 0.949888387027 Henry Cohn, 2026, needs more optimization.
4 792 0.949937433690 Henry Cohn, 2026, needs more optimization.
4 793 0.949989750186 Henry Cohn, 2026, needs more optimization.
4 794 0.949990996985 Henry Cohn, 2026, needs more optimization.
4 795 0.950018077494 Henry Cohn, 2026, needs more optimization.
4 796 0.950052272705 Henry Cohn, 2026, needs more optimization.
4 797 0.950071960003 Henry Cohn, 2026, needs more optimization.
4 798 0.950090336964 Henry Cohn, 2026, needs more optimization.
4 799 0.950137129360 Henry Cohn, 2026, needs more optimization.
4 800 0.950162327666 Henry Cohn, 2026, needs more optimization.
4 801 0.950164850476 Henry Cohn, 2026, needs more optimization.
4 802 0.950168450827 Henry Cohn, 2026, needs more optimization.
4 803 0.950212243578 Henry Cohn, 2026, needs more optimization.
4 804 0.950237932324 Henry Cohn, 2026, needs more optimization.
4 805 0.950268737989 Henry Cohn, 2026, needs more optimization.
4 806 0.950296520661 Henry Cohn, 2026, needs more optimization.
4 807 0.950314407050 Henry Cohn, 2026, needs more optimization.
4 808 0.950365117534 Henry Cohn, 2026, needs more optimization.
4 809 0.950366408762 Henry Cohn, 2026, needs more optimization.
4 810 0.950415319981 Henry Cohn, 2026, needs more optimization.
4 811 0.950418597636 Henry Cohn, 2026, needs more optimization.
4 812 0.950466101888 Henry Cohn, 2026, needs more optimization.
4 813 0.950486450299 Henry Cohn, 2026, needs more optimization.
4 814 0.950519507929 Henry Cohn, 2026, needs more optimization.
4 815 0.950522924790 Henry Cohn, 2026, needs more optimization.
4 816 0.950548368615 Henry Cohn, 2026, needs more optimization.
4 817 0.950562564196 Henry Cohn, 2026, needs more optimization.
4 818 0.950567855728 Henry Cohn, 2026, needs more optimization.
4 819 0.950571143365 Henry Cohn, 2026, needs more optimization.
4 820 0.950600399066 Henry Cohn, 2026, needs more optimization.
4 821 0.950613132539 Henry Cohn, 2026, needs more optimization.
4 822 0.950616133350 Henry Cohn, 2026, needs more optimization.
4 823 0.950618083866 Henry Cohn, 2026, needs more optimization.
4 824 0.950783672506 Henry Cohn, 2026, needs more optimization.
4 825 0.950784234601 Henry Cohn, 2026, needs more optimization.
4 826 0.950785037965 Henry Cohn, 2026, needs more optimization.
4 827 0.950785992625 Henry Cohn, 2026, needs more optimization.
4 828 0.950786501723 Henry Cohn, 2026, needs more optimization.
4 829 0.950787414175 Henry Cohn, 2026, needs more optimization.
4 830 0.950788870796 Henry Cohn, 2026, needs more optimization.
4 831 0.950790865322 Henry Cohn, 2026, needs more optimization.
4 832 0.950791781680 Henry Cohn, 2026, needs more optimization.
4 833 0.950791870889 Henry Cohn, 2026, needs more optimization.
4 834 0.950793565414 Henry Cohn, 2026, needs more optimization.
4 835 0.950794471947 Henry Cohn, 2026, needs more optimization.
4 836 0.950795413157 Henry Cohn, 2026, needs more optimization.
4 837 0.950795677351 Henry Cohn, 2026, needs more optimization.
4 838 0.950796998582 Henry Cohn, 2026, needs more optimization.
4 840 0.950797547280 Henry Cohn, 2025, needs more optimization.
4 841 0.950955648144 Henry Cohn, 2026, needs more optimization.
4 842 0.951052062313 Henry Cohn, 2026, needs more optimization.
4 843 0.951118475901 Henry Cohn, 2026, needs more optimization.
4 844 0.951235550244 Henry Cohn, 2026, needs more optimization.
4 845 0.951287707295 Henry Cohn, 2026, needs more optimization.
4 846 0.951404214537 Henry Cohn, 2026, needs more optimization.
4 847 0.951467821148 Henry Cohn, 2026, needs more optimization.
4 848 0.951552114074 Henry Cohn, 2026, needs more optimization.
4 849 0.951612720239 Henry Cohn, 2026, needs more optimization.
4 850 0.951689389223 Henry Cohn, 2026, needs more optimization.
4 851 0.951797684087 Henry Cohn, 2026, needs more optimization.
4 852 0.951836726287 Henry Cohn, 2026, needs more optimization.
4 853 0.951908221851 Henry Cohn, 2026, needs more optimization.
4 854 0.951987051546 Henry Cohn, 2026, needs more optimization.
4 855 0.952036941947 Henry Cohn, 2026, needs more optimization.
4 856 0.952135299987 Henry Cohn, 2026, needs more optimization.
4 857 0.952191618329 Henry Cohn, 2026, needs more optimization.
4 858 0.952232393250 Henry Cohn, 2026, needs more optimization.
4 859 0.952304988341 Henry Cohn, 2026, needs more optimization.
4 860 0.952374309723 Henry Cohn, 2026, needs more optimization.
4 861 0.952476139491 Henry Cohn, 2026, needs more optimization.
4 862 0.952489029549 Henry Cohn, 2026, needs more optimization.
4 863 0.952569830310 Henry Cohn, 2026, needs more optimization.
4 864 0.952616760577 Henry Cohn, 2026, needs more optimization.
4 865 0.952690554913 Henry Cohn, 2026, needs more optimization.
4 866 0.952773092049 Henry Cohn, 2026, needs more optimization.
4 867 0.952837166259 Henry Cohn, 2026, needs more optimization.
4 868 0.952844089566 Henry Cohn, 2026, needs more optimization.
4 869 0.952844882392 Henry Cohn, 2026, needs more optimization.
4 870 0.952849002283 Henry Cohn, 2026, needs more optimization.
4 871 0.952872338516 Henry Cohn, 2026, needs more optimization.
4 872 0.952917907875 Henry Cohn, 2026, needs more optimization.
4 873 0.952950755488 Henry Cohn, 2026, needs more optimization.
4 874 0.952962427453 Henry Cohn, 2026, needs more optimization.
4 875 0.953000535577 Henry Cohn, 2026, needs more optimization.
4 876 0.953014226290 Henry Cohn, 2026, needs more optimization.
4 877 0.953069172989 Henry Cohn, 2026, needs more optimization.
4 878 0.953112695671 Henry Cohn, 2026, needs more optimization.
4 879 0.953154681075 Henry Cohn, 2026, needs more optimization.
4 880 0.953172076511 Henry Cohn, 2026, needs more optimization.
4 881 0.953218919758 Henry Cohn, 2026, needs more optimization.
4 882 0.953261994346 Henry Cohn, 2026, needs more optimization.
4 883 0.953292381315 Henry Cohn, 2026, needs more optimization.
4 884 0.953301932273 Henry Cohn, 2026, needs more optimization.
4 885 0.953337203181 Henry Cohn, 2026, needs more optimization.
4 886 0.953394160874 Henry Cohn, 2026, needs more optimization.
4 887 0.953416891638 Henry Cohn, 2026, needs more optimization.
4 888 0.953422239756 Henry Cohn, 2026, needs more optimization.
4 889 0.953473089597 Henry Cohn, 2026, needs more optimization.
4 890 0.953542161707 Henry Cohn, 2026, needs more optimization.
4 891 0.953577463762 Henry Cohn, 2026, needs more optimization.
4 892 0.953594208115 Henry Cohn, 2026, needs more optimization.
4 893 0.953641878032 Henry Cohn, 2026, needs more optimization.
4 894 0.953641880786 Henry Cohn, 2026, needs more optimization.
4 895 0.953696463190 Henry Cohn, 2026, needs more optimization.
4 896 0.953697563559 Henry Cohn, 2026, needs more optimization.
4 897 0.953714094510 Henry Cohn, 2026, needs more optimization.
4 898 0.953776146418 Henry Cohn, 2026, needs more optimization.
4 899 0.953783740464 Henry Cohn, 2026, needs more optimization.
4 900 0.953839740761 Henry Cohn, 2026, needs more optimization.
4 901 0.953855632936 Henry Cohn, 2026, needs more optimization.
4 902 0.953892134802 Henry Cohn, 2026, needs more optimization.
4 903 0.953932291069 Henry Cohn, 2026, needs more optimization.
4 904 0.953972653700 Henry Cohn, 2026, needs more optimization.
4 905 0.954046618433 Henry Cohn, 2026, needs more optimization.
4 906 0.954083682650 Henry Cohn, 2026, needs more optimization.
4 907 0.954116981720 Henry Cohn, 2026, needs more optimization.
4 908 0.954119171799 Henry Cohn, 2026, needs more optimization.
4 909 0.954120178168 Henry Cohn, 2026, needs more optimization.
4 910 0.954139390169 Henry Cohn, 2026, needs more optimization.
4 911 0.954148151810 Henry Cohn, 2026, needs more optimization.
4 912 0.954156238395 Henry Cohn, 2026, needs more optimization.
4 913 0.954158076169 Henry Cohn, 2026, needs more optimization.
4 914 0.954189277276 Henry Cohn, 2026, needs more optimization.
4 915 0.954211932743 Henry Cohn, 2026, needs more optimization.
4 916 0.954241497440 Henry Cohn, 2026, needs more optimization.
4 917 0.954300040812 Henry Cohn, 2026, needs more optimization.
4 918 0.954336131435 Henry Cohn, 2026, needs more optimization.
4 919 0.954387122733 Henry Cohn, 2026, needs more optimization.
4 920 0.954436260169 Henry Cohn, 2026, needs more optimization.
4 921 0.954439554001 Henry Cohn, 2026, needs more optimization.
4 922 0.954485741907 Henry Cohn, 2026, needs more optimization.
4 923 0.954545891532 Henry Cohn, 2026, needs more optimization.
4 924 0.954586511643 Henry Cohn, 2026, needs more optimization.
4 925 0.954611986356 Henry Cohn, 2026, needs more optimization.
4 926 0.954615840237 Henry Cohn, 2026, needs more optimization.
4 927 0.954675205958 Henry Cohn, 2026, needs more optimization.
4 928 0.954733765794 Henry Cohn, 2026, needs more optimization.
4 929 0.954784500901 Henry Cohn, 2026, needs more optimization.
4 930 0.954827119605 Henry Cohn, 2026, needs more optimization.
4 931 0.954892633205 Henry Cohn, 2026, needs more optimization.
4 932 0.954920625772 Henry Cohn, 2026, needs more optimization.
4 933 0.955008682083 Henry Cohn, 2026, needs more optimization.
4 934 0.955010487590 Henry Cohn, 2026, needs more optimization.
4 935 0.955019221900 Henry Cohn, 2026, needs more optimization.
4 936 0.955077651638 Henry Cohn, 2026, needs more optimization.
4 937 0.955098604541 Henry Cohn, 2026, needs more optimization.
4 938 0.955131409543 Henry Cohn, 2026, needs more optimization.
4 939 0.955145153269 Henry Cohn, 2026, needs more optimization.
4 940 0.955164701600 Henry Cohn, 2026, needs more optimization.
4 941 0.955208533343 Henry Cohn, 2026, needs more optimization.
4 942 0.955247926715 Henry Cohn, 2026, needs more optimization.
4 943 0.955275664530 Henry Cohn, 2026, needs more optimization.
4 944 0.955321294402 Henry Cohn, 2026, needs more optimization.
4 945 0.955348985018 Henry Cohn, 2026, needs more optimization.
4 946 0.955389214870 Henry Cohn, 2026, needs more optimization.
4 947 0.955396688631 Henry Cohn, 2026, needs more optimization.
4 948 0.955463995553 Henry Cohn, 2026, needs more optimization.
4 949 0.955495987881 Henry Cohn, 2026, needs more optimization.
4 950 0.955541503868 Henry Cohn, 2026, needs more optimization.
4 951 0.955545110942 Henry Cohn, 2026, needs more optimization.
4 952 0.955547728712 Henry Cohn, 2026, needs more optimization.
4 954 0.955568075817 Henry Cohn, 2026, needs more optimization.
4 955 0.955597841157 Henry Cohn, 2026, needs more optimization.
4 956 0.955645740001 Henry Cohn, 2026, needs more optimization.
4 957 0.955649494495 Henry Cohn, 2026, needs more optimization.
4 958 0.955683940906 Henry Cohn, 2026, needs more optimization.
4 959 0.955725688876 Henry Cohn, 2026, needs more optimization.
4 960 0.955787000120 Henry Cohn, 2026, needs more optimization.
4 961 0.955903058305 Henry Cohn, 2026, needs more optimization.
4 962 0.955915274279 Henry Cohn, 2026, needs more optimization.
4 963 0.955922055690 Henry Cohn, 2026, needs more optimization.
4 964 0.956031053373 Henry Cohn, 2026, needs more optimization.
4 965 0.956049323288 Henry Cohn, 2026, needs more optimization.
4 966 0.956072726092 Henry Cohn, 2026, needs more optimization.
4 967 0.956078910481 Henry Cohn, 2026, needs more optimization.
4 968 0.956088564323 Henry Cohn, 2026, needs more optimization.
4 969 0.956105234503 Henry Cohn, 2026, needs more optimization.
4 970 0.956120519679 Henry Cohn, 2026, needs more optimization.
4 971 0.956127800420 Henry Cohn, 2026, needs more optimization.
4 972 0.956149363741 Henry Cohn, 2026, needs more optimization.
4 973 0.956164229033 Henry Cohn, 2026, needs more optimization.
4 974 0.956173152719 Henry Cohn, 2026, needs more optimization.
4 975 0.956188074138 Henry Cohn, 2026, needs more optimization.
4 976 0.956227055056 Henry Cohn, 2026, needs more optimization.
4 977 0.956298552339 Henry Cohn, 2026, needs more optimization.
4 978 0.956306186233 Henry Cohn, 2026, needs more optimization.
4 979 0.956335659912 Henry Cohn, 2026, needs more optimization.
4 980 0.956379507689 Henry Cohn, 2026, needs more optimization.
4 981 0.956447936290 Henry Cohn, 2026, needs more optimization.
4 982 0.956447951112 Henry Cohn, 2026, needs more optimization.
4 983 0.956519066201 Henry Cohn, 2026, needs more optimization.
4 984 0.956638909119 Henry Cohn, 2026, needs more optimization.
4 985 0.956642063244 Henry Cohn, 2026, needs more optimization.
4 986 0.956657962080 Henry Cohn, 2026, needs more optimization.
4 987 0.956658904829 Henry Cohn, 2026, needs more optimization.
4 988 0.956664711435 Henry Cohn, 2026, needs more optimization.
4 989 0.956718208510 Henry Cohn, 2026, needs more optimization.
4 990 0.956774892016 Henry Cohn, 2026, needs more optimization.
4 991 0.956834011764 Henry Cohn, 2026, needs more optimization.
4 992 0.956878283969 Henry Cohn, 2026, needs more optimization.
4 993 0.956950286327 Henry Cohn, 2026, needs more optimization.
4 994 0.956981150628 Henry Cohn, 2026, needs more optimization.
4 995 0.957034687604 Henry Cohn, 2026, needs more optimization.
4 996 0.957060051341 Henry Cohn, 2026, needs more optimization.
4 997 0.957126476698 Henry Cohn, 2026, needs more optimization.
4 998 0.957148536933 Henry Cohn, 2026, needs more optimization.
4 999 0.957195815316 Henry Cohn, 2026, needs more optimization.
4 1000 0.957241281845 Henry Cohn, 2026, needs more optimization.
4 1001 0.957259283408 Henry Cohn, 2026, needs more optimization.
4 1002 0.957293627063 Henry Cohn, 2026, needs more optimization.
4 1003 0.957338851184 Henry Cohn, 2026, needs more optimization.
4 1004 0.957354812486 Henry Cohn, 2026, needs more optimization.
4 1005 0.957373564300 Henry Cohn, 2026, needs more optimization.
4 1006 0.957379507560 Henry Cohn, 2026, needs more optimization.
4 1007 0.957395777274 Henry Cohn, 2026, needs more optimization.
4 1008 0.957445945067 Henry Cohn, 2026, needs more optimization.
4 1009 0.957468080801 Henry Cohn, 2026, needs more optimization.
4 1011 0.957476083617 Henry Cohn, 2026, needs more optimization.
4 1012 0.957516973546 Henry Cohn, 2026, needs more optimization.
4 1013 0.957580697245 Henry Cohn, 2026, needs more optimization.
4 1014 0.957608910554 Henry Cohn, 2026, needs more optimization.
4 1015 0.957635683926 Henry Cohn, 2026, needs more optimization.
4 1016 0.957663308174 Henry Cohn, 2026, needs more optimization.
4 1017 0.957673525651 Henry Cohn, 2026, needs more optimization.
4 1018 0.957717244077 Henry Cohn, 2026, needs more optimization.
4 1019 0.957740842320 Henry Cohn, 2026, needs more optimization.
4 1020 0.957756564847 Henry Cohn, 2026, needs more optimization.
4 1021 0.957779273338 Henry Cohn, 2026, needs more optimization.
4 1022 0.957786481135 Henry Cohn, 2026, needs more optimization.
4 1023 0.957843444734 Henry Cohn, 2026, needs more optimization.
4 1024 0.957881992874 Henry Cohn, 2026, needs more optimization.
5 11 0.132853542599 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996; K. J. Nurmela, Constructing spherical codes by global optimization methods, Research Report A32, Digital Systems Laboratory, Helsinki University of Technology, 1995, https://research.ics.aalto.fi/publications/info/bibdb.HUT-TCS-A32.shtml.
45⁢x3−25⁢x2−5⁢x+1
5 12 0.153931605034 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996; K. J. Nurmela, Constructing spherical codes by global optimization methods, Research Report A32, Digital Systems Laboratory, Helsinki University of Technology, 1995, https://research.ics.aalto.fi/publications/info/bibdb.HUT-TCS-A32.shtml.
25⁢x4+30⁢x3+24⁢x2+2⁢x−1
5 13 0.187259851883 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996; K. J. Nurmela, Constructing spherical codes by global optimization methods, Research Report A32, Digital Systems Laboratory, Helsinki University of Technology, 1995, https://research.ics.aalto.fi/publications/info/bibdb.HUT-TCS-A32.shtml.
17⁢x3−5⁢x2−5⁢x+1
5 14 0.2 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996; K. J. Nurmela, Constructing spherical codes by global optimization methods, Research Report A32, Digital Systems Laboratory, Helsinki University of Technology, 1995, https://research.ics.aalto.fi/publications/info/bibdb.HUT-TCS-A32.shtml.
5⁢x−1
5 15 0.2 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996; K. J. Nurmela, Constructing spherical codes by global optimization methods, Research Report A32, Digital Systems Laboratory, Helsinki University of Technology, 1995, https://research.ics.aalto.fi/publications/info/bibdb.HUT-TCS-A32.shtml.
5⁢x−1
5 16* 0.2 T. Gosset, On the regular and semi-regular figures in space of n dimensions, Messenger Math. 29 (1900), 43–48; V. I. Levenšteĭn, On bounds for packings in n-dimensional Euclidean space (Russian), Dokl. Akad. Nauk SSSR 245 (1979), 1299–1303, English translation in Soviet Math. Dokl. 20 (1979), 417–421.
5⁢x−1
5 17 0.270475835269 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996; K. J. Nurmela, Constructing spherical codes by global optimization methods, Research Report A32, Digital Systems Laboratory, Helsinki University of Technology, 1995, https://research.ics.aalto.fi/publications/info/bibdb.HUT-TCS-A32.shtml.
9⁢x4−16⁢x3−10⁢x2+1
5 18 0.275501741660 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996; K. J. Nurmela, Constructing spherical codes by global optimization methods, Research Report A32, Digital Systems Laboratory, Helsinki University of Technology, 1995, https://research.ics.aalto.fi/publications/info/bibdb.HUT-TCS-A32.shtml.
484⁢x5−488⁢x4+97⁢x3+17⁢x2−x−1
5 19 0.291822399025 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996; K. J. Nurmela, Constructing spherical codes by global optimization methods, Research Report A32, Digital Systems Laboratory, Helsinki University of Technology, 1995, https://research.ics.aalto.fi/publications/info/bibdb.HUT-TCS-A32.shtml.
57⁢x6−38⁢x5−109⁢x4+32⁢x3+23⁢x2−10⁢x+1
5 20 0.299385692900 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996; K. J. Nurmela, Constructing spherical codes by global optimization methods, Research Report A32, Digital Systems Laboratory, Helsinki University of Technology, 1995, https://research.ics.aalto.fi/publications/info/bibdb.HUT-TCS-A32.shtml.
5⁢x3+13⁢x2−x−1
5 21 0.314916957176 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996; K. J. Nurmela, Constructing spherical codes by global optimization methods, Research Report A32, Digital Systems Laboratory, Helsinki University of Technology, 1995, https://research.ics.aalto.fi/publications/info/bibdb.HUT-TCS-A32.shtml.
Minimal polynomial listed in plain text data
5 22 0.354995034167 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
5 23 0.369772696944 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
5 24 0.374232982466 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996; K. J. Nurmela, Constructing spherical codes by global optimization methods, Research Report A32, Digital Systems Laboratory, Helsinki University of Technology, 1995, https://research.ics.aalto.fi/publications/info/bibdb.HUT-TCS-A32.shtml.
1620⁢x10+5508⁢x9−5751⁢x8−2406⁢x7+2055⁢x6+276⁢x5+559⁢x4−210⁢x3−127⁢x2+48⁢x−4
5 25 0.379621025394 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996; K. J. Nurmela, Constructing spherical codes by global optimization methods, Research Report A32, Digital Systems Laboratory, Helsinki University of Technology, 1995, https://research.ics.aalto.fi/publications/info/bibdb.HUT-TCS-A32.shtml.
5 26 0.390240659505 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
Minimal polynomial listed in plain text data
5 27 0.401659264277 H. Cohn, Small spherical and projective codes, data set, 2022, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
Minimal polynomial listed in plain text data
5 28 0.408169699093 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
5 29 0.411034435092 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
Minimal polynomial listed in plain text data
5 30 0.413029776123 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996; K. J. Nurmela, Constructing spherical codes by global optimization methods, Research Report A32, Digital Systems Laboratory, Helsinki University of Technology, 1995, https://research.ics.aalto.fi/publications/info/bibdb.HUT-TCS-A32.shtml.
269⁢x7−1419⁢x6−283⁢x5+405⁢x4+15⁢x3−9⁢x2−x−1
5 31 0.433911863960 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996; K. J. Nurmela, Constructing spherical codes by global optimization methods, Research Report A32, Digital Systems Laboratory, Helsinki University of Technology, 1995, https://research.ics.aalto.fi/publications/info/bibdb.HUT-TCS-A32.shtml.
Minimal polynomial listed in plain text data
5 32 0.441830743928 H. Cohn, Small spherical and projective codes, data set, 2022, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
8⁢x10−40⁢x9+74⁢x8−78⁢x7+73⁢x6−10⁢x5−3⁢x4+18⁢x3−9⁢x2−2⁢x+1
5 33 0.460004535963 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996; K. J. Nurmela, Constructing spherical codes by global optimization methods, Research Report A32, Digital Systems Laboratory, Helsinki University of Technology, 1995, https://research.ics.aalto.fi/publications/info/bibdb.HUT-TCS-A32.shtml.
5 34 0.470482910392 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
5 35 0.478437929066 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
5 36 0.483999000231 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
49⁢x6−6⁢x5−53⁢x4+12⁢x3+13⁢x2−2⁢x−1
5 37 0.493828518526 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
5 38 0.496243746648 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
5 39 0.499971927191 Henry Cohn, 2025.
5 40 0.5 A. Korkine and G. Zolotareff, Sur les formes quadratiques, Math. Ann. 6 (1873), 366–389, doi:10.1007/BF01442795; J. Leech, Five dimensional non-lattice sphere packings, Canad. Math. Bull. 10 (1967), 387–393, doi:10.4153/CMB-1967-037-5; F. Szöllősi, A note on five dimensional kissing arrangements, Math. Res. Lett. 30 (2023), no. 5, 1609–1615, doi:10.4310/MRL.2023.v30.n5.a13, arXiv:2301.08272; H. Cohn and I. Rajagopal, Variations on five-dimensional sphere packings, preprint, 2024, arXiv:2412.00937.
2⁢x−1
5 41 0.514994652513 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
5 42 0.518241155863 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
5 43 0.524709601830 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
5 44 0.527457712324 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
5 45 0.535068808289 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
5 46 0.538291308677 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
5 47 0.540668770936 Henry Cohn, 2025.
5 48 0.545112501822 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
5 49 0.546918160679 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
7⁢x2−2⁢x−1
5 50 0.546918160679 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996; T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
7⁢x2−2⁢x−1
5 51 0.554740414282 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
5 52 0.560107395820 Henry Cohn, 2025.
5 53 0.566883217391 Henry Cohn, 2025.
5 54 0.571075948469 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
5 55 0.574604319465 Henry Cohn, 2025.
5 56 0.577211861101 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
5 57 0.577350269190 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
3⁢x2−1
5 58 0.581466614772 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
5 59 0.586915485192 Henry Cohn, 2025.
5 60 0.593346597794 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
5 61 0.596251134208 Henry Cohn, 2025.
5 62 0.599005179291 Henry Cohn, 2023.
5 63 0.603554375176 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
5 64 0.605837370318 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
5 65 0.608465017856 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
5 66 0.608980005147 Henry Cohn, 2025.
5 67 0.611900403428 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
5 68 0.615240038880 Henry Cohn, 2025.
5 69 0.616793716634 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
5 70 0.617072261706 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
5 71 0.617972684614 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
5 72 0.617972684614 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
5 73 0.618033988750 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
x2+x−1
5 74 0.618033988750 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996; T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
x2+x−1
5 75 0.624659315083 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
5 76 0.631404527694 Henry Cohn, 2025.
5 77 0.636485570257 Henry Cohn, 2025.
5 78 0.640236043820 Henry Cohn, 2025.
5 79 0.643657523051 Henry Cohn, 2025.
5 80 0.646960184204 Henry Cohn, 2025.
5 81 0.648893901838 Henry Cohn, 2025.
5 82 0.651451517528 Henry Cohn, 2025.
5 83 0.655404165086 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
5 84 0.657612544747 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
5 85 0.659252981910 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
5 86 0.660931731561 Henry Cohn, 2025.
5 87 0.662618952049 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
5 88 0.664476994912 Henry Cohn, 2025.
5 89 0.666241382508 Henry Cohn, 2025.
5 90 0.666666666667 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996; T. Ericson and V. Zinoviev, Spherical codes generated by binary partitions of symmetric pointsets, IEEE Trans. Inform. Theory 41 (1995), 107–129, doi:10.1109/18.370114.
3⁢x−2
5 91 0.670415108805 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
5 92 0.672086633602 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
5 93 0.673631229212 Henry Cohn, 2026.
5 94 0.674852218199 Henry Cohn, 2026.
5 95 0.676048898306 Henry Cohn, 2026.
5 96 0.677473018556 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
5 97 0.679241845577 Henry Cohn, 2025.
5 98 0.680270697922 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
5 99 0.681881045310 Henry Cohn, 2025.
5 100 0.683153263764 Henry Cohn, 2025.
5 101 0.685186090412 Henry Cohn, 2025.
5 102 0.687443384073 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
5 103 0.688710548823 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
5 104 0.689379879811 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
5 105 0.690713474104 Henry Cohn, 2025.
5 106 0.692005491905 Henry Cohn, 2025.
5 107 0.693863512900 Henry Cohn, 2025.
5 108 0.695352226010 Henry Cohn, 2025.
5 109 0.696434500115 Henry Cohn, 2025.
5 110 0.698102767792 Henry Cohn, 2025.
5 111 0.699314990430 Henry Cohn, 2025.
5 112 0.700443897808 Henry Cohn, 2025.
5 113 0.701786576995 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
5 114 0.703016293967 Henry Cohn, 2025.
5 115 0.704057149283 Henry Cohn, 2025.
5 116 0.705292505873 Henry Cohn, 2025.
5 117 0.706879377909 Henry Cohn, 2025.
5 118 0.708028481260 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
5 119 0.709224052004 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
5 120 0.710406057156 Henry Cohn, 2025.
5 121 0.711530217808 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
5 122 0.712249276837 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
5 123 0.713918633096 Henry Cohn, 2025.
5 124 0.715011517303 Henry Cohn, 2026.
5 125 0.716344500109 Henry Cohn, 2026.
5 126 0.717125378112 Henry Cohn, 2025.
5 127 0.718593652896 Henry Cohn, 2025.
5 128 0.719621301444 Henry Cohn, 2025.
5 129 0.720947646950 Henry Cohn, 2025.
5 130 0.721711816020 Henry Cohn, 2025.
5 131 0.723073961702 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
5 132 0.724187140976 Henry Cohn, 2026, needs more optimization.
5 133 0.725083698449 Henry Cohn, 2026, needs more optimization.
5 134 0.726469758062 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
5 135 0.727645837450 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
5 136 0.728599347940 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
5 137 0.729817090478 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
5 138 0.730143082796 Henry Cohn, 2025.
5 139 0.730886192569 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
5 140 0.731687221493 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
5 141 0.732578967128 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
5 142 0.733679133859 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
5 143 0.734506087652 Henry Cohn, 2025.
5 144 0.735003136698 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
5 145 0.735906191775 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
5 146 0.736194287921 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
5 147 0.736967148066 Henry Cohn, 2025.
5 148 0.737200174837 Henry Cohn, 2025.
5 149 0.737884019958 Henry Cohn, 2025.
5 150 0.738295981996 Henry Cohn, 2025.
5 151 0.739207005875 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
5 152 0.739822026342 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
5 153 0.740691989282 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
5 154 0.741254575296 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
5 155 0.742161234709 Henry Cohn, 2025.
5 156 0.742808811623 Henry Cohn, 2025.
5 157 0.743243329545 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
5 158 0.743483872286 Henry Cohn, 2026, needs more optimization.
5 159 0.743825044322 Henry Cohn, 2025.
5 160 0.744143092099 Henry Cohn, 2025.
5 161 0.747768123526 Henry Cohn, 2025.
5 162 0.748843925322 Henry Cohn, 2025.
5 163 0.750218552457 Henry Cohn, 2025.
5 164 0.750876806783 Henry Cohn, 2025.
5 165 0.752014635865 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
5 166 0.752534073395 Henry Cohn, 2025.
5 167 0.753532673949 Henry Cohn, 2025.
5 168 0.754218675211 Henry Cohn, 2025.
5 169 0.755303939743 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
5 170 0.755993792807 Henry Cohn, 2025.
5 171 0.756639843272 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
5 172 0.757288355849 Henry Cohn, 2025.
5 173 0.758578456997 Henry Cohn, 2026, needs more optimization.
5 174 0.759690412033 Henry Cohn, 2025.
5 175 0.760597483271 Henry Cohn, 2025.
5 176 0.761278064091 Henry Cohn, 2025.
5 177 0.762146522896 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
5 178 0.762707574996 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
5 179 0.763250840235 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
5 180 0.763782659007 Henry Cohn, 2026, needs more optimization.
5 181 0.764383502728 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
5 182 0.764931584025 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
5 183 0.765412714647 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
5 184 0.766071024911 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
5 185 0.766467911185 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
5 186 0.767013593230 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
5 187 0.767582500943 Henry Cohn, 2026, needs more optimization.
5 188 0.768310810081 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
5 189 0.768858890426 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
5 190 0.769180117156 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
5 191 0.769658710744 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
5 192 0.769977051705 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
5 193 0.770603326548 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
5 194 0.771545350448 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
5 195 0.771843697482 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
5 196 0.772686004252 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
5 197 0.773356887560 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
5 198 0.773814208717 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
5 199 0.774581761939 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
5 200 0.775252580389 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
5 201 0.775791056188 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
5 202 0.776506621110 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
5 203 0.777039070171 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
5 204 0.777693255841 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
5 205 0.778206826860 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
5 206 0.778711434346 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
5 207 0.779361491430 Henry Cohn, 2026, needs more optimization.
5 208 0.779864508023 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
5 209 0.780497353055 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
5 210 0.780972884880 Henry Cohn, 2026, needs more optimization.
5 211 0.781577235609 Henry Cohn, 2026, needs more optimization.
5 212 0.782104147835 Henry Cohn, 2026, needs more optimization.
5 213 0.782728089506 Henry Cohn, 2026, needs more optimization.
5 214 0.783192830728 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
5 215 0.783780705881 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
5 216 0.784372066946 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
5 217 0.784896362259 Henry Cohn, 2026, needs more optimization.
5 218 0.785309143586 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
5 219 0.785804798484 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
5 220 0.786139025249 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
5 221 0.786559368648 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
5 222 0.787044138912 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
5 223 0.787515891885 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
5 224 0.788115134678 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
5 225 0.788489879204 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
5 226 0.789051514806 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
5 227 0.789390868273 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
5 228 0.790015123137 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
5 229 0.790532551101 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
5 230 0.790887712056 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
5 231 0.791403820519 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
5 232 0.791801086497 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
5 233 0.792236723534 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
5 234 0.792698632640 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
5 235 0.793372157350 Henry Cohn, 2026, needs more optimization.
5 236 0.793997898780 Henry Cohn, 2026, needs more optimization.
5 237 0.794422977064 Henry Cohn, 2026, needs more optimization.
5 238 0.795014640201 Henry Cohn, 2025.
5 239 0.795425406950 Henry Cohn, 2025.
5 240 0.795938099707 Henry Cohn, 2025.
5 241 0.796065311911 Henry Cohn, 2025.
5 242 0.796357275110 Henry Cohn, 2026, needs more optimization.
5 243 0.796601631484 Henry Cohn, 2026, needs more optimization.
5 244 0.796898445762 Henry Cohn, 2026, needs more optimization.
5 245 0.797264978189 Henry Cohn, 2026, needs more optimization.
5 246 0.797740685154 Henry Cohn, 2026, needs more optimization.
5 247 0.797961068192 Henry Cohn, 2026, needs more optimization.
5 248 0.798549025930 Henry Cohn, 2026, needs more optimization.
5 249 0.798774889917 Henry Cohn, 2026, needs more optimization.
5 250 0.798942711861 Henry Cohn, 2026, needs more optimization.
5 251 0.799360589750 Henry Cohn, 2026, needs more optimization.
5 252 0.799655743307 Henry Cohn, 2026, needs more optimization.
5 253 0.800146780510 Henry Cohn, 2026, needs more optimization.
5 254 0.800361565067 Henry Cohn, 2026, needs more optimization.
5 255 0.800622899209 Henry Cohn, 2026, needs more optimization.
5 256 0.801104406643 Henry Cohn, 2026, needs more optimization.
5 257 0.801507262095 Henry Cohn, 2026, needs more optimization.
5 258 0.801975757066 Henry Cohn, 2026, needs more optimization.
5 259 0.802392535257 Henry Cohn, 2026, needs more optimization.
5 260 0.802825045012 Henry Cohn, 2026, needs more optimization.
5 261 0.803199820448 Henry Cohn, 2026, needs more optimization.
5 262 0.803528360555 Henry Cohn, 2026, needs more optimization.
5 263 0.803880217748 Henry Cohn, 2026, needs more optimization.
5 264 0.804081182594 Henry Cohn, 2026, needs more optimization.
5 265 0.804461873167 Henry Cohn, 2026, needs more optimization.
5 266 0.804570277310 Henry Cohn, 2026, needs more optimization.
5 267 0.804872949246 Henry Cohn, 2026, needs more optimization.
5 268 0.805063737167 Henry Cohn, 2026, needs more optimization.
5 269 0.805323879173 Henry Cohn, 2026, needs more optimization.
5 270 0.805497289899 Henry Cohn, 2026, needs more optimization.
5 271 0.805737892270 Henry Cohn, 2026, needs more optimization.
5 272 0.805999314314 Henry Cohn, 2026, needs more optimization.
5 273 0.806034506816 Henry Cohn, 2026, needs more optimization.
5 274 0.806099575012 Henry Cohn, 2026, needs more optimization.
5 275 0.806247499196 Henry Cohn, 2026, needs more optimization.
5 276 0.806327563861 Henry Cohn, 2026, needs more optimization.
5 277 0.806496995009 Henry Cohn, 2026, needs more optimization.
5 278 0.806697926439 Henry Cohn, 2026, needs more optimization.
5 279 0.806779417294 Henry Cohn, 2026, needs more optimization.
5 280 0.807055737375 Henry Cohn, 2026, needs more optimization.
5 281 0.807116873412 Henry Cohn, 2026, needs more optimization.
5 282 0.807160196460 Henry Cohn, 2026, needs more optimization.
5 283 0.807741790346 Henry Cohn, 2026, needs more optimization.
5 284 0.808229711311 Henry Cohn, 2026, needs more optimization.
5 285 0.808652880685 Henry Cohn, 2026, needs more optimization.
5 286 0.809185175075 Henry Cohn, 2026, needs more optimization.
5 287 0.809590215780 Henry Cohn, 2026, needs more optimization.
5 288 0.810241325830 Henry Cohn, 2026, needs more optimization.
5 289 0.810467358660 Henry Cohn, 2026, needs more optimization.
5 290 0.811081555913 Henry Cohn, 2026, needs more optimization.
5 291 0.811567080954 Henry Cohn, 2026, needs more optimization.
5 292 0.812208837819 Henry Cohn, 2026, needs more optimization.
5 293 0.812702082856 Henry Cohn, 2026, needs more optimization.
5 294 0.813139769562 Henry Cohn, 2026, needs more optimization.
5 295 0.813586354352 Henry Cohn, 2026, needs more optimization.
5 296 0.813997556325 Henry Cohn, 2026, needs more optimization.
5 297 0.814424999584 Henry Cohn, 2026, needs more optimization.
5 298 0.815067997631 Henry Cohn, 2026, needs more optimization.
5 299 0.815433700290 Henry Cohn, 2026, needs more optimization.
5 300 0.815847945049 Henry Cohn, 2026, needs more optimization.
5 301 0.816404044325 Henry Cohn, 2026, needs more optimization.
5 302 0.817000628229 Henry Cohn, 2026, needs more optimization.
5 303 0.817467399235 Henry Cohn, 2026, needs more optimization.
5 304 0.817785714689 Henry Cohn, 2026, needs more optimization.
5 305 0.818194019506 Henry Cohn, 2026, needs more optimization.
5 306 0.818530939462 Henry Cohn, 2026, needs more optimization.
5 307 0.818934851712 Henry Cohn, 2026, needs more optimization.
5 308 0.819271321405 Henry Cohn, 2026, needs more optimization.
5 309 0.819565479957 Henry Cohn, 2026, needs more optimization.
5 310 0.819748110540 Henry Cohn, 2026, needs more optimization.
5 311 0.819765316449 Henry Cohn, 2026, needs more optimization.
5 312 0.819813710039 Henry Cohn, 2026, needs more optimization.
5 313 0.819873570321 Henry Cohn, 2026, needs more optimization.
5 314 0.819882211053 Henry Cohn, 2026, needs more optimization.
5 315 0.819896863509 Henry Cohn, 2026, needs more optimization.
5 316 0.819948818516 Henry Cohn, 2026, needs more optimization.
5 317 0.820204250461 Henry Cohn, 2026, needs more optimization.
5 318 0.820654852438 Henry Cohn, 2026, needs more optimization.
5 319 0.820661955221 Henry Cohn, 2026, needs more optimization.
5 320 0.820677046620 Henry Cohn, 2026, needs more optimization.
5 321 0.820938627112 Henry Cohn, 2026, needs more optimization.
5 322 0.821203295795 Henry Cohn, 2026, needs more optimization.
5 323 0.821646558865 Henry Cohn, 2026, needs more optimization.
5 324 0.822153055262 Henry Cohn, 2026, needs more optimization.
5 325 0.822382085802 Henry Cohn, 2026, needs more optimization.
5 326 0.822986247537 Henry Cohn, 2026, needs more optimization.
5 327 0.823129093709 Henry Cohn, 2026, needs more optimization.
5 328 0.823345347812 Henry Cohn, 2026, needs more optimization.
5 329 0.823604364966 Henry Cohn, 2026, needs more optimization.
5 330 0.823733029802 Henry Cohn, 2026, needs more optimization.
5 331 0.823956961350 Henry Cohn, 2026, needs more optimization.
5 332 0.824259692949 Henry Cohn, 2026, needs more optimization.
5 333 0.824462498614 Henry Cohn, 2026, needs more optimization.
5 334 0.824959302712 Henry Cohn, 2026, needs more optimization.
5 335 0.825216772441 Henry Cohn, 2026, needs more optimization.
5 336 0.825245541668 Henry Cohn, 2026, needs more optimization.
5 337 0.825621439673 Henry Cohn, 2026, needs more optimization.
5 338 0.826033000851 Henry Cohn, 2026, needs more optimization.
5 339 0.826186125719 Henry Cohn, 2026, needs more optimization.
5 340 0.826612099133 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
5 341 0.827020672419 Henry Cohn, 2026, needs more optimization.
5 342 0.827285586110 Henry Cohn, 2026, needs more optimization.
5 343 0.827468005343 Henry Cohn, 2026, needs more optimization.
5 344 0.827698286916 Henry Cohn, 2026, needs more optimization.
5 345 0.827998189114 Henry Cohn, 2026, needs more optimization.
5 346 0.828228758265 Henry Cohn, 2026, needs more optimization.
5 347 0.828522871637 Henry Cohn, 2026, needs more optimization.
5 348 0.828641460249 Henry Cohn, 2026, needs more optimization.
5 349 0.828829375108 Henry Cohn, 2026, needs more optimization.
5 350 0.829094197400 Henry Cohn, 2026, needs more optimization.
5 351 0.829588104704 Henry Cohn, 2026, needs more optimization.
5 352 0.830094624139 Henry Cohn, 2026, needs more optimization.
5 353 0.830243179811 Henry Cohn, 2026, needs more optimization.
5 354 0.830490623713 Henry Cohn, 2026, needs more optimization.
5 355 0.830838425397 Henry Cohn, 2026, needs more optimization.
5 356 0.831105524214 Henry Cohn, 2026, needs more optimization.
5 357 0.831422779809 Henry Cohn, 2026, needs more optimization.
5 358 0.831857412500 Henry Cohn, 2026, needs more optimization.
5 359 0.831980432967 Henry Cohn, 2026, needs more optimization.
5 360 0.832227083673 Henry Cohn, 2026, needs more optimization.
5 361 0.832554394585 Henry Cohn, 2026, needs more optimization.
5 362 0.832968324138 Henry Cohn, 2026, needs more optimization.
5 363 0.833310585883 Henry Cohn, 2026, needs more optimization.
5 364 0.833567660034 Henry Cohn, 2026, needs more optimization.
5 365 0.833833326546 Henry Cohn, 2026, needs more optimization.
5 366 0.833945786325 Henry Cohn, 2026, needs more optimization.
5 367 0.834333532495 Henry Cohn, 2026, needs more optimization.
5 368 0.834498641447 Henry Cohn, 2026, needs more optimization.
5 369 0.835029796106 Henry Cohn, 2026, needs more optimization.
5 370 0.835194566500 Henry Cohn, 2026, needs more optimization.
5 371 0.835265822758 Henry Cohn, 2026, needs more optimization.
5 372 0.835715199755 Henry Cohn, 2026, needs more optimization.
5 373 0.835839469037 Henry Cohn, 2026, needs more optimization.
5 374 0.836250821008 Henry Cohn, 2026, needs more optimization.
5 375 0.836438411222 Henry Cohn, 2026, needs more optimization.
5 376 0.836870378889 Henry Cohn, 2026, needs more optimization.
5 377 0.837241095833 Henry Cohn, 2026, needs more optimization.
5 378 0.837290772525 Henry Cohn, 2026, needs more optimization.
5 379 0.837503793563 Henry Cohn, 2026, needs more optimization.
5 380 0.837634838538 Henry Cohn, 2026, needs more optimization.
5 381 0.838342651937 Henry Cohn, 2026, needs more optimization.
5 382 0.838645238996 Henry Cohn, 2026, needs more optimization.
5 383 0.838819074272 Henry Cohn, 2026, needs more optimization.
5 384 0.839041535672 Henry Cohn, 2026, needs more optimization.
5 385 0.839334048467 Henry Cohn, 2026, needs more optimization.
5 386 0.839436622765 Henry Cohn, 2026, needs more optimization.
5 387 0.839745660723 Henry Cohn, 2026, needs more optimization.
5 388 0.839882872536 Henry Cohn, 2026, needs more optimization.
5 389 0.840101744876 Henry Cohn, 2026, needs more optimization.
5 390 0.840409883682 Henry Cohn, 2026, needs more optimization.
5 391 0.840653398916 Henry Cohn, 2026, needs more optimization.
5 392 0.840781839903 Henry Cohn, 2026, needs more optimization.
5 393 0.841199877309 Henry Cohn, 2026, needs more optimization.
5 394 0.841350742422 Henry Cohn, 2026, needs more optimization.
5 395 0.841405005255 Henry Cohn, 2026, needs more optimization.
5 396 0.841691388451 Henry Cohn, 2026, needs more optimization.
5 397 0.841775049045 Henry Cohn, 2026, needs more optimization.
5 398 0.841989761948 Henry Cohn, 2026, needs more optimization.
5 399 0.842166314677 Henry Cohn, 2026, needs more optimization.
5 400 0.842486928652 Henry Cohn, 2026, needs more optimization.
5 401 0.842721650182 Henry Cohn, 2026, needs more optimization.
5 402 0.842843985854 Henry Cohn, 2026, needs more optimization.
5 403 0.842955674639 Henry Cohn, 2026, needs more optimization.
5 404 0.843113970123 Henry Cohn, 2026, needs more optimization.
5 405 0.843307431720 Henry Cohn, 2026, needs more optimization.
5 406 0.843603205683 Henry Cohn, 2026, needs more optimization.
5 407 0.843759018076 Henry Cohn, 2026, needs more optimization.
5 408 0.843898313457 Henry Cohn, 2026, needs more optimization.
5 409 0.843944117687 Henry Cohn, 2026, needs more optimization.
5 410 0.844092013171 Henry Cohn, 2026, needs more optimization.
5 411 0.844384326319 Henry Cohn, 2026, needs more optimization.
5 412 0.844512773440 Henry Cohn, 2026, needs more optimization.
5 413 0.844804885963 Henry Cohn, 2026, needs more optimization.
5 414 0.844818390866 Henry Cohn, 2026, needs more optimization.
5 415 0.845182359228 Henry Cohn, 2026, needs more optimization.
5 416 0.845414857191 Henry Cohn, 2026, needs more optimization.
5 417 0.845502742662 Henry Cohn, 2026, needs more optimization.
5 418 0.845700492726 Henry Cohn, 2026, needs more optimization.
5 419 0.845785037012 Henry Cohn, 2026, needs more optimization.
5 420 0.845954019216 Henry Cohn, 2026, needs more optimization.
5 421 0.846095965144 Henry Cohn, 2026, needs more optimization.
5 422 0.846394176275 Henry Cohn, 2026, needs more optimization.
5 423 0.846451463553 Henry Cohn, 2026, needs more optimization.
5 424 0.846737416042 Henry Cohn, 2026, needs more optimization.
5 425 0.846953828024 Henry Cohn, 2026, needs more optimization.
5 426 0.847133702805 Henry Cohn, 2026, needs more optimization.
5 427 0.847324575820 Henry Cohn, 2026, needs more optimization.
5 428 0.847527900538 Henry Cohn, 2026, needs more optimization.
5 429 0.847673005702 Henry Cohn, 2026, needs more optimization.
5 430 0.847921905944 Henry Cohn, 2026, needs more optimization.
5 431 0.848159382486 Henry Cohn, 2026, needs more optimization.
5 432 0.848172505170 Henry Cohn, 2026, needs more optimization.
5 433 0.848465703664 Henry Cohn, 2026, needs more optimization.
5 434 0.848685346154 Henry Cohn, 2026, needs more optimization.
5 435 0.848869517996 Henry Cohn, 2026, needs more optimization.
5 436 0.848969937914 Henry Cohn, 2026, needs more optimization.
5 437 0.849134024172 Henry Cohn, 2026, needs more optimization.
5 438 0.849416287869 Henry Cohn, 2026, needs more optimization.
5 439 0.849619803394 Henry Cohn, 2026, needs more optimization.
5 440 0.849658377768 Henry Cohn, 2026, needs more optimization.
5 441 0.849850955353 Henry Cohn, 2026, needs more optimization.
5 442 0.849965017491 Henry Cohn, 2026, needs more optimization.
5 443 0.850121451511 Henry Cohn, 2026, needs more optimization.
5 444 0.850398707640 Henry Cohn, 2026, needs more optimization.
5 445 0.850633592900 Henry Cohn, 2026, needs more optimization.
5 446 0.850843076587 Henry Cohn, 2026, needs more optimization.
5 447 0.850997319525 Henry Cohn, 2026, needs more optimization.
5 448 0.851072892540 Henry Cohn, 2026, needs more optimization.
5 449 0.851136594878 Henry Cohn, 2026, needs more optimization.
5 450 0.851508210244 Henry Cohn, 2026, needs more optimization.
5 451 0.851708515687 Henry Cohn, 2026, needs more optimization.
5 452 0.851797628155 Henry Cohn, 2026, needs more optimization.
5 453 0.851809135356 Henry Cohn, 2026, needs more optimization.
5 454 0.852030004551 Henry Cohn, 2026, needs more optimization.
5 455 0.852309415242 Henry Cohn, 2026, needs more optimization.
5 456 0.852370436069 Henry Cohn, 2026, needs more optimization.
5 457 0.852574363575 Henry Cohn, 2026, needs more optimization.
5 458 0.852737519380 Henry Cohn, 2026, needs more optimization.
5 459 0.852813820235 Henry Cohn, 2026, needs more optimization.
5 460 0.853035239655 Henry Cohn, 2026, needs more optimization.
5 461 0.853250800827 Henry Cohn, 2026, needs more optimization.
5 462 0.853452247297 Henry Cohn, 2026, needs more optimization.
5 463 0.853536329123 Henry Cohn, 2026, needs more optimization.
5 464 0.853626004225 Henry Cohn, 2026, needs more optimization.
5 465 0.853853846230 Henry Cohn, 2026, needs more optimization.
5 466 0.854012762433 Henry Cohn, 2026, needs more optimization.
5 467 0.854070932073 Henry Cohn, 2026, needs more optimization.
5 468 0.854359590981 Henry Cohn, 2026, needs more optimization.
5 469 0.854473913815 Henry Cohn, 2026, needs more optimization.
5 470 0.854639232912 Henry Cohn, 2026, needs more optimization.
5 471 0.854694670864 Henry Cohn, 2026, needs more optimization.
5 472 0.854786207555 Henry Cohn, 2026, needs more optimization.
5 473 0.854970814638 Henry Cohn, 2026, needs more optimization.
5 474 0.855266799970 Henry Cohn, 2026, needs more optimization.
5 475 0.855291746173 Henry Cohn, 2026, needs more optimization.
5 476 0.855431104944 Henry Cohn, 2026, needs more optimization.
5 477 0.855636044252 Henry Cohn, 2026, needs more optimization.
5 478 0.855799085152 Henry Cohn, 2026, needs more optimization.
5 479 0.855908330312 Henry Cohn, 2026, needs more optimization.
5 480 0.856091361478 Henry Cohn, 2026, needs more optimization.
5 481 0.856261643777 Henry Cohn, 2026, needs more optimization.
5 482 0.856446289047 Henry Cohn, 2026, needs more optimization.
5 483 0.856663277713 Henry Cohn, 2026, needs more optimization.
5 484 0.856699846839 Henry Cohn, 2026, needs more optimization.
5 485 0.856722158023 Henry Cohn, 2026, needs more optimization.
5 486 0.856883833912 Henry Cohn, 2026, needs more optimization.
5 487 0.857088136661 Henry Cohn, 2026, needs more optimization.
5 488 0.857248448220 Henry Cohn, 2026, needs more optimization.
5 489 0.857360976818 Henry Cohn, 2026, needs more optimization.
5 490 0.857427559011 Henry Cohn, 2026, needs more optimization.
5 491 0.857603266625 Henry Cohn, 2026, needs more optimization.
5 492 0.857832941341 Henry Cohn, 2026, needs more optimization.
5 493 0.857880114548 Henry Cohn, 2026, needs more optimization.
5 494 0.857958770928 Henry Cohn, 2026, needs more optimization.
5 495 0.858156941815 Henry Cohn, 2026, needs more optimization.
5 496 0.858495831186 Henry Cohn, 2026, needs more optimization.
5 497 0.858636315714 Henry Cohn, 2026, needs more optimization.
5 498 0.858740147710 Henry Cohn, 2026, needs more optimization.
5 499 0.858852017683 Henry Cohn, 2026, needs more optimization.
5 500 0.859113792366 Henry Cohn, 2026, needs more optimization.
5 501 0.859270658587 Henry Cohn, 2026, needs more optimization.
5 502 0.859506675580 Henry Cohn, 2026, needs more optimization.
5 503 0.859513109838 Henry Cohn, 2026, needs more optimization.
5 504 0.859622067767 Henry Cohn, 2026, needs more optimization.
5 505 0.859743295253 Henry Cohn, 2026, needs more optimization.
5 506 0.859866426789 Henry Cohn, 2026, needs more optimization.
5 507 0.860047380502 Henry Cohn, 2026, needs more optimization.
5 508 0.860120641541 Henry Cohn, 2026, needs more optimization.
5 509 0.860259706698 Henry Cohn, 2026, needs more optimization.
5 510 0.860468121401 Henry Cohn, 2026, needs more optimization.
5 511 0.860636956296 Henry Cohn, 2026, needs more optimization.
5 512 0.860673886892 Henry Cohn, 2026, needs more optimization.
5 513 0.860737065673 Henry Cohn, 2026, needs more optimization.
5 514 0.860855589807 Henry Cohn, 2026, needs more optimization.
5 515 0.860999057133 Henry Cohn, 2026, needs more optimization.
5 516 0.861222460872 Henry Cohn, 2026, needs more optimization.
5 517 0.861327460479 Henry Cohn, 2026, needs more optimization.
5 518 0.861466572643 Henry Cohn, 2026, needs more optimization.
5 519 0.861608771353 Henry Cohn, 2026, needs more optimization.
5 520 0.861723548746 Henry Cohn, 2026, needs more optimization.
5 521 0.861738716105 Henry Cohn, 2026, needs more optimization.
5 522 0.861956001249 Henry Cohn, 2026, needs more optimization.
5 523 0.862167868780 Henry Cohn, 2026, needs more optimization.
5 524 0.862240511012 Henry Cohn, 2026, needs more optimization.
5 525 0.862461051856 Henry Cohn, 2026, needs more optimization.
5 526 0.862648821814 Henry Cohn, 2026, needs more optimization.
5 527 0.862658333486 Henry Cohn, 2026, needs more optimization.
5 528 0.862757704068 Henry Cohn, 2026, needs more optimization.
5 529 0.862969097844 Henry Cohn, 2026, needs more optimization.
5 530 0.863033047305 Henry Cohn, 2026, needs more optimization.
5 531 0.863195187887 Henry Cohn, 2026, needs more optimization.
5 532 0.863294709382 Henry Cohn, 2026, needs more optimization.
5 533 0.863511391071 Henry Cohn, 2026, needs more optimization.
5 534 0.863651384996 Henry Cohn, 2026, needs more optimization.
5 535 0.863750784320 Henry Cohn, 2026, needs more optimization.
5 536 0.863914564022 Henry Cohn, 2026, needs more optimization.
5 537 0.863992967024 Henry Cohn, 2026, needs more optimization.
5 538 0.864134034140 Henry Cohn, 2026, needs more optimization.
5 539 0.864268157062 Henry Cohn, 2026, needs more optimization.
5 540 0.864339906405 Henry Cohn, 2026, needs more optimization.
5 541 0.864607029568 Henry Cohn, 2026, needs more optimization.
5 542 0.864719040204 Henry Cohn, 2026, needs more optimization.
5 543 0.864791202577 Henry Cohn, 2026, needs more optimization.
5 544 0.864935120574 Henry Cohn, 2026, needs more optimization.
5 545 0.865014308603 Henry Cohn, 2026, needs more optimization.
5 546 0.865110927487 Henry Cohn, 2026, needs more optimization.
5 547 0.865276087560 Henry Cohn, 2026, needs more optimization.
5 548 0.865413154275 Henry Cohn, 2026, needs more optimization.
5 549 0.865492385935 Henry Cohn, 2026, needs more optimization.
5 550 0.865542373006 Henry Cohn, 2026, needs more optimization.
5 551 0.865756432444 Henry Cohn, 2026, needs more optimization.
5 552 0.865803881137 Henry Cohn, 2026, needs more optimization.
5 553 0.865974319346 Henry Cohn, 2026, needs more optimization.
5 554 0.866165810142 Henry Cohn, 2026, needs more optimization.
5 555 0.866199293079 Henry Cohn, 2026, needs more optimization.
5 556 0.866233484159 Henry Cohn, 2026, needs more optimization.
5 557 0.866439788630 Henry Cohn, 2026, needs more optimization.
5 558 0.866540264809 Henry Cohn, 2026, needs more optimization.
5 559 0.866794107397 Henry Cohn, 2026, needs more optimization.
5 560 0.867009559009 Henry Cohn, 2026, needs more optimization.
5 561 0.867015298355 Henry Cohn, 2026, needs more optimization.
5 562 0.867287334462 Henry Cohn, 2026, needs more optimization.
5 563 0.867387516743 Henry Cohn, 2026, needs more optimization.
5 564 0.867441564403 Henry Cohn, 2026, needs more optimization.
5 565 0.867443080337 Henry Cohn, 2026, needs more optimization.
5 566 0.867567423383 Henry Cohn, 2026, needs more optimization.
5 567 0.867771199891 Henry Cohn, 2026, needs more optimization.
5 568 0.867869608757 Henry Cohn, 2026, needs more optimization.
5 569 0.867958382846 Henry Cohn, 2026, needs more optimization.
5 570 0.868116110895 Henry Cohn, 2026, needs more optimization.
5 571 0.868294301180 Henry Cohn, 2026, needs more optimization.
5 572 0.868370381611 Henry Cohn, 2026, needs more optimization.
5 573 0.868451056584 Henry Cohn, 2026, needs more optimization.
5 574 0.868666791316 Henry Cohn, 2026, needs more optimization.
5 575 0.868669185272 Henry Cohn, 2026, needs more optimization.
5 576 0.868800872127 Henry Cohn, 2026, needs more optimization.
5 577 0.868901734456 Henry Cohn, 2026, needs more optimization.
5 578 0.868964149469 Henry Cohn, 2026, needs more optimization.
5 579 0.869108272730 Henry Cohn, 2026, needs more optimization.
5 580 0.869303939159 Henry Cohn, 2026, needs more optimization.
5 581 0.869444873482 Henry Cohn, 2026, needs more optimization.
5 582 0.869504322759 Henry Cohn, 2026, needs more optimization.
5 583 0.869619311507 Henry Cohn, 2026, needs more optimization.
5 584 0.869694163816 Henry Cohn, 2026, needs more optimization.
5 585 0.869882930852 Henry Cohn, 2026, needs more optimization.
5 586 0.870012441905 Henry Cohn, 2026, needs more optimization.
5 587 0.870087390645 Henry Cohn, 2026, needs more optimization.
5 588 0.870089237104 Henry Cohn, 2026, needs more optimization.
5 589 0.870174572273 Henry Cohn, 2026, needs more optimization.
5 590 0.870344360141 Henry Cohn, 2026, needs more optimization.
5 591 0.870372210675 Henry Cohn, 2026, needs more optimization.
5 592 0.870421093997 Henry Cohn, 2026, needs more optimization.
5 593 0.870576290268 Henry Cohn, 2026, needs more optimization.
5 594 0.870725741504 Henry Cohn, 2026, needs more optimization.
5 595 0.870811006656 Henry Cohn, 2026, needs more optimization.
5 596 0.870901167359 Henry Cohn, 2026, needs more optimization.
5 597 0.871007990849 Henry Cohn, 2026, needs more optimization.
5 598 0.871204563133 Henry Cohn, 2026, needs more optimization.
5 599 0.871263185671 Henry Cohn, 2026, needs more optimization.
5 600 0.871357840641 Henry Cohn, 2026, needs more optimization.
5 601 0.871564015322 Henry Cohn, 2026, needs more optimization.
5 602 0.871570952256 Henry Cohn, 2026, needs more optimization.
5 603 0.871657740933 Henry Cohn, 2026, needs more optimization.
5 604 0.871749566934 Henry Cohn, 2026, needs more optimization.
5 605 0.871760304053 Henry Cohn, 2026, needs more optimization.
5 606 0.871839378886 Henry Cohn, 2026, needs more optimization.
5 607 0.871971878702 Henry Cohn, 2026, needs more optimization.
5 608 0.872051497455 Henry Cohn, 2026, needs more optimization.
5 609 0.872237072303 Henry Cohn, 2026, needs more optimization.
5 610 0.872324987498 Henry Cohn, 2026, needs more optimization.
5 611 0.872401388126 Henry Cohn, 2026, needs more optimization.
5 612 0.872538756674 Henry Cohn, 2026, needs more optimization.
5 613 0.872628910734 Henry Cohn, 2026, needs more optimization.
5 614 0.872796229134 Henry Cohn, 2026, needs more optimization.
5 615 0.872874450733 Henry Cohn, 2026, needs more optimization.
5 616 0.873038824110 Henry Cohn, 2026, needs more optimization.
5 617 0.873150762149 Henry Cohn, 2026, needs more optimization.
5 618 0.873298620656 Henry Cohn, 2026, needs more optimization.
5 619 0.873410371837 Henry Cohn, 2026, needs more optimization.
5 620 0.873492093314 Henry Cohn, 2026, needs more optimization.
5 621 0.873597877607 Henry Cohn, 2026, needs more optimization.
5 622 0.873688364178 Henry Cohn, 2026, needs more optimization.
5 623 0.873776310632 Henry Cohn, 2026, needs more optimization.
5 624 0.873922917740 Henry Cohn, 2026, needs more optimization.
5 625 0.874065819161 Henry Cohn, 2026, needs more optimization.
5 626 0.874128817035 Henry Cohn, 2026, needs more optimization.
5 627 0.874158249692 Henry Cohn, 2026, needs more optimization.
5 628 0.874259146941 Henry Cohn, 2026, needs more optimization.
5 629 0.874405130686 Henry Cohn, 2026, needs more optimization.
5 630 0.874562936645 Henry Cohn, 2026, needs more optimization.
5 631 0.874614017711 Henry Cohn, 2026, needs more optimization.
5 632 0.874756358765 Henry Cohn, 2026, needs more optimization.
5 633 0.874890832233 Henry Cohn, 2026, needs more optimization.
5 634 0.874980276351 Henry Cohn, 2026, needs more optimization.
5 635 0.875107531071 Henry Cohn, 2026, needs more optimization.
5 636 0.875214858697 Henry Cohn, 2026, needs more optimization.
5 637 0.875295414514 Henry Cohn, 2026, needs more optimization.
5 638 0.875321481654 Henry Cohn, 2026, needs more optimization.
5 639 0.875385736491 Henry Cohn, 2026, needs more optimization.
5 640 0.875568864324 Henry Cohn, 2026, needs more optimization.
5 641 0.875583936234 Henry Cohn, 2026, needs more optimization.
5 642 0.875648194236 Henry Cohn, 2026, needs more optimization.
5 643 0.875768584431 Henry Cohn, 2026, needs more optimization.
5 644 0.875772538255 Henry Cohn, 2026, needs more optimization.
5 645 0.876024665253 Henry Cohn, 2026, needs more optimization.
5 646 0.876098426814 Henry Cohn, 2026, needs more optimization.
5 647 0.876268685546 Henry Cohn, 2026, needs more optimization.
5 648 0.876310735352 Henry Cohn, 2026, needs more optimization.
5 649 0.876432021890 Henry Cohn, 2026, needs more optimization.
5 650 0.876493124963 Henry Cohn, 2026, needs more optimization.
5 651 0.876592562186 Henry Cohn, 2026, needs more optimization.
5 652 0.876638892868 Henry Cohn, 2026, needs more optimization.
5 653 0.876675935625 Henry Cohn, 2026, needs more optimization.
5 654 0.876775581419 Henry Cohn, 2026, needs more optimization.
5 655 0.876906999525 Henry Cohn, 2026, needs more optimization.
5 656 0.876991539620 Henry Cohn, 2026, needs more optimization.
5 657 0.877133985243 Henry Cohn, 2026, needs more optimization.
5 658 0.877257146443 Henry Cohn, 2026, needs more optimization.
5 659 0.877332150868 Henry Cohn, 2026, needs more optimization.
5 660 0.877435126829 Henry Cohn, 2026, needs more optimization.
5 661 0.877449204378 Henry Cohn, 2026, needs more optimization.
5 662 0.877545058549 Henry Cohn, 2026, needs more optimization.
5 663 0.877640466725 Henry Cohn, 2026, needs more optimization.
5 664 0.877775659839 Henry Cohn, 2026, needs more optimization.
5 665 0.877781201301 Henry Cohn, 2026, needs more optimization.
5 666 0.877864123125 Henry Cohn, 2026, needs more optimization.
5 667 0.877924680748 Henry Cohn, 2026, needs more optimization.
5 668 0.877994271216 Henry Cohn, 2026, needs more optimization.
5 669 0.878174452533 Henry Cohn, 2026, needs more optimization.
5 670 0.878186914222 Henry Cohn, 2026, needs more optimization.
5 671 0.878368862862 Henry Cohn, 2026, needs more optimization.
5 672 0.878443281857 Henry Cohn, 2026, needs more optimization.
5 673 0.878534099642 Henry Cohn, 2026, needs more optimization.
5 674 0.878648219049 Henry Cohn, 2026, needs more optimization.
5 675 0.878671865592 Henry Cohn, 2026, needs more optimization.
5 676 0.878772517655 Henry Cohn, 2026, needs more optimization.
5 677 0.878901191881 Henry Cohn, 2026, needs more optimization.
5 678 0.879037609126 Henry Cohn, 2026, needs more optimization.
5 679 0.879081140773 Henry Cohn, 2026, needs more optimization.
5 680 0.879121363288 Henry Cohn, 2026, needs more optimization.
5 681 0.879261113099 Henry Cohn, 2026, needs more optimization.
5 682 0.879349432604 Henry Cohn, 2026, needs more optimization.
5 683 0.879413658928 Henry Cohn, 2026, needs more optimization.
5 684 0.879531314024 Henry Cohn, 2026, needs more optimization.
5 685 0.879567542316 Henry Cohn, 2026, needs more optimization.
5 686 0.879607043385 Henry Cohn, 2026, needs more optimization.
5 687 0.879826163825 Henry Cohn, 2026, needs more optimization.
5 688 0.879923455125 Henry Cohn, 2026, needs more optimization.
5 689 0.880002007566 Henry Cohn, 2026, needs more optimization.
5 690 0.880053142103 Henry Cohn, 2026, needs more optimization.
5 691 0.880163616416 Henry Cohn, 2026, needs more optimization.
5 692 0.880261588144 Henry Cohn, 2026, needs more optimization.
5 693 0.880323346834 Henry Cohn, 2026, needs more optimization.
5 694 0.880416713946 Henry Cohn, 2026, needs more optimization.
5 695 0.880471524630 Henry Cohn, 2026, needs more optimization.
5 696 0.880547758545 Henry Cohn, 2026, needs more optimization.
5 697 0.880621630536 Henry Cohn, 2026, needs more optimization.
5 698 0.880700251476 Henry Cohn, 2026, needs more optimization.
5 699 0.880810240809 Henry Cohn, 2026, needs more optimization.
5 700 0.880833578702 Henry Cohn, 2026, needs more optimization.
5 701 0.880992769024 Henry Cohn, 2026, needs more optimization.
5 702 0.881068336545 Henry Cohn, 2026, needs more optimization.
5 703 0.881074945298 Henry Cohn, 2026, needs more optimization.
5 704 0.881198499985 Henry Cohn, 2026, needs more optimization.
5 705 0.881228831974 Henry Cohn, 2026, needs more optimization.
5 706 0.881337068637 Henry Cohn, 2026, needs more optimization.
5 707 0.881445238390 Henry Cohn, 2026, needs more optimization.
5 708 0.881597892341 Henry Cohn, 2026, needs more optimization.
5 709 0.881726591333 Henry Cohn, 2026, needs more optimization.
5 710 0.881730058192 Henry Cohn, 2026, needs more optimization.
5 711 0.881787957298 Henry Cohn, 2026, needs more optimization.
5 712 0.881857943027 Henry Cohn, 2026, needs more optimization.
5 713 0.881947794183 Henry Cohn, 2026, needs more optimization.
5 714 0.882026898858 Henry Cohn, 2026, needs more optimization.
5 715 0.882125182368 Henry Cohn, 2026, needs more optimization.
5 716 0.882203768563 Henry Cohn, 2026, needs more optimization.
5 717 0.882308606501 Henry Cohn, 2026, needs more optimization.
5 718 0.882423200591 Henry Cohn, 2026, needs more optimization.
5 719 0.882439070315 Henry Cohn, 2026, needs more optimization.
5 720 0.882559623196 Henry Cohn, 2026, needs more optimization.
5 721 0.882614598626 Henry Cohn, 2026, needs more optimization.
5 722 0.882717123713 Henry Cohn, 2026, needs more optimization.
5 723 0.882809088468 Henry Cohn, 2026, needs more optimization.
5 724 0.882892187293 Henry Cohn, 2026, needs more optimization.
5 725 0.882970832072 Henry Cohn, 2026, needs more optimization.
5 726 0.883100301240 Henry Cohn, 2026, needs more optimization.
5 727 0.883129795275 Henry Cohn, 2026, needs more optimization.
5 728 0.883248056349 Henry Cohn, 2026, needs more optimization.
5 729 0.883298458774 Henry Cohn, 2026, needs more optimization.
5 730 0.883341789181 Henry Cohn, 2026, needs more optimization.
5 731 0.883429383882 Henry Cohn, 2026, needs more optimization.
5 732 0.883518226266 Henry Cohn, 2026, needs more optimization.
5 733 0.883592767819 Henry Cohn, 2026, needs more optimization.
5 734 0.883680718527 Henry Cohn, 2026, needs more optimization.
5 735 0.883725877896 Henry Cohn, 2026, needs more optimization.
5 736 0.883801917895 Henry Cohn, 2026, needs more optimization.
5 737 0.883864196251 Henry Cohn, 2026, needs more optimization.
5 738 0.883968646140 Henry Cohn, 2026, needs more optimization.
5 739 0.884044157702 Henry Cohn, 2026, needs more optimization.
5 740 0.884126997442 Henry Cohn, 2026, needs more optimization.
5 741 0.884310752205 Henry Cohn, 2026, needs more optimization.
5 742 0.884395851907 Henry Cohn, 2026, needs more optimization.
5 743 0.884509413333 Henry Cohn, 2026, needs more optimization.
5 744 0.884613154581 Henry Cohn, 2026, needs more optimization.
5 745 0.884661292296 Henry Cohn, 2026, needs more optimization.
5 746 0.884751144796 Henry Cohn, 2026, needs more optimization.
5 747 0.884824317638 Henry Cohn, 2026, needs more optimization.
5 748 0.884911852468 Henry Cohn, 2026, needs more optimization.
5 749 0.884967176920 Henry Cohn, 2026, needs more optimization.
5 750 0.885020872585 Henry Cohn, 2026, needs more optimization.
5 751 0.885121977133 Henry Cohn, 2026, needs more optimization.
5 752 0.885182869690 Henry Cohn, 2026, needs more optimization.
5 753 0.885220115807 Henry Cohn, 2026, needs more optimization.
5 754 0.885313789673 Henry Cohn, 2026, needs more optimization.
5 755 0.885361583651 Henry Cohn, 2026, needs more optimization.
5 756 0.885405920690 Henry Cohn, 2026, needs more optimization.
5 757 0.885482311501 Henry Cohn, 2026, needs more optimization.
5 758 0.885579574423 Henry Cohn, 2026, needs more optimization.
5 759 0.885619098377 Henry Cohn, 2026, needs more optimization.
5 760 0.885674207704 Henry Cohn, 2026, needs more optimization.
5 761 0.885792354988 Henry Cohn, 2026, needs more optimization.
5 762 0.885852291781 Henry Cohn, 2026, needs more optimization.
5 763 0.885935010585 Henry Cohn, 2026, needs more optimization.
5 764 0.886055073269 Henry Cohn, 2026, needs more optimization.
5 765 0.886147678316 Henry Cohn, 2026, needs more optimization.
5 766 0.886224626533 Henry Cohn, 2026, needs more optimization.
5 767 0.886257305017 Henry Cohn, 2026, needs more optimization.
5 768 0.886276949978 Henry Cohn, 2026, needs more optimization.
5 769 0.886326447651 Henry Cohn, 2026, needs more optimization.
5 770 0.886396284630 Henry Cohn, 2026, needs more optimization.
5 771 0.886478203163 Henry Cohn, 2026, needs more optimization.
5 772 0.886552860977 Henry Cohn, 2026, needs more optimization.
5 773 0.886629364733 Henry Cohn, 2026, needs more optimization.
5 774 0.886729041790 Henry Cohn, 2026, needs more optimization.
5 775 0.886817030311 Henry Cohn, 2026, needs more optimization.
5 776 0.886926791056 Henry Cohn, 2026, needs more optimization.
5 777 0.886938306580 Henry Cohn, 2026, needs more optimization.
5 778 0.887039286400 Henry Cohn, 2026, needs more optimization.
5 779 0.887106887598 Henry Cohn, 2026, needs more optimization.
5 780 0.887255942191 Henry Cohn, 2026, needs more optimization.
5 781 0.887275270502 Henry Cohn, 2026, needs more optimization.
5 782 0.887277942631 Henry Cohn, 2026, needs more optimization.
5 783 0.887327485987 Henry Cohn, 2026, needs more optimization.
5 784 0.887399638692 Henry Cohn, 2026, needs more optimization.
5 785 0.887468768246 Henry Cohn, 2026, needs more optimization.
5 786 0.887523755388 Henry Cohn, 2026, needs more optimization.
5 787 0.887642165907 Henry Cohn, 2026, needs more optimization.
5 788 0.887720894108 Henry Cohn, 2026, needs more optimization.
5 789 0.887793334680 Henry Cohn, 2026, needs more optimization.
5 790 0.887892160168 Henry Cohn, 2026, needs more optimization.
5 791 0.887897966073 Henry Cohn, 2026, needs more optimization.
5 792 0.887989360711 Henry Cohn, 2026, needs more optimization.
5 793 0.888048429444 Henry Cohn, 2026, needs more optimization.
5 794 0.888128674599 Henry Cohn, 2026, needs more optimization.
5 795 0.888172921456 Henry Cohn, 2026, needs more optimization.
5 796 0.888230019352 Henry Cohn, 2026, needs more optimization.
5 797 0.888306668193 Henry Cohn, 2026, needs more optimization.
5 798 0.888387744022 Henry Cohn, 2026, needs more optimization.
5 799 0.888471300909 Henry Cohn, 2026, needs more optimization.
5 800 0.888518571109 Henry Cohn, 2026, needs more optimization.
5 801 0.888549483214 Henry Cohn, 2026, needs more optimization.
5 802 0.888647925638 Henry Cohn, 2026, needs more optimization.
5 803 0.888778764195 Henry Cohn, 2026, needs more optimization.
5 804 0.888897682449 Henry Cohn, 2026, needs more optimization.
5 805 0.888913820440 Henry Cohn, 2026, needs more optimization.
5 806 0.888950728339 Henry Cohn, 2026, needs more optimization.
5 807 0.889002753504 Henry Cohn, 2026, needs more optimization.
5 808 0.889098051318 Henry Cohn, 2026, needs more optimization.
5 809 0.889220593589 Henry Cohn, 2026, needs more optimization.
5 810 0.889234419889 Henry Cohn, 2026, needs more optimization.
5 811 0.889369961501 Henry Cohn, 2026, needs more optimization.
5 812 0.889455683318 Henry Cohn, 2026, needs more optimization.
5 813 0.889527722381 Henry Cohn, 2026, needs more optimization.
5 814 0.889657019686 Henry Cohn, 2026, needs more optimization.
5 815 0.889691600578 Henry Cohn, 2026, needs more optimization.
5 816 0.889694338987 Henry Cohn, 2026, needs more optimization.
5 817 0.889711653227 Henry Cohn, 2026, needs more optimization.
5 818 0.889819148023 Henry Cohn, 2026, needs more optimization.
5 819 0.889855766057 Henry Cohn, 2026, needs more optimization.
5 820 0.889878877469 Henry Cohn, 2026, needs more optimization.
5 821 0.889981806798 Henry Cohn, 2026, needs more optimization.
5 822 0.890017549561 Henry Cohn, 2026, needs more optimization.
5 823 0.890104121451 Henry Cohn, 2026, needs more optimization.
5 824 0.890248066616 Henry Cohn, 2026, needs more optimization.
5 825 0.890340043496 Henry Cohn, 2026, needs more optimization.
5 826 0.890340059783 Henry Cohn, 2026, needs more optimization.
5 827 0.890419311351 Henry Cohn, 2026, needs more optimization.
5 828 0.890537753010 Henry Cohn, 2026, needs more optimization.
5 829 0.890543867285 Henry Cohn, 2026, needs more optimization.
5 830 0.890626382802 Henry Cohn, 2026, needs more optimization.
5 831 0.890713052908 Henry Cohn, 2026, needs more optimization.
5 832 0.890713077407 Henry Cohn, 2026, needs more optimization.
5 833 0.890723614037 Henry Cohn, 2026, needs more optimization.
5 834 0.890780278108 Henry Cohn, 2026, needs more optimization.
5 835 0.890867058871 Henry Cohn, 2026, needs more optimization.
5 836 0.891001836358 Henry Cohn, 2026, needs more optimization.
5 837 0.891081749590 Henry Cohn, 2026, needs more optimization.
5 838 0.891157416643 Henry Cohn, 2026, needs more optimization.
5 839 0.891220776808 Henry Cohn, 2026, needs more optimization.
5 840 0.891290256147 Henry Cohn, 2026, needs more optimization.
5 841 0.891365671978 Henry Cohn, 2026, needs more optimization.
5 842 0.891413438679 Henry Cohn, 2026, needs more optimization.
5 843 0.891497073691 Henry Cohn, 2026, needs more optimization.
5 844 0.891523497587 Henry Cohn, 2026, needs more optimization.
5 845 0.891546154925 Henry Cohn, 2026, needs more optimization.
5 846 0.891653729567 Henry Cohn, 2026, needs more optimization.
5 847 0.891720810747 Henry Cohn, 2026, needs more optimization.
5 848 0.891803294249 Henry Cohn, 2026, needs more optimization.
5 849 0.891859481163 Henry Cohn, 2026, needs more optimization.
5 850 0.891897896412 Henry Cohn, 2026, needs more optimization.
5 851 0.891944505485 Henry Cohn, 2026, needs more optimization.
5 852 0.892047280887 Henry Cohn, 2026, needs more optimization.
5 853 0.892101949948 Henry Cohn, 2026, needs more optimization.
5 854 0.892148935669 Henry Cohn, 2026, needs more optimization.
5 855 0.892172117498 Henry Cohn, 2026, needs more optimization.
5 856 0.892353781871 Henry Cohn, 2026, needs more optimization.
5 857 0.892354703888 Henry Cohn, 2026, needs more optimization.
5 858 0.892395435493 Henry Cohn, 2026, needs more optimization.
5 859 0.892503710281 Henry Cohn, 2026, needs more optimization.
5 860 0.892574675572 Henry Cohn, 2026, needs more optimization.
5 861 0.892591538718 Henry Cohn, 2026, needs more optimization.
5 862 0.892625327965 Henry Cohn, 2026, needs more optimization.
5 863 0.892692965051 Henry Cohn, 2026, needs more optimization.
5 864 0.892754849096 Henry Cohn, 2026, needs more optimization.
5 865 0.892870380543 Henry Cohn, 2026, needs more optimization.
5 866 0.892879812468 Henry Cohn, 2026, needs more optimization.
5 867 0.892993852460 Henry Cohn, 2026, needs more optimization.
5 868 0.893077924999 Henry Cohn, 2026, needs more optimization.
5 869 0.893080474119 Henry Cohn, 2026, needs more optimization.
5 870 0.893170138028 Henry Cohn, 2026, needs more optimization.
5 871 0.893249233448 Henry Cohn, 2026, needs more optimization.
5 872 0.893301025663 Henry Cohn, 2026, needs more optimization.
5 873 0.893319229119 Henry Cohn, 2026, needs more optimization.
5 874 0.893377806698 Henry Cohn, 2026, needs more optimization.
5 875 0.893472150758 Henry Cohn, 2026, needs more optimization.
5 876 0.893522011094 Henry Cohn, 2026, needs more optimization.
5 877 0.893612535450 Henry Cohn, 2026, needs more optimization.
5 878 0.893661618050 Henry Cohn, 2026, needs more optimization.
5 879 0.893723100851 Henry Cohn, 2026, needs more optimization.
5 880 0.893796607547 Henry Cohn, 2026, needs more optimization.
5 881 0.893799338944 Henry Cohn, 2026, needs more optimization.
5 882 0.893815342184 Henry Cohn, 2026, needs more optimization.
5 883 0.893944906448 Henry Cohn, 2026, needs more optimization.
5 884 0.894001591891 Henry Cohn, 2026, needs more optimization.
5 885 0.894070272381 Henry Cohn, 2026, needs more optimization.
5 886 0.894123948913 Henry Cohn, 2026, needs more optimization.
5 887 0.894210766752 Henry Cohn, 2026, needs more optimization.
5 888 0.894287884662 Henry Cohn, 2026, needs more optimization.
5 889 0.894298171851 Henry Cohn, 2026, needs more optimization.
5 890 0.894353374476 Henry Cohn, 2026, needs more optimization.
5 891 0.894388349955 Henry Cohn, 2026, needs more optimization.
5 892 0.894525313713 Henry Cohn, 2026, needs more optimization.
5 893 0.894577680072 Henry Cohn, 2026, needs more optimization.
5 894 0.894638659678 Henry Cohn, 2026, needs more optimization.
5 895 0.894640818820 Henry Cohn, 2026, needs more optimization.
5 896 0.894725763426 Henry Cohn, 2026, needs more optimization.
5 897 0.894729430422 Henry Cohn, 2026, needs more optimization.
5 898 0.894815529350 Henry Cohn, 2026, needs more optimization.
5 899 0.894872792436 Henry Cohn, 2026, needs more optimization.
5 900 0.894893321616 Henry Cohn, 2026, needs more optimization.
5 901 0.894966992467 Henry Cohn, 2026, needs more optimization.
5 902 0.895045335244 Henry Cohn, 2026, needs more optimization.
5 903 0.895142798579 Henry Cohn, 2026, needs more optimization.
5 904 0.895209339173 Henry Cohn, 2026, needs more optimization.
5 905 0.895273846277 Henry Cohn, 2026, needs more optimization.
5 906 0.895385295979 Henry Cohn, 2026, needs more optimization.
5 907 0.895387086078 Henry Cohn, 2026, needs more optimization.
5 908 0.895469997493 Henry Cohn, 2026, needs more optimization.
5 909 0.895494358014 Henry Cohn, 2026, needs more optimization.
5 910 0.895554488551 Henry Cohn, 2026, needs more optimization.
5 911 0.895662017054 Henry Cohn, 2026, needs more optimization.
5 912 0.895697151011 Henry Cohn, 2026, needs more optimization.
5 913 0.895773385490 Henry Cohn, 2026, needs more optimization.
5 914 0.895817411528 Henry Cohn, 2026, needs more optimization.
5 915 0.895835930898 Henry Cohn, 2026, needs more optimization.
5 916 0.895926898626 Henry Cohn, 2026, needs more optimization.
5 917 0.895958512608 Henry Cohn, 2026, needs more optimization.
5 918 0.896047065049 Henry Cohn, 2026, needs more optimization.
5 919 0.896056541486 Henry Cohn, 2026, needs more optimization.
5 920 0.896155943347 Henry Cohn, 2026, needs more optimization.
5 921 0.896172509378 Henry Cohn, 2026, needs more optimization.
5 922 0.896266439777 Henry Cohn, 2026, needs more optimization.
5 923 0.896287886483 Henry Cohn, 2026, needs more optimization.
5 924 0.896375773438 Henry Cohn, 2026, needs more optimization.
5 925 0.896392975064 Henry Cohn, 2026, needs more optimization.
5 926 0.896458360832 Henry Cohn, 2026, needs more optimization.
5 927 0.896478747636 Henry Cohn, 2026, needs more optimization.
5 928 0.896559400123 Henry Cohn, 2026, needs more optimization.
5 929 0.896621402869 Henry Cohn, 2026, needs more optimization.
5 930 0.896692811080 Henry Cohn, 2026, needs more optimization.
5 931 0.896764898313 Henry Cohn, 2026, needs more optimization.
5 932 0.896824616291 Henry Cohn, 2026, needs more optimization.
5 933 0.896864926468 Henry Cohn, 2026, needs more optimization.
5 934 0.896922272712 Henry Cohn, 2026, needs more optimization.
5 935 0.896990544561 Henry Cohn, 2026, needs more optimization.
5 936 0.897003889523 Henry Cohn, 2026, needs more optimization.
5 937 0.897072081509 Henry Cohn, 2026, needs more optimization.
5 938 0.897153283648 Henry Cohn, 2026, needs more optimization.
5 939 0.897167680638 Henry Cohn, 2026, needs more optimization.
5 940 0.897210032060 Henry Cohn, 2026, needs more optimization.
5 941 0.897251669147 Henry Cohn, 2026, needs more optimization.
5 942 0.897324527247 Henry Cohn, 2026, needs more optimization.
5 943 0.897426483193 Henry Cohn, 2026, needs more optimization.
5 944 0.897503280626 Henry Cohn, 2026, needs more optimization.
5 945 0.897522795310 Henry Cohn, 2026, needs more optimization.
5 946 0.897574150432 Henry Cohn, 2026, needs more optimization.
5 947 0.897647743656 Henry Cohn, 2026, needs more optimization.
5 948 0.897720425803 Henry Cohn, 2026, needs more optimization.
5 949 0.897796269456 Henry Cohn, 2026, needs more optimization.
5 950 0.897847154951 Henry Cohn, 2026, needs more optimization.
5 951 0.897900865957 Henry Cohn, 2026, needs more optimization.
5 952 0.897949372923 Henry Cohn, 2026, needs more optimization.
5 953 0.897974766168 Henry Cohn, 2026, needs more optimization.
5 954 0.897989970716 Henry Cohn, 2026, needs more optimization.
5 955 0.897993641127 Henry Cohn, 2026, needs more optimization.
5 956 0.898013025834 Henry Cohn, 2026, needs more optimization.
5 957 0.898093123218 Henry Cohn, 2026, needs more optimization.
5 958 0.898195019491 Henry Cohn, 2026, needs more optimization.
5 959 0.898241499165 Henry Cohn, 2026, needs more optimization.
5 960 0.898259297396 Henry Cohn, 2026, needs more optimization.
5 961 0.898350985452 Henry Cohn, 2026, needs more optimization.
5 962 0.898394842288 Henry Cohn, 2026, needs more optimization.
5 963 0.898410557948 Henry Cohn, 2026, needs more optimization.
5 964 0.898493758946 Henry Cohn, 2026, needs more optimization.
5 965 0.898526797930 Henry Cohn, 2026, needs more optimization.
5 966 0.898573023330 Henry Cohn, 2026, needs more optimization.
5 967 0.898582698258 Henry Cohn, 2026, needs more optimization.
5 968 0.898723663322 Henry Cohn, 2026, needs more optimization.
5 969 0.898809144589 Henry Cohn, 2026, needs more optimization.
5 970 0.898829269613 Henry Cohn, 2026, needs more optimization.
5 971 0.898874640864 Henry Cohn, 2026, needs more optimization.
5 972 0.898895667711 Henry Cohn, 2026, needs more optimization.
5 973 0.898933468906 Henry Cohn, 2026, needs more optimization.
5 974 0.899017074128 Henry Cohn, 2026, needs more optimization.
5 975 0.899093980593 Henry Cohn, 2026, needs more optimization.
5 976 0.899120310113 Henry Cohn, 2026, needs more optimization.
5 977 0.899142236103 Henry Cohn, 2026, needs more optimization.
5 978 0.899221282200 Henry Cohn, 2026, needs more optimization.
5 979 0.899224691401 Henry Cohn, 2026, needs more optimization.
5 980 0.899328332110 Henry Cohn, 2026, needs more optimization.
5 981 0.899360737305 Henry Cohn, 2026, needs more optimization.
5 982 0.899422850284 Henry Cohn, 2026, needs more optimization.
5 983 0.899480927491 Henry Cohn, 2026, needs more optimization.
5 984 0.899493849328 Henry Cohn, 2026, needs more optimization.
5 985 0.899617556016 Henry Cohn, 2026, needs more optimization.
5 986 0.899697283207 Henry Cohn, 2026, needs more optimization.
5 987 0.899712797484 Henry Cohn, 2026, needs more optimization.
5 988 0.899770019992 Henry Cohn, 2026, needs more optimization.
5 989 0.899856487483 Henry Cohn, 2026, needs more optimization.
5 990 0.899871367114 Henry Cohn, 2026, needs more optimization.
5 991 0.899894654776 Henry Cohn, 2026, needs more optimization.
5 992 0.899923326375 Henry Cohn, 2026, needs more optimization.
5 993 0.899992749423 Henry Cohn, 2026, needs more optimization.
5 994 0.900048299972 Henry Cohn, 2026, needs more optimization.
5 995 0.900104096617 Henry Cohn, 2026, needs more optimization.
5 996 0.900203356643 Henry Cohn, 2026, needs more optimization.
5 997 0.900241109572 Henry Cohn, 2026, needs more optimization.
5 998 0.900318588116 Henry Cohn, 2026, needs more optimization.
5 999 0.900394008168 Henry Cohn, 2026, needs more optimization.
5 1000 0.900398100792 Henry Cohn, 2026, needs more optimization.
5 1001 0.900454417632 Henry Cohn, 2026, needs more optimization.
5 1002 0.900500776580 Henry Cohn, 2026, needs more optimization.
5 1003 0.900551176128 Henry Cohn, 2026, needs more optimization.
5 1004 0.900558267595 Henry Cohn, 2026, needs more optimization.
5 1005 0.900623181960 Henry Cohn, 2026, needs more optimization.
5 1006 0.900676989707 Henry Cohn, 2026, needs more optimization.
5 1007 0.900684712008 Henry Cohn, 2026, needs more optimization.
5 1008 0.900831216945 Henry Cohn, 2026, needs more optimization.
5 1009 0.900844323757 Henry Cohn, 2026, needs more optimization.
5 1010 0.900906178181 Henry Cohn, 2026, needs more optimization.
5 1011 0.900956376945 Henry Cohn, 2026, needs more optimization.
5 1012 0.900967101604 Henry Cohn, 2026, needs more optimization.
5 1013 0.901008974700 Henry Cohn, 2026, needs more optimization.
5 1014 0.901094864000 Henry Cohn, 2026, needs more optimization.
5 1015 0.901105294288 Henry Cohn, 2026, needs more optimization.
5 1016 0.901109583524 Henry Cohn, 2026, needs more optimization.
5 1017 0.901151869393 Henry Cohn, 2026, needs more optimization.
5 1018 0.901203311911 Henry Cohn, 2026, needs more optimization.
5 1019 0.901292993021 Henry Cohn, 2026, needs more optimization.
5 1020 0.901302755735 Henry Cohn, 2026, needs more optimization.
5 1021 0.901387245381 Henry Cohn, 2026, needs more optimization.
5 1022 0.901434646356 Henry Cohn, 2026, needs more optimization.
5 1023 0.901472132318 Henry Cohn, 2026, needs more optimization.
5 1024 0.901474900590 Henry Cohn, 2026, needs more optimization.
6 13 0.113079752148 P. G. Adams, A numerical approach to Tamme's problem in Euclidean n-space, Master of Science thesis, Oregon State University, 1997, https://hdl.handle.net/1957/33911.
96⁢x3−36⁢x2−6⁢x+1
6 14 0.132490920324 J. Wang, Finding and investigating exact spherical codes, Experiment. Math. 18 (2009), 249–256, https://projecteuclid.org/euclid.em/1259158434.
Minimal polynomial listed in plain text data
6 15 0.144948974279 J. Wang, Finding and investigating exact spherical codes, Experiment. Math. 18 (2009), 249–256, https://projecteuclid.org/euclid.em/1259158434.
20⁢x2+4⁢x−1
6 16 0.171071421043 H. Cohn, Small spherical and projective codes, data set, updated 2024, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
6400⁢x5+960⁢x4−1024⁢x3−32⁢x2+31⁢x−1
6 17 0.183274337024 P. G. Adams, A numerical approach to Tamme's problem in Euclidean n-space, Master of Science thesis, Oregon State University, 1997, https://hdl.handle.net/1957/33911.
400⁢x4+240⁢x3+16⁢x2−8⁢x−1
6 18 0.197812188602 J. Wang, Finding and investigating exact spherical codes, Experiment. Math. 18 (2009), 249–256, https://projecteuclid.org/euclid.em/1259158434.
784⁢x8−280⁢x7−1191⁢x6+120⁢x5+218⁢x4−62⁢x3−31⁢x2+2⁢x+1
6 19 0.200226025892 J. Wang, Finding and investigating exact spherical codes, Experiment. Math. 18 (2009), 249–256, https://projecteuclid.org/euclid.em/1259158434.
6 20 0.214285714286 J. Wang, Finding and investigating exact spherical codes, Experiment. Math. 18 (2009), 249–256, https://projecteuclid.org/euclid.em/1259158434.
14⁢x−3
6 21 0.242852848014 J. Wang, Finding and investigating exact spherical codes, Experiment. Math. 18 (2009), 249–256, https://projecteuclid.org/euclid.em/1259158434.
6 22 0.248865699460 H. Cohn, Small spherical and projective codes, data set, 2022, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
6 23 0.25 J. Wang, Finding and investigating exact spherical codes, Experiment. Math. 18 (2009), 249–256, https://projecteuclid.org/euclid.em/1259158434.
4⁢x−1
6 24 0.25 J. Wang, Finding and investigating exact spherical codes, Experiment. Math. 18 (2009), 249–256, https://projecteuclid.org/euclid.em/1259158434.
4⁢x−1
6 25 0.25 J. Wang, Finding and investigating exact spherical codes, Experiment. Math. 18 (2009), 249–256, https://projecteuclid.org/euclid.em/1259158434.
4⁢x−1
6 26 0.25 J. Wang, Finding and investigating exact spherical codes, Experiment. Math. 18 (2009), 249–256, https://projecteuclid.org/euclid.em/1259158434.
4⁢x−1
6 27* 0.25 T. Gosset, On the regular and semi-regular figures in space of n dimensions, Messenger Math. 29 (1900), 43–48; V. I. Levenšteĭn, On bounds for packings in n-dimensional Euclidean space (Russian), Dokl. Akad. Nauk SSSR 245 (1979), 1299–1303, English translation in Soviet Math. Dokl. 20 (1979), 417–421.
4⁢x−1
6 28 0.3 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
10⁢x−3
6 29 0.327844830882 H. Cohn, Small spherical and projective codes, data set, 2022, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
6 30 0.333157886299 H. Cohn, Small spherical and projective codes, data set, updated 2024, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
6 31 0.333333333334 J. Wang, Finding and investigating exact spherical codes, Experiment. Math. 18 (2009), 249–256, https://projecteuclid.org/euclid.em/1259158434.
3⁢x−1
6 32 0.333333333334 J. H. van Lint and J. J. Seidel, Equilateral point sets in elliptic geometry, Indag. Math. 28 (1966), 335–348, https://research.tue.nl/en/publications/equilateral-point-sets-in-elliptic-geometry.
3⁢x−1
6 33 0.344948974279 J. Wang, Finding and investigating exact spherical codes, Experiment. Math. 18 (2009), 249–256, https://projecteuclid.org/euclid.em/1259158434.
20⁢x2−4⁢x−1
6 34 0.346451336111 J. Wang, Finding and investigating exact spherical codes, Experiment. Math. 18 (2009), 249–256, https://projecteuclid.org/euclid.em/1259158434.
64⁢x5+64⁢x4−76⁢x3+7⁢x2+6⁢x−1
6 35 0.358257569496 J. Wang, Finding and investigating exact spherical codes, Experiment. Math. 18 (2009), 249–256, https://projecteuclid.org/euclid.em/1259158434.
5⁢x2+x−1
6 36 0.358257569496 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
5⁢x2+x−1
6 37 0.366623377687 J. Wang, Finding and investigating exact spherical codes, Experiment. Math. 18 (2009), 249–256, https://projecteuclid.org/euclid.em/1259158434.
64⁢x4+96⁢x3−80⁢x2+16⁢x−1
6 38 0.367688450451 J. Wang, Finding and investigating exact spherical codes, Experiment. Math. 18 (2009), 249–256, https://projecteuclid.org/euclid.em/1259158434.
7424⁢x8+1280⁢x7−3904⁢x6−768⁢x5+448⁢x4+80⁢x3−1
6 39 0.384936289161 J. Wang, Finding and investigating exact spherical codes, Experiment. Math. 18 (2009), 249–256, https://projecteuclid.org/euclid.em/1259158434.
6 40 0.386096677606 J. Wang, Finding and investigating exact spherical codes, Experiment. Math. 18 (2009), 249–256, https://projecteuclid.org/euclid.em/1259158434.
31⁢x4−12⁢x3−14⁢x2+8⁢x−1
6 41 0.389434811673 Henry Cohn, 2023.
6 42 0.390388203203 J. H. Conway, R. H. Hardin, and N. J. A. Sloane, Packing lines, planes, etc.: packings in Grassmannian spaces, Experiment. Math. 5 (1996), 139–159, https://projecteuclid.org/euclid.em/1047565645; T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
4⁢x2+x−1
6 43 0.399773924374 J. Wang, Finding and investigating exact spherical codes, Experiment. Math. 18 (2009), 249–256, https://projecteuclid.org/euclid.em/1259158434.
1024⁢x9−4096⁢x8−1536⁢x7+1024⁢x6+704⁢x5+64⁢x4−96⁢x3−16⁢x2+4⁢x−1
6 44 0.405666616164 Henry Cohn, 2023.
6 45 0.426943864061 Henry Cohn, 2025.
6 46 0.435705030667 Henry Cohn, 2025.
6 47 0.441020734927 A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
6 48 0.443609864234 Henry Cohn, 2025.
6 49 0.446060501890 Henry Cohn, 2023.
6 50 0.446739131277 Henry Cohn, 2023.
58⁢x3−50⁢x2+13⁢x−1
6 51 0.456479386398 Henry Cohn, 2025.
6 52 0.458253528717 Henry Cohn, 2023.
6 53 0.459145031877 Henry Cohn, 2025.
6 54 0.462714285892 Henry Cohn, 2023.
4104⁢x4−216⁢x3−3654⁢x2+1955⁢x−289
6 55 0.472467412878 Henry Cohn, 2024.
6 56 0.475645784548 Henry Cohn, 2023.
33024⁢x6+14848⁢x5−45568⁢x4+5832⁢x3+12257⁢x2−4922⁢x+529
6 57 0.479790821500 Henry Cohn, 2025.
6 58 0.482548584905 Henry Cohn, 2024.
20⁢x2+9⁢x−9
6 59 0.486085706237 A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
6 60 0.486876290376 Henry Cohn, 2025.
6 61 0.491730182082 Henry Cohn, 2025.
6 62 0.495376595904 Henry Cohn, 2023.
6 63 0.498122491823 Henry Cohn, 2023.
6 64 0.498522963739 Henry Cohn, 2025.
6 65 0.499974913357 Henry Cohn, 2025.
6 66 0.499976896430 Henry Cohn, 2026.
6 67 0.499991659867 Henry Cohn, 2026.
6 72 0.5 A. Korkine and G. Zolotareff, Sur les formes quadratiques, Math. Ann. 6 (1873), 366–389, doi:10.1007/BF01442795; J. Leech, Six and seven dimensional non-lattice sphere packings, Canad. Math. Bull. 12 (1969), 151–155, doi:10.4153/CMB-1969-014-1; J. H. Conway and N. J. A. Sloane, What are all the best sphere packings in low dimensions?, Discrete Comput. Geom. 13 (1995), 383–403, doi:10.1007/BF02574051; H. Cohn, Y. Jiao, A. Kumar, and S. Torquato, Rigidity of spherical codes, Geom. Topol. 15 (2011), 2235–2273, doi:10.2140/gt.2011.15.2235, arXiv:1102.5060.
2⁢x−1
6 73 0.513985952311 Henry Cohn, 2025.
6 74 0.521539568537 Henry Cohn, 2025.
6 75 0.524373608780 Henry Cohn, 2026.
6 76 0.524881252881 Henry Cohn, 2026.
6 77 0.527287929827 Henry Cohn, 2025.
6 78 0.528662896579 Henry Cohn, 2025.
6 79 0.533648501058 Henry Cohn, 2025.
6 80 0.536468893038 Henry Cohn, 2025.
6 81 0.538396586915 Henry Cohn, 2026.
6 82 0.539382071135 Henry Cohn, 2026.
6 83 0.543248902467 Henry Cohn, 2026.
6 84 0.545957959230 Henry Cohn, 2026, needs more optimization.
6 85 0.546038397748 Henry Cohn, 2026.
6 86 0.548916479202 Matevž Kovačič, 2026, https://github.com/matevz-kovacic/active-model.
6 87 0.550379697504 A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
6 88 0.552456735670 Henry Cohn, 2025.
6 89 0.555561660912 Henry Cohn, 2025, needs more optimization.
6 90 0.557506870643 Henry Cohn, 2026, needs more optimization.
6 91 0.557588802583 Henry Cohn, 2026.
6 92 0.560971622256 Henry Cohn, 2025.
6 93 0.563013323310 Henry Cohn, 2023.
6 94 0.565350375903 Henry Cohn, 2024.
6 95 0.565789396150 Henry Cohn, 2023.
6 96 0.565950871118 Henry Cohn, 2023.
6 97 0.568133461901 Henry Cohn, 2025.
6 98 0.571037776392 Matevž Kovačič, 2026, https://github.com/matevz-kovacic/active-model.
6 99 0.573881665753 Henry Cohn, 2023.
6 100 0.574916276575 Henry Cohn, 2024.
6 101 0.578318097782 A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
6 102 0.580736682189 Henry Cohn, 2023, needs more optimization.
6 103 0.581239830251 A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
6 104 0.582504372840 Henry Cohn, 2026, needs more optimization.
6 105 0.583291339461 A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
6 106 0.583371498649 Henry Cohn, 2026.
6 107 0.583372432432 Henry Cohn, 2026.
6 108 0.584228700283 Henry Cohn, 2026.
6 109 0.585348750770 Henry Cohn, 2026.
6 110 0.585555924412 A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
6 111 0.585638229827 Henry Cohn, 2026.
6 112 0.585693130025 Henry Cohn, 2026.
6 113 0.586622932873 Henry Cohn, 2025.
6 114 0.588109690133 Henry Cohn, 2023.
6 115 0.596004657476 A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
6 116 0.596439214295 Henry Cohn, 2025.
6 117 0.596439359703 Henry Cohn, 2025, needs more optimization.
6 118 0.596439417437 Henry Cohn, 2026.
6 119 0.598424125415 Henry Cohn, 2025.
6 120 0.599016149465 A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
6 121 0.603688760597 A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
6 122 0.605232558247 A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
6 123 0.606415945860 A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
6 125 0.607973280229 Henry Cohn, 2026, needs more optimization.
6 126 0.610385711272 Henry Cohn, 2026.
6 127 0.616412773395 Henry Cohn, 2026.
6 128 0.618886710990 Henry Cohn, 2026.
6 129 0.620224367829 Henry Cohn, 2025.
6 130 0.623410242886 Henry Cohn, 2026, needs more optimization.
6 132 0.624698587658 Henry Cohn, 2026, needs more optimization.
6 133 0.626200565619 Henry Cohn, 2026, needs more optimization.
6 134 0.628625328947 Henry Cohn, 2026, needs more optimization.
6 135 0.630530656158 Henry Cohn, 2026, needs more optimization.
6 136 0.631774376880 Henry Cohn, 2026, needs more optimization.
6 137 0.633402294823 Henry Cohn, 2025.
6 138 0.634581517382 Henry Cohn, 2026, needs more optimization.
6 139 0.636150042225 Henry Cohn, 2026, needs more optimization.
6 140 0.637374263264 Henry Cohn, 2026, needs more optimization.
6 141 0.639325003085 Henry Cohn, 2026, needs more optimization.
6 142 0.639907720797 Henry Cohn, 2026, needs more optimization.
6 143 0.641418520213 Henry Cohn, 2026, needs more optimization.
6 144 0.642197635997 Henry Cohn, 2026, needs more optimization.
6 145 0.643736553697 Henry Cohn, 2026, needs more optimization.
6 146 0.644835823726 Henry Cohn, 2026, needs more optimization.
6 147 0.645786741328 Henry Cohn, 2026, needs more optimization.
6 148 0.646694161647 Henry Cohn, 2026, needs more optimization.
6 149 0.647934344411 Henry Cohn, 2026, needs more optimization.
6 150 0.649234363496 Henry Cohn, 2026, needs more optimization.
6 151 0.649894104895 Henry Cohn, 2026, needs more optimization.
6 152 0.651009745432 Henry Cohn, 2026, needs more optimization.
6 153 0.651424838401 Henry Cohn, 2026, needs more optimization.
6 154 0.651891077139 Henry Cohn, 2026, needs more optimization.
6 155 0.652677694649 Henry Cohn, 2026, needs more optimization.
6 156 0.653218828402 Henry Cohn, 2026, needs more optimization.
6 157 0.653539053075 Henry Cohn, 2026, needs more optimization.
6 158 0.654174169895 Henry Cohn, 2026, needs more optimization.
6 159 0.654917497394 Henry Cohn, 2026, needs more optimization.
6 160 0.655640275823 Henry Cohn, 2026, needs more optimization.
6 161 0.656172727972 Henry Cohn, 2026, needs more optimization.
6 162 0.656797245916 Henry Cohn, 2026, needs more optimization.
6 163 0.657620192189 Henry Cohn, 2026, needs more optimization.
6 164 0.658348653642 Henry Cohn, 2026, needs more optimization.
6 165 0.659084509520 Henry Cohn, 2026, needs more optimization.
6 166 0.659931336472 Henry Cohn, 2026, needs more optimization.
6 167 0.660355875176 Henry Cohn, 2026, needs more optimization.
6 168 0.660627528646 Henry Cohn, 2026, needs more optimization.
6 169 0.661754053888 Henry Cohn, 2026, needs more optimization.
6 170 0.662663966597 Henry Cohn, 2026, needs more optimization.
6 171 0.663635354345 Henry Cohn, 2026, needs more optimization.
6 172 0.664135030350 Henry Cohn, 2026, needs more optimization.
6 173 0.664451438570 Henry Cohn, 2026, needs more optimization.
6 174 0.664870950288 Henry Cohn, 2026, needs more optimization.
6 175 0.665443411314 Henry Cohn, 2026, needs more optimization.
6 176 0.666108316168 Henry Cohn, 2026, needs more optimization.
6 177 0.667548831820 Henry Cohn, 2026, needs more optimization.
6 178 0.668541726252 Henry Cohn, 2026, needs more optimization.
6 179 0.670026054447 Henry Cohn, 2026, needs more optimization.
6 180 0.671113494040 Henry Cohn, 2026, needs more optimization.
6 181 0.671959630941 Henry Cohn, 2026, needs more optimization.
6 182 0.672541542400 Henry Cohn, 2026, needs more optimization.
6 183 0.673120391466 Henry Cohn, 2026, needs more optimization.
6 184 0.673479432664 Henry Cohn, 2026, needs more optimization.
6 185 0.674052746169 Henry Cohn, 2026, needs more optimization.
6 186 0.674292180631 Henry Cohn, 2026, needs more optimization.
6 187 0.674648752351 Henry Cohn, 2026, needs more optimization.
6 188 0.675448996075 Henry Cohn, 2026, needs more optimization.
6 189 0.676165824000 Henry Cohn, 2026, needs more optimization.
6 190 0.677079062813 Henry Cohn, 2026, needs more optimization.
6 191 0.678090048687 Henry Cohn, 2026, needs more optimization.
6 192 0.678538993914 Henry Cohn, 2026, needs more optimization.
6 193 0.679065210648 Henry Cohn, 2026, needs more optimization.
6 194 0.679780411125 Henry Cohn, 2026, needs more optimization.
6 195 0.680832050419 Henry Cohn, 2026, needs more optimization.
6 196 0.681042163443 Henry Cohn, 2026, needs more optimization.
6 197 0.681777361862 Henry Cohn, 2026, needs more optimization.
6 198 0.682600728399 Henry Cohn, 2026, needs more optimization.
6 199 0.683180906975 Henry Cohn, 2026, needs more optimization.
6 200 0.683918738918 Henry Cohn, 2026, needs more optimization.
6 201 0.684423960591 Henry Cohn, 2026, needs more optimization.
6 202 0.684695807095 Henry Cohn, 2026, needs more optimization.
6 203 0.685464316067 Henry Cohn, 2026, needs more optimization.
6 204 0.685824072471 Henry Cohn, 2026, needs more optimization.
6 205 0.686229429138 Henry Cohn, 2026, needs more optimization.
6 206 0.686784247805 Henry Cohn, 2026, needs more optimization.
6 207 0.687792664686 Henry Cohn, 2026, needs more optimization.
6 208 0.688115875441 Henry Cohn, 2026, needs more optimization.
6 209 0.688653947068 Henry Cohn, 2026, needs more optimization.
6 210 0.689119669405 Henry Cohn, 2026, needs more optimization.
6 211 0.689772455312 Henry Cohn, 2026, needs more optimization.
6 212 0.690463198425 Henry Cohn, 2026, needs more optimization.
6 213 0.691196768958 Henry Cohn, 2026, needs more optimization.
6 214 0.691935634490 Henry Cohn, 2026, needs more optimization.
6 215 0.692810411301 Henry Cohn, 2026, needs more optimization.
6 216 0.693151133181 Henry Cohn, 2026, needs more optimization.
6 217 0.694030817995 Henry Cohn, 2026, needs more optimization.
6 218 0.694428133214 Henry Cohn, 2026, needs more optimization.
6 219 0.694881763545 Henry Cohn, 2026, needs more optimization.
6 220 0.695009246996 Henry Cohn, 2026, needs more optimization.
6 221 0.695418366142 Henry Cohn, 2026, needs more optimization.
6 222 0.695867575619 Henry Cohn, 2026, needs more optimization.
6 223 0.696218097426 Henry Cohn, 2026, needs more optimization.
6 224 0.697123573666 Henry Cohn, 2026, needs more optimization.
6 225 0.697415677677 Henry Cohn, 2026, needs more optimization.
6 226 0.697996733888 Henry Cohn, 2026, needs more optimization.
6 227 0.698315779214 Henry Cohn, 2026, needs more optimization.
6 228 0.698897624639 Henry Cohn, 2026, needs more optimization.
6 229 0.699495105657 Henry Cohn, 2026, needs more optimization.
6 230 0.699810621517 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
6 243 0.7 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
10⁢x−7
6 244 0.703811225569 Henry Cohn, 2026, needs more optimization.
6 245 0.703829064960 Henry Cohn, 2026, needs more optimization.
6 247 0.704068291221 Henry Cohn, 2026, needs more optimization.
6 248 0.704239232973 Henry Cohn, 2026, needs more optimization.
6 249 0.704292043779 Henry Cohn, 2026, needs more optimization.
6 250 0.704483687828 Henry Cohn, 2026, needs more optimization.
6 251 0.704633068602 Henry Cohn, 2026, needs more optimization.
6 252 0.704726065719 Henry Cohn, 2026, needs more optimization.
6 253 0.704943057084 Henry Cohn, 2026, needs more optimization.
6 254 0.705090523351 Henry Cohn, 2026, needs more optimization.
6 255 0.705176652829 Henry Cohn, 2026, needs more optimization.
6 256 0.705181763211 Henry Cohn, 2026, needs more optimization.
6 257 0.705432059080 Henry Cohn, 2026, needs more optimization.
6 258 0.706001251636 Henry Cohn, 2026, needs more optimization.
6 259 0.706716718619 Henry Cohn, 2026, needs more optimization.
6 260 0.707187161621 Henry Cohn, 2026, needs more optimization.
6 261 0.707854912555 Henry Cohn, 2026, needs more optimization.
6 262 0.708781132131 Henry Cohn, 2026, needs more optimization.
6 263 0.709272032981 Henry Cohn, 2026, needs more optimization.
6 264 0.709773900620 Henry Cohn, 2026, needs more optimization.
6 265 0.711047799367 Henry Cohn, 2026, needs more optimization.
6 266 0.712056158723 Henry Cohn, 2026, needs more optimization.
6 267 0.712797549428 Henry Cohn, 2026, needs more optimization.
6 268 0.713114273493 Henry Cohn, 2026, needs more optimization.
6 269 0.713601345738 Henry Cohn, 2026, needs more optimization.
6 270 0.714525044859 Henry Cohn, 2026, needs more optimization.
6 271 0.715193035860 Henry Cohn, 2026, needs more optimization.
6 272 0.716089085390 Henry Cohn, 2026, needs more optimization.
6 273 0.716724836699 Henry Cohn, 2026, needs more optimization.
6 274 0.717514232491 Henry Cohn, 2026, needs more optimization.
6 275 0.718332543147 Henry Cohn, 2026, needs more optimization.
6 276 0.718921350111 Henry Cohn, 2026, needs more optimization.
6 277 0.719526311640 Henry Cohn, 2026, needs more optimization.
6 278 0.720053174881 Henry Cohn, 2026, needs more optimization.
6 279 0.720802822121 Henry Cohn, 2026, needs more optimization.
6 280 0.721677417954 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
6 281 0.722070189457 Henry Cohn, 2026, needs more optimization.
6 282 0.722538082444 Henry Cohn, 2026, needs more optimization.
6 283 0.723276635304 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
6 284 0.723876567321 Henry Cohn, 2026, needs more optimization.
6 285 0.724560497991 Henry Cohn, 2026, needs more optimization.
6 286 0.725089860320 Henry Cohn, 2026, needs more optimization.
6 287 0.725210861714 Henry Cohn, 2026, needs more optimization.
6 288 0.725756204385 Henry Cohn, 2026, needs more optimization.
6 289 0.725756277806 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
6 290 0.726303490253 Henry Cohn, 2026, needs more optimization.
6 291 0.726997243048 Henry Cohn, 2026, needs more optimization.
6 292 0.727966382875 Henry Cohn, 2026, needs more optimization.
6 293 0.728393704045 Henry Cohn, 2026, needs more optimization.
6 294 0.728865960565 Henry Cohn, 2026, needs more optimization.
6 295 0.729390664112 Henry Cohn, 2026, needs more optimization.
6 296 0.729924070292 Henry Cohn, 2026, needs more optimization.
6 297 0.730347732498 Henry Cohn, 2026, needs more optimization.
6 298 0.730780453282 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
6 299 0.731065269229 Henry Cohn, 2026, needs more optimization.
6 300 0.731538373606 Henry Cohn, 2026, needs more optimization.
6 301 0.731951805775 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
6 302 0.732412464529 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
6 303 0.732808651445 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
6 304 0.732993374900 Henry Cohn, 2026, needs more optimization.
6 305 0.733453239030 Henry Cohn, 2026, needs more optimization.
6 306 0.733834261990 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
6 307 0.734120145998 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
6 308 0.734489715727 Henry Cohn, 2026, needs more optimization.
6 309 0.734665674190 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
6 310 0.734886388184 Henry Cohn, 2026, needs more optimization.
6 311 0.735452735086 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
6 312 0.735998644134 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
6 313 0.736458341752 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
6 314 0.736857326928 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
6 315 0.737274367491 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
6 316 0.737705983538 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
6 317 0.738037187207 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
6 318 0.738541628508 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
6 319 0.739003636587 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
6 320 0.739367333014 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
6 321 0.740392507328 Henry Cohn, 2026, needs more optimization.
6 322 0.740718623472 Henry Cohn, 2026, needs more optimization.
6 323 0.741210649064 Henry Cohn, 2026, needs more optimization.
6 324 0.741472277385 Henry Cohn, 2026, needs more optimization.
6 325 0.742100535452 Henry Cohn, 2026, needs more optimization.
6 326 0.742386151341 Henry Cohn, 2026, needs more optimization.
6 327 0.742830477483 Henry Cohn, 2026, needs more optimization.
6 328 0.742903969411 Henry Cohn, 2026, needs more optimization.
6 329 0.743336911920 Henry Cohn, 2026, needs more optimization.
6 330 0.743703583645 Henry Cohn, 2026, needs more optimization.
6 331 0.744121710687 Henry Cohn, 2026, needs more optimization.
6 332 0.744375581136 Henry Cohn, 2026, needs more optimization.
6 333 0.744404080573 Henry Cohn, 2026, needs more optimization.
6 334 0.744692647756 Henry Cohn, 2026, needs more optimization.
6 335 0.745155499023 Henry Cohn, 2026, needs more optimization.
6 336 0.745795172280 Henry Cohn, 2026, needs more optimization.
6 337 0.746050970072 Henry Cohn, 2026, needs more optimization.
6 338 0.746536810251 Henry Cohn, 2026, needs more optimization.
6 339 0.746541484650 Henry Cohn, 2026, needs more optimization.
6 340 0.746547327615 Henry Cohn, 2026, needs more optimization.
6 341 0.746549800600 Henry Cohn, 2026, needs more optimization.
6 342 0.746555037918 Henry Cohn, 2026, needs more optimization.
6 343 0.748201872568 Henry Cohn, 2026, needs more optimization.
6 344 0.748891333107 Henry Cohn, 2026, needs more optimization.
6 345 0.749168886017 Henry Cohn, 2026, needs more optimization.
6 346 0.749361533116 Henry Cohn, 2026, needs more optimization.
6 347 0.749672574610 Henry Cohn, 2026, needs more optimization.
6 348 0.750060948395 Henry Cohn, 2026, needs more optimization.
6 349 0.750323250801 Henry Cohn, 2026, needs more optimization.
6 350 0.750535324476 Henry Cohn, 2026, needs more optimization.
6 351 0.750816019938 Henry Cohn, 2026, needs more optimization.
6 352 0.751167366847 Henry Cohn, 2026, needs more optimization.
6 353 0.751504887645 Henry Cohn, 2026, needs more optimization.
6 354 0.751707781559 Henry Cohn, 2026, needs more optimization.
6 355 0.751875015808 Henry Cohn, 2026, needs more optimization.
6 356 0.752154535514 Henry Cohn, 2026, needs more optimization.
6 357 0.752448097554 Henry Cohn, 2026, needs more optimization.
6 358 0.752900568948 Henry Cohn, 2026, needs more optimization.
6 359 0.753214276804 Henry Cohn, 2026, needs more optimization.
6 360 0.753274216061 Henry Cohn, 2026, needs more optimization.
6 361 0.753631114511 Henry Cohn, 2026, needs more optimization.
6 362 0.754025228210 Henry Cohn, 2026, needs more optimization.
6 363 0.754158167199 Henry Cohn, 2026, needs more optimization.
6 364 0.754546850909 Henry Cohn, 2026, needs more optimization.
6 365 0.754688774749 Henry Cohn, 2026, needs more optimization.
6 366 0.755029583027 Henry Cohn, 2026, needs more optimization.
6 367 0.755301213009 Henry Cohn, 2026, needs more optimization.
6 368 0.755542124057 Henry Cohn, 2026, needs more optimization.
6 369 0.755894584699 Henry Cohn, 2026, needs more optimization.
6 370 0.756118715648 Henry Cohn, 2026, needs more optimization.
6 371 0.756591999949 Henry Cohn, 2026, needs more optimization.
6 372 0.756694702296 Henry Cohn, 2026, needs more optimization.
6 373 0.757058978386 Henry Cohn, 2026, needs more optimization.
6 374 0.757260927893 Henry Cohn, 2026, needs more optimization.
6 375 0.757512930404 Henry Cohn, 2026, needs more optimization.
6 376 0.757928584430 Henry Cohn, 2026, needs more optimization.
6 377 0.758154656885 Henry Cohn, 2026, needs more optimization.
6 378 0.758496973623 Henry Cohn, 2026, needs more optimization.
6 379 0.758921958365 Henry Cohn, 2026, needs more optimization.
6 380 0.759281532699 Henry Cohn, 2026, needs more optimization.
6 381 0.759287188836 Henry Cohn, 2026, needs more optimization.
6 382 0.759553828960 Henry Cohn, 2026, needs more optimization.
6 383 0.759651144367 Henry Cohn, 2026, needs more optimization.
6 384 0.759895034414 Henry Cohn, 2026, needs more optimization.
6 385 0.760293490745 Henry Cohn, 2026, needs more optimization.
6 386 0.760400152116 Henry Cohn, 2026, needs more optimization.
6 387 0.760665940114 Henry Cohn, 2026, needs more optimization.
6 388 0.761094843796 Henry Cohn, 2026, needs more optimization.
6 389 0.761277408237 Henry Cohn, 2026, needs more optimization.
6 390 0.761719412074 Henry Cohn, 2026, needs more optimization.
6 391 0.761743903441 Henry Cohn, 2026, needs more optimization.
6 392 0.762056837313 Henry Cohn, 2026, needs more optimization.
6 393 0.762147020533 Henry Cohn, 2026, needs more optimization.
6 394 0.762396033611 Henry Cohn, 2026, needs more optimization.
6 395 0.762808555436 Henry Cohn, 2026, needs more optimization.
6 396 0.763162430869 Henry Cohn, 2026, needs more optimization.
6 397 0.763205345818 Henry Cohn, 2026, needs more optimization.
6 398 0.763520494846 Henry Cohn, 2026, needs more optimization.
6 399 0.763761786023 Henry Cohn, 2026, needs more optimization.
6 400 0.763829216813 Henry Cohn, 2026, needs more optimization.
6 401 0.764132137583 Henry Cohn, 2026, needs more optimization.
6 402 0.764333777135 Henry Cohn, 2026, needs more optimization.
6 403 0.764553451385 Henry Cohn, 2026, needs more optimization.
6 404 0.764898868902 Henry Cohn, 2026, needs more optimization.
6 405 0.765049126009 Henry Cohn, 2026, needs more optimization.
6 406 0.765251881874 Henry Cohn, 2026, needs more optimization.
6 407 0.765554760762 Henry Cohn, 2026, needs more optimization.
6 408 0.765775905542 Henry Cohn, 2026, needs more optimization.
6 409 0.765829596901 Henry Cohn, 2026, needs more optimization.
6 410 0.766020547392 Henry Cohn, 2026, needs more optimization.
6 411 0.766324786941 Henry Cohn, 2026, needs more optimization.
6 412 0.766583398021 Henry Cohn, 2026, needs more optimization.
6 413 0.766729780804 Henry Cohn, 2026, needs more optimization.
6 414 0.767055465298 Henry Cohn, 2026, needs more optimization.
6 415 0.767434170300 Henry Cohn, 2026, needs more optimization.
6 416 0.767448222137 Henry Cohn, 2026, needs more optimization.
6 417 0.768007147668 Henry Cohn, 2026, needs more optimization.
6 418 0.768185944537 Henry Cohn, 2026, needs more optimization.
6 419 0.768267219762 Henry Cohn, 2026, needs more optimization.
6 420 0.768681426369 Henry Cohn, 2026, needs more optimization.
6 421 0.768858491706 Henry Cohn, 2026, needs more optimization.
6 422 0.769113280656 Henry Cohn, 2026, needs more optimization.
6 423 0.769297208100 Henry Cohn, 2026, needs more optimization.
6 424 0.769565411744 Henry Cohn, 2026, needs more optimization.
6 425 0.769819834776 Henry Cohn, 2026, needs more optimization.
6 426 0.770072640071 Henry Cohn, 2026, needs more optimization.
6 427 0.770112754737 Henry Cohn, 2026, needs more optimization.
6 428 0.770408862110 Henry Cohn, 2026, needs more optimization.
6 429 0.770523122177 Henry Cohn, 2026, needs more optimization.
6 430 0.770828186021 Henry Cohn, 2026, needs more optimization.
6 431 0.770920789190 Henry Cohn, 2026, needs more optimization.
6 432 0.771048530093 Henry Cohn, 2026, needs more optimization.
6 433 0.771341538295 Henry Cohn, 2026, needs more optimization.
6 434 0.771483828651 Henry Cohn, 2026, needs more optimization.
6 435 0.771776053637 Henry Cohn, 2026, needs more optimization.
6 436 0.771820556665 Henry Cohn, 2026, needs more optimization.
6 437 0.771948691950 Henry Cohn, 2026, needs more optimization.
6 438 0.772124005201 Henry Cohn, 2026, needs more optimization.
6 439 0.772515797546 Henry Cohn, 2026, needs more optimization.
6 440 0.772633502270 Henry Cohn, 2026, needs more optimization.
6 441 0.772898014379 Henry Cohn, 2026, needs more optimization.
6 442 0.773078267758 Henry Cohn, 2026, needs more optimization.
6 443 0.773241999150 Henry Cohn, 2026, needs more optimization.
6 444 0.773374860258 Henry Cohn, 2026, needs more optimization.
6 445 0.773765808863 Henry Cohn, 2026, needs more optimization.
6 446 0.774045335435 Henry Cohn, 2026, needs more optimization.
6 447 0.774215321356 Henry Cohn, 2026, needs more optimization.
6 448 0.774388239003 Henry Cohn, 2026, needs more optimization.
6 449 0.774712503032 Henry Cohn, 2026, needs more optimization.
6 450 0.774821207861 Henry Cohn, 2026, needs more optimization.
6 451 0.775055478001 Henry Cohn, 2026, needs more optimization.
6 452 0.775195265624 Henry Cohn, 2026, needs more optimization.
6 453 0.775424039881 Henry Cohn, 2026, needs more optimization.
6 454 0.775479034329 Henry Cohn, 2026, needs more optimization.
6 455 0.775844162997 Henry Cohn, 2026, needs more optimization.
6 456 0.776060647477 Henry Cohn, 2026, needs more optimization.
6 457 0.776313469909 Henry Cohn, 2026, needs more optimization.
6 458 0.776420378220 Henry Cohn, 2026, needs more optimization.
6 459 0.776648116094 Henry Cohn, 2026, needs more optimization.
6 460 0.776745024753 Henry Cohn, 2026, needs more optimization.
6 461 0.776780023563 Henry Cohn, 2026, needs more optimization.
6 462 0.777135317332 Henry Cohn, 2026, needs more optimization.
6 463 0.777364236562 Henry Cohn, 2026, needs more optimization.
6 464 0.777438678661 Henry Cohn, 2026, needs more optimization.
6 465 0.777662660066 Henry Cohn, 2026, needs more optimization.
6 466 0.777930710595 Henry Cohn, 2026, needs more optimization.
6 467 0.778019503277 Henry Cohn, 2026, needs more optimization.
6 468 0.778280099466 Henry Cohn, 2026, needs more optimization.
6 469 0.778330000874 Henry Cohn, 2026, needs more optimization.
6 470 0.778710697369 Henry Cohn, 2026, needs more optimization.
6 471 0.778902495149 Henry Cohn, 2026, needs more optimization.
6 472 0.779173675191 Henry Cohn, 2026, needs more optimization.
6 473 0.779465600609 Henry Cohn, 2026, needs more optimization.
6 474 0.779641642919 Henry Cohn, 2026, needs more optimization.
6 475 0.779678431603 Henry Cohn, 2026, needs more optimization.
6 476 0.779727697904 Henry Cohn, 2026, needs more optimization.
6 477 0.779843720094 Henry Cohn, 2026, needs more optimization.
6 478 0.780129330095 Henry Cohn, 2026, needs more optimization.
6 479 0.780334733069 Henry Cohn, 2026, needs more optimization.
6 480 0.780544516155 Henry Cohn, 2026, needs more optimization.
6 481 0.780686578591 Henry Cohn, 2026, needs more optimization.
6 482 0.780895222420 Henry Cohn, 2026, needs more optimization.
6 483 0.781069934649 Henry Cohn, 2026, needs more optimization.
6 484 0.781376662148 Henry Cohn, 2026, needs more optimization.
6 485 0.781541866561 Henry Cohn, 2026, needs more optimization.
6 486 0.781631963196 Henry Cohn, 2026, needs more optimization.
6 487 0.781955071902 Henry Cohn, 2026, needs more optimization.
6 488 0.782125042734 Henry Cohn, 2026, needs more optimization.
6 489 0.782377327952 Henry Cohn, 2026, needs more optimization.
6 490 0.782441705680 Henry Cohn, 2026, needs more optimization.
6 491 0.782691545546 Henry Cohn, 2026, needs more optimization.
6 492 0.782793796837 Henry Cohn, 2026, needs more optimization.
6 493 0.783008718486 Henry Cohn, 2026, needs more optimization.
6 494 0.783254239036 Henry Cohn, 2026, needs more optimization.
6 495 0.783276031250 Henry Cohn, 2026, needs more optimization.
6 496 0.783452416656 Henry Cohn, 2026, needs more optimization.
6 497 0.783649962319 Henry Cohn, 2026, needs more optimization.
6 498 0.783834402090 Henry Cohn, 2026, needs more optimization.
6 499 0.783840263927 Henry Cohn, 2026, needs more optimization.
6 500 0.784062321707 Henry Cohn, 2026, needs more optimization.
6 501 0.784438857427 Henry Cohn, 2026, needs more optimization.
6 502 0.784671697704 Henry Cohn, 2026, needs more optimization.
6 503 0.784865983420 Henry Cohn, 2026, needs more optimization.
6 504 0.785008081204 Henry Cohn, 2026, needs more optimization.
6 505 0.785164862007 Henry Cohn, 2026, needs more optimization.
6 506 0.785344328166 Henry Cohn, 2026, needs more optimization.
6 507 0.785472390025 Henry Cohn, 2026, needs more optimization.
6 508 0.785608688249 Henry Cohn, 2026, needs more optimization.
6 509 0.785861805163 Henry Cohn, 2026, needs more optimization.
6 510 0.786017726821 Henry Cohn, 2026, needs more optimization.
6 511 0.786276636903 Henry Cohn, 2026, needs more optimization.
6 512 0.786285940551 Henry Cohn, 2026, needs more optimization.
6 513 0.786400810490 Henry Cohn, 2026, needs more optimization.
6 514 0.786565931452 Henry Cohn, 2026, needs more optimization.
6 515 0.786632449053 Henry Cohn, 2026, needs more optimization.
6 516 0.786774046795 Henry Cohn, 2026, needs more optimization.
6 517 0.786913218630 Henry Cohn, 2026, needs more optimization.
6 518 0.787265128324 Henry Cohn, 2026, needs more optimization.
6 519 0.787280244188 Henry Cohn, 2026, needs more optimization.
6 520 0.787429234724 Henry Cohn, 2026, needs more optimization.
6 521 0.787664113669 Henry Cohn, 2026, needs more optimization.
6 522 0.787796345144 Henry Cohn, 2026, needs more optimization.
6 523 0.788007788108 Henry Cohn, 2026, needs more optimization.
6 524 0.788228758458 Henry Cohn, 2026, needs more optimization.
6 525 0.788430563366 Henry Cohn, 2026, needs more optimization.
6 526 0.788562976701 Henry Cohn, 2026, needs more optimization.
6 527 0.788866479091 Henry Cohn, 2026, needs more optimization.
6 528 0.788917288468 Henry Cohn, 2026, needs more optimization.
6 529 0.789113973369 Henry Cohn, 2026, needs more optimization.
6 530 0.789223575612 Henry Cohn, 2026, needs more optimization.
6 531 0.789405078604 Henry Cohn, 2026, needs more optimization.
6 532 0.789541623596 Henry Cohn, 2026, needs more optimization.
6 533 0.789657031902 Henry Cohn, 2026, needs more optimization.
6 534 0.789756436100 Henry Cohn, 2026, needs more optimization.
6 535 0.790016550881 Henry Cohn, 2026, needs more optimization.
6 536 0.790056138852 Henry Cohn, 2026, needs more optimization.
6 537 0.790290111838 Henry Cohn, 2026, needs more optimization.
6 538 0.790475590684 Henry Cohn, 2026, needs more optimization.
6 539 0.790492246764 Henry Cohn, 2026, needs more optimization.
6 540 0.790696072978 Henry Cohn, 2026, needs more optimization.
6 541 0.790876624882 Henry Cohn, 2026, needs more optimization.
6 542 0.790903544182 Henry Cohn, 2026, needs more optimization.
6 543 0.791091493591 Henry Cohn, 2026, needs more optimization.
6 544 0.791287066424 Henry Cohn, 2026, needs more optimization.
6 545 0.791480835856 Henry Cohn, 2026, needs more optimization.
6 546 0.791753496700 Henry Cohn, 2026, needs more optimization.
6 547 0.791796789597 Henry Cohn, 2026, needs more optimization.
6 548 0.791970414467 Henry Cohn, 2026, needs more optimization.
6 549 0.792112080575 Henry Cohn, 2026, needs more optimization.
6 550 0.792218655607 Henry Cohn, 2026, needs more optimization.
6 551 0.792440693396 Henry Cohn, 2026, needs more optimization.
6 552 0.792559337017 Henry Cohn, 2026, needs more optimization.
6 553 0.792703818265 Henry Cohn, 2026, needs more optimization.
6 554 0.792867520102 Henry Cohn, 2026, needs more optimization.
6 555 0.793005114076 Henry Cohn, 2026, needs more optimization.
6 556 0.793260479272 Henry Cohn, 2026, needs more optimization.
6 557 0.793312076980 Henry Cohn, 2026, needs more optimization.
6 558 0.793371005518 Henry Cohn, 2026, needs more optimization.
6 559 0.793487790622 Henry Cohn, 2026, needs more optimization.
6 560 0.793734837753 Henry Cohn, 2026, needs more optimization.
6 561 0.793990365233 Henry Cohn, 2026, needs more optimization.
6 562 0.793992789269 Henry Cohn, 2026, needs more optimization.
6 563 0.794209331678 Henry Cohn, 2026, needs more optimization.
6 564 0.794224195102 Henry Cohn, 2026, needs more optimization.
6 565 0.794448264563 Henry Cohn, 2026, needs more optimization.
6 566 0.794613028361 Henry Cohn, 2026, needs more optimization.
6 567 0.794774352417 Henry Cohn, 2026, needs more optimization.
6 568 0.795012944625 Henry Cohn, 2026, needs more optimization.
6 569 0.795031837171 Henry Cohn, 2026, needs more optimization.
6 570 0.795151284266 Henry Cohn, 2026, needs more optimization.
6 571 0.795223873506 Henry Cohn, 2026, needs more optimization.
6 572 0.795372708364 Henry Cohn, 2026, needs more optimization.
6 573 0.795571705527 Henry Cohn, 2026, needs more optimization.
6 574 0.795655125135 Henry Cohn, 2026, needs more optimization.
6 575 0.795873343956 Henry Cohn, 2026, needs more optimization.
6 576 0.796074504920 Henry Cohn, 2026, needs more optimization.
6 577 0.796191267467 Henry Cohn, 2026, needs more optimization.
6 578 0.796324950480 Henry Cohn, 2026, needs more optimization.
6 579 0.796570666878 Henry Cohn, 2026, needs more optimization.
6 580 0.796703884438 Henry Cohn, 2026, needs more optimization.
6 581 0.796751901714 Henry Cohn, 2026, needs more optimization.
6 582 0.796935198518 Henry Cohn, 2026, needs more optimization.
6 583 0.797063396873 Henry Cohn, 2026, needs more optimization.
6 584 0.797348157487 Henry Cohn, 2026, needs more optimization.
6 585 0.797375935229 Henry Cohn, 2026, needs more optimization.
6 586 0.797377705987 Henry Cohn, 2026, needs more optimization.
6 587 0.797506939525 Henry Cohn, 2026, needs more optimization.
6 588 0.797679508555 Henry Cohn, 2026, needs more optimization.
6 589 0.797817253969 Henry Cohn, 2026, needs more optimization.
6 590 0.797910928249 Henry Cohn, 2026, needs more optimization.
6 591 0.798112573157 Henry Cohn, 2026, needs more optimization.
6 592 0.798367973674 Henry Cohn, 2026, needs more optimization.
6 593 0.798457048321 Henry Cohn, 2026, needs more optimization.
6 594 0.798644425031 Henry Cohn, 2026, needs more optimization.
6 595 0.798783203575 Henry Cohn, 2026, needs more optimization.
6 596 0.798920532360 Henry Cohn, 2026, needs more optimization.
6 597 0.799043119104 Henry Cohn, 2026, needs more optimization.
6 598 0.799233568559 Henry Cohn, 2026, needs more optimization.
6 599 0.799356612818 Henry Cohn, 2026, needs more optimization.
6 600 0.799532892456 Henry Cohn, 2026, needs more optimization.
6 601 0.799659012682 Henry Cohn, 2026, needs more optimization.
6 602 0.799772260172 Henry Cohn, 2026, needs more optimization.
6 603 0.799910052198 Henry Cohn, 2026, needs more optimization.
6 604 0.800057954983 Henry Cohn, 2026, needs more optimization.
6 605 0.800201376426 Henry Cohn, 2026, needs more optimization.
6 606 0.800211081333 Henry Cohn, 2026, needs more optimization.
6 607 0.800469454393 Henry Cohn, 2026, needs more optimization.
6 608 0.800480506369 Henry Cohn, 2026, needs more optimization.
6 609 0.800618933317 Henry Cohn, 2026, needs more optimization.
6 610 0.800759288408 Henry Cohn, 2026, needs more optimization.
6 611 0.800997617334 Henry Cohn, 2026, needs more optimization.
6 612 0.801125936396 Henry Cohn, 2026, needs more optimization.
6 613 0.801159472697 Henry Cohn, 2026, needs more optimization.
6 614 0.801441336786 Henry Cohn, 2026, needs more optimization.
6 615 0.801480505446 Henry Cohn, 2026, needs more optimization.
6 616 0.801642621139 Henry Cohn, 2026, needs more optimization.
6 617 0.801644772931 Henry Cohn, 2026, needs more optimization.
6 618 0.801781108797 Henry Cohn, 2026, needs more optimization.
6 619 0.801905257656 Henry Cohn, 2026, needs more optimization.
6 620 0.801962418739 Henry Cohn, 2026, needs more optimization.
6 621 0.802155949872 Henry Cohn, 2026, needs more optimization.
6 622 0.802418969434 Henry Cohn, 2026, needs more optimization.
6 623 0.802560377832 Henry Cohn, 2026, needs more optimization.
6 624 0.802573805045 Henry Cohn, 2026, needs more optimization.
6 625 0.802699803330 Henry Cohn, 2026, needs more optimization.
6 626 0.802893393204 Henry Cohn, 2026, needs more optimization.
6 627 0.802912374599 Henry Cohn, 2026, needs more optimization.
6 628 0.802993797425 Henry Cohn, 2026, needs more optimization.
6 629 0.803181949257 Henry Cohn, 2026, needs more optimization.
6 630 0.803288391015 Henry Cohn, 2026, needs more optimization.
6 631 0.803406859361 Henry Cohn, 2026, needs more optimization.
6 632 0.803551695288 Henry Cohn, 2026, needs more optimization.
6 633 0.803753269935 Henry Cohn, 2026, needs more optimization.
6 634 0.803972924069 Henry Cohn, 2026, needs more optimization.
6 635 0.803986640773 Henry Cohn, 2026, needs more optimization.
6 636 0.804077378267 Henry Cohn, 2026, needs more optimization.
6 637 0.804211991671 Henry Cohn, 2026, needs more optimization.
6 638 0.804378807116 Henry Cohn, 2026, needs more optimization.
6 639 0.804379865537 Henry Cohn, 2026, needs more optimization.
6 640 0.804586122508 Henry Cohn, 2026, needs more optimization.
6 641 0.804604405801 Henry Cohn, 2026, needs more optimization.
6 642 0.804663290819 Henry Cohn, 2026, needs more optimization.
6 643 0.804766598690 Henry Cohn, 2026, needs more optimization.
6 644 0.804939569756 Henry Cohn, 2026, needs more optimization.
6 645 0.805177143288 Henry Cohn, 2026, needs more optimization.
6 646 0.805254018823 Henry Cohn, 2026, needs more optimization.
6 647 0.805428708397 Henry Cohn, 2026, needs more optimization.
6 648 0.805449569725 Henry Cohn, 2026, needs more optimization.
6 649 0.805546180061 Henry Cohn, 2026, needs more optimization.
6 650 0.805651356929 Henry Cohn, 2026, needs more optimization.
6 651 0.805794215540 Henry Cohn, 2026, needs more optimization.
6 652 0.805921443896 Henry Cohn, 2026, needs more optimization.
6 653 0.806067249783 Henry Cohn, 2026, needs more optimization.
6 654 0.806182518616 Henry Cohn, 2026, needs more optimization.
6 655 0.806367634591 Henry Cohn, 2026, needs more optimization.
6 656 0.806396066248 Henry Cohn, 2026, needs more optimization.
6 657 0.806530893023 Henry Cohn, 2026, needs more optimization.
6 658 0.806594405409 Henry Cohn, 2026, needs more optimization.
6 659 0.806708903240 Henry Cohn, 2026, needs more optimization.
6 660 0.806749701935 Henry Cohn, 2026, needs more optimization.
6 661 0.806892166992 Henry Cohn, 2026, needs more optimization.
6 662 0.807082160083 Henry Cohn, 2026, needs more optimization.
6 663 0.807251286564 Henry Cohn, 2026, needs more optimization.
6 664 0.807282856762 Henry Cohn, 2026, needs more optimization.
6 665 0.807559501062 Henry Cohn, 2026, needs more optimization.
6 666 0.807578913124 Henry Cohn, 2026, needs more optimization.
6 667 0.807738868522 Henry Cohn, 2026, needs more optimization.
6 668 0.807776999619 Henry Cohn, 2026, needs more optimization.
6 669 0.807819621632 Henry Cohn, 2026, needs more optimization.
6 670 0.807890815552 Henry Cohn, 2026, needs more optimization.
6 671 0.808064173527 Henry Cohn, 2026, needs more optimization.
6 672 0.808129076706 Henry Cohn, 2026, needs more optimization.
6 673 0.808284888147 Henry Cohn, 2026, needs more optimization.
6 674 0.808454476202 Henry Cohn, 2026, needs more optimization.
6 675 0.808542942911 Henry Cohn, 2026, needs more optimization.
6 676 0.808752247244 Henry Cohn, 2026, needs more optimization.
6 677 0.808925618162 Henry Cohn, 2026, needs more optimization.
6 678 0.808977553361 Henry Cohn, 2026, needs more optimization.
6 679 0.809095644145 Henry Cohn, 2026, needs more optimization.
6 680 0.809197980219 Henry Cohn, 2026, needs more optimization.
6 681 0.809367571718 Henry Cohn, 2026, needs more optimization.
6 682 0.809508563100 Henry Cohn, 2026, needs more optimization.
6 683 0.809570381100 Henry Cohn, 2026, needs more optimization.
6 684 0.809704030004 Henry Cohn, 2026, needs more optimization.
6 685 0.809808123836 Henry Cohn, 2026, needs more optimization.
6 686 0.809901222873 Henry Cohn, 2026, needs more optimization.
6 687 0.809947533533 Henry Cohn, 2026, needs more optimization.
6 688 0.810112204993 Henry Cohn, 2026, needs more optimization.
6 689 0.810278351949 Henry Cohn, 2026, needs more optimization.
6 690 0.810364726817 Henry Cohn, 2026, needs more optimization.
6 691 0.810468489997 Henry Cohn, 2026, needs more optimization.
6 692 0.810571587759 Henry Cohn, 2026, needs more optimization.
6 693 0.810669400328 Henry Cohn, 2026, needs more optimization.
6 694 0.810820936033 Henry Cohn, 2026, needs more optimization.
6 695 0.810853765537 Henry Cohn, 2026, needs more optimization.
6 696 0.811064007322 Henry Cohn, 2026, needs more optimization.
6 697 0.811156182717 Henry Cohn, 2026, needs more optimization.
6 698 0.811429054132 Henry Cohn, 2026, needs more optimization.
6 699 0.811547676724 Henry Cohn, 2026, needs more optimization.
6 700 0.811670259678 Henry Cohn, 2026, needs more optimization.
6 701 0.811690737392 Henry Cohn, 2026, needs more optimization.
6 702 0.811744595398 Henry Cohn, 2026, needs more optimization.
6 703 0.811870937445 Henry Cohn, 2026, needs more optimization.
6 704 0.811886613167 Henry Cohn, 2026, needs more optimization.
6 705 0.811969655613 Henry Cohn, 2026, needs more optimization.
6 706 0.812131470610 Henry Cohn, 2026, needs more optimization.
6 707 0.812327864400 Henry Cohn, 2026, needs more optimization.
6 708 0.812445949579 Henry Cohn, 2026, needs more optimization.
6 709 0.812551941906 Henry Cohn, 2026, needs more optimization.
6 710 0.812662053245 Henry Cohn, 2026, needs more optimization.
6 711 0.812741483060 Henry Cohn, 2026, needs more optimization.
6 712 0.812903197014 Henry Cohn, 2026, needs more optimization.
6 713 0.813006451187 Henry Cohn, 2026, needs more optimization.
6 714 0.813147641450 Henry Cohn, 2026, needs more optimization.
6 715 0.813300029512 Henry Cohn, 2026, needs more optimization.
6 716 0.813305135633 Henry Cohn, 2026, needs more optimization.
6 717 0.813333682183 Henry Cohn, 2026, needs more optimization.
6 718 0.813476335360 Henry Cohn, 2026, needs more optimization.
6 719 0.813613497061 Henry Cohn, 2026, needs more optimization.
6 720 0.813658721378 Henry Cohn, 2026, needs more optimization.
6 721 0.813808670395 Henry Cohn, 2026, needs more optimization.
6 722 0.813939447363 Henry Cohn, 2026, needs more optimization.
6 723 0.813954548264 Henry Cohn, 2026, needs more optimization.
6 724 0.814055286790 Henry Cohn, 2026, needs more optimization.
6 725 0.814197622080 Henry Cohn, 2026, needs more optimization.
6 726 0.814314783134 Henry Cohn, 2026, needs more optimization.
6 727 0.814485855612 Henry Cohn, 2026, needs more optimization.
6 728 0.814494772988 Henry Cohn, 2026, needs more optimization.
6 729 0.814545366725 Henry Cohn, 2026, needs more optimization.
6 730 0.814683699116 Henry Cohn, 2026, needs more optimization.
6 731 0.814841766561 Henry Cohn, 2026, needs more optimization.
6 732 0.814846898863 Henry Cohn, 2026, needs more optimization.
6 733 0.814911279900 Henry Cohn, 2026, needs more optimization.
6 734 0.815064855673 Henry Cohn, 2026, needs more optimization.
6 735 0.815092865255 Henry Cohn, 2026, needs more optimization.
6 736 0.815200391041 Henry Cohn, 2026, needs more optimization.
6 737 0.815345836707 Henry Cohn, 2026, needs more optimization.
6 738 0.815534480356 Henry Cohn, 2026, needs more optimization.
6 739 0.815622415513 Henry Cohn, 2026, needs more optimization.
6 740 0.815757971886 Henry Cohn, 2026, needs more optimization.
6 741 0.815871158202 Henry Cohn, 2026, needs more optimization.
6 742 0.816007259905 Henry Cohn, 2026, needs more optimization.
6 743 0.816027602319 Henry Cohn, 2026, needs more optimization.
6 744 0.816066216933 Henry Cohn, 2026, needs more optimization.
6 745 0.816200845559 Henry Cohn, 2026, needs more optimization.
6 746 0.816297910660 Henry Cohn, 2026, needs more optimization.
6 747 0.816512636442 Henry Cohn, 2026, needs more optimization.
6 748 0.816584160484 Henry Cohn, 2026, needs more optimization.
6 749 0.816586863596 Henry Cohn, 2026, needs more optimization.
6 750 0.816802948303 Henry Cohn, 2026, needs more optimization.
6 751 0.816947224053 Henry Cohn, 2026, needs more optimization.
6 752 0.816969481398 Henry Cohn, 2026, needs more optimization.
6 753 0.817114900823 Henry Cohn, 2026, needs more optimization.
6 754 0.817236210299 Henry Cohn, 2026, needs more optimization.
6 755 0.817239161708 Henry Cohn, 2026, needs more optimization.
6 756 0.817374183819 Henry Cohn, 2026, needs more optimization.
6 757 0.817455793966 Henry Cohn, 2026, needs more optimization.
6 758 0.817487090764 Henry Cohn, 2026, needs more optimization.
6 759 0.817672634375 Henry Cohn, 2026, needs more optimization.
6 760 0.817688102203 Henry Cohn, 2026, needs more optimization.
6 761 0.817731640849 Henry Cohn, 2026, needs more optimization.
6 762 0.817911113615 Henry Cohn, 2026, needs more optimization.
6 763 0.818092791232 Henry Cohn, 2026, needs more optimization.
6 764 0.818166320615 Henry Cohn, 2026, needs more optimization.
6 765 0.818293383622 Henry Cohn, 2026, needs more optimization.
6 766 0.818338308244 Henry Cohn, 2026, needs more optimization.
6 767 0.818383112047 Henry Cohn, 2026, needs more optimization.
6 768 0.818552321061 Henry Cohn, 2026, needs more optimization.
6 769 0.818614910072 Henry Cohn, 2026, needs more optimization.
6 770 0.818796598006 Henry Cohn, 2026, needs more optimization.
6 771 0.818811503012 Henry Cohn, 2026, needs more optimization.
6 772 0.818895995252 Henry Cohn, 2026, needs more optimization.
6 773 0.818930884205 Henry Cohn, 2026, needs more optimization.
6 774 0.819065229540 Henry Cohn, 2026, needs more optimization.
6 775 0.819098459600 Henry Cohn, 2026, needs more optimization.
6 776 0.819215122616 Henry Cohn, 2026, needs more optimization.
6 777 0.819286978371 Henry Cohn, 2026, needs more optimization.
6 778 0.819461187329 Henry Cohn, 2026, needs more optimization.
6 779 0.819542272389 Henry Cohn, 2026, needs more optimization.
6 780 0.819640701051 Henry Cohn, 2026, needs more optimization.
6 781 0.819687944003 Henry Cohn, 2026, needs more optimization.
6 782 0.819716498311 Henry Cohn, 2026, needs more optimization.
6 783 0.819821698846 Henry Cohn, 2026, needs more optimization.
6 784 0.819931674385 Henry Cohn, 2026, needs more optimization.
6 785 0.819971510334 Henry Cohn, 2026, needs more optimization.
6 786 0.820156163296 Henry Cohn, 2026, needs more optimization.
6 787 0.820173498227 Henry Cohn, 2026, needs more optimization.
6 788 0.820326306445 Henry Cohn, 2026, needs more optimization.
6 789 0.820411066060 Henry Cohn, 2026, needs more optimization.
6 790 0.820514412035 Henry Cohn, 2026, needs more optimization.
6 791 0.820568029108 Henry Cohn, 2026, needs more optimization.
6 792 0.820775584103 Henry Cohn, 2026, needs more optimization.
6 793 0.820777185824 Henry Cohn, 2026, needs more optimization.
6 794 0.820977681817 Henry Cohn, 2026, needs more optimization.
6 795 0.820987552116 Henry Cohn, 2026, needs more optimization.
6 796 0.820994458310 Henry Cohn, 2026, needs more optimization.
6 797 0.821048821362 Henry Cohn, 2026, needs more optimization.
6 798 0.821151549995 Henry Cohn, 2026, needs more optimization.
6 799 0.821261148722 Henry Cohn, 2026, needs more optimization.
6 800 0.821415789721 Henry Cohn, 2026, needs more optimization.
6 801 0.821558140064 Henry Cohn, 2026, needs more optimization.
6 802 0.821660771957 Henry Cohn, 2026, needs more optimization.
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6 807 0.821936251612 Henry Cohn, 2026, needs more optimization.
6 808 0.821974342562 Henry Cohn, 2026, needs more optimization.
6 809 0.822125648162 Henry Cohn, 2026, needs more optimization.
6 810 0.822290800769 Henry Cohn, 2026, needs more optimization.
6 811 0.822348702020 Henry Cohn, 2026, needs more optimization.
6 812 0.822487016540 Henry Cohn, 2026, needs more optimization.
6 813 0.822636888845 Henry Cohn, 2026, needs more optimization.
6 814 0.822685148490 Henry Cohn, 2026, needs more optimization.
6 815 0.822760207195 Henry Cohn, 2026, needs more optimization.
6 816 0.822790302020 Henry Cohn, 2026, needs more optimization.
6 817 0.822972027463 Henry Cohn, 2026, needs more optimization.
6 818 0.823013509114 Henry Cohn, 2026, needs more optimization.
6 819 0.823124327877 Henry Cohn, 2026, needs more optimization.
6 820 0.823158866410 Henry Cohn, 2026, needs more optimization.
6 821 0.823312032365 Henry Cohn, 2026, needs more optimization.
6 822 0.823425090375 Henry Cohn, 2026, needs more optimization.
6 823 0.823634787852 Henry Cohn, 2026, needs more optimization.
6 824 0.823638634066 Henry Cohn, 2026, needs more optimization.
6 825 0.823712356380 Henry Cohn, 2026, needs more optimization.
6 826 0.823851673776 Henry Cohn, 2026, needs more optimization.
6 827 0.823988848860 Henry Cohn, 2026, needs more optimization.
6 828 0.823991425689 Henry Cohn, 2026, needs more optimization.
6 829 0.824032851882 Henry Cohn, 2026, needs more optimization.
6 830 0.824123254770 Henry Cohn, 2026, needs more optimization.
6 831 0.824245286006 Henry Cohn, 2026, needs more optimization.
6 832 0.824306972703 Henry Cohn, 2026, needs more optimization.
6 833 0.824353380156 Henry Cohn, 2026, needs more optimization.
6 834 0.824456022336 Henry Cohn, 2026, needs more optimization.
6 835 0.824516925497 Henry Cohn, 2026, needs more optimization.
6 836 0.824526636586 Henry Cohn, 2026, needs more optimization.
6 837 0.824643580141 Henry Cohn, 2026, needs more optimization.
6 838 0.824727652868 Henry Cohn, 2026, needs more optimization.
6 839 0.824871822318 Henry Cohn, 2026, needs more optimization.
6 840 0.824901582819 Henry Cohn, 2026, needs more optimization.
6 841 0.824989509132 Henry Cohn, 2026, needs more optimization.
6 842 0.825097259096 Henry Cohn, 2026, needs more optimization.
6 843 0.825129362461 Henry Cohn, 2026, needs more optimization.
6 844 0.825310935702 Henry Cohn, 2026, needs more optimization.
6 845 0.825390765441 Henry Cohn, 2026, needs more optimization.
6 846 0.825550853768 Henry Cohn, 2026, needs more optimization.
6 847 0.825558859189 Henry Cohn, 2026, needs more optimization.
6 848 0.825579227672 Henry Cohn, 2026, needs more optimization.
6 849 0.825775662596 Henry Cohn, 2026, needs more optimization.
6 850 0.825857259926 Henry Cohn, 2026, needs more optimization.
6 851 0.825860667359 Henry Cohn, 2026, needs more optimization.
6 852 0.825999311876 Henry Cohn, 2026, needs more optimization.
6 853 0.826135640725 Henry Cohn, 2026, needs more optimization.
6 854 0.826225307695 Henry Cohn, 2026, needs more optimization.
6 855 0.826390520625 Henry Cohn, 2026, needs more optimization.
6 856 0.826404628823 Henry Cohn, 2026, needs more optimization.
6 857 0.826505417336 Henry Cohn, 2026, needs more optimization.
6 858 0.826623674433 Henry Cohn, 2026, needs more optimization.
6 859 0.826623674534 Henry Cohn, 2026, needs more optimization.
6 860 0.826624782996 Henry Cohn, 2026, needs more optimization.
6 861 0.826631859155 Henry Cohn, 2026, needs more optimization.
6 862 0.826709211871 Henry Cohn, 2026, needs more optimization.
6 863 0.826871655379 Henry Cohn, 2026, needs more optimization.
6 864 0.827005448058 Henry Cohn, 2026, needs more optimization.
6 865 0.827013668771 Henry Cohn, 2026, needs more optimization.
6 866 0.827183329674 Henry Cohn, 2026, needs more optimization.
6 867 0.827199668001 Henry Cohn, 2026, needs more optimization.
6 868 0.827212284475 Henry Cohn, 2026, needs more optimization.
6 869 0.827342067932 Henry Cohn, 2026, needs more optimization.
6 870 0.827544303231 Henry Cohn, 2026, needs more optimization.
6 871 0.827544316008 Henry Cohn, 2026, needs more optimization.
6 872 0.827545591245 Henry Cohn, 2026, needs more optimization.
6 873 0.827648963549 Henry Cohn, 2026, needs more optimization.
6 874 0.827653765861 Henry Cohn, 2026, needs more optimization.
6 875 0.827657657793 Henry Cohn, 2026, needs more optimization.
6 876 0.827667139037 Henry Cohn, 2026, needs more optimization.
6 877 0.827816512705 Henry Cohn, 2026, needs more optimization.
6 878 0.827859911063 Henry Cohn, 2026, needs more optimization.
6 879 0.827882155399 Henry Cohn, 2026, needs more optimization.
6 880 0.827914350076 Henry Cohn, 2026, needs more optimization.
6 881 0.827974325884 Henry Cohn, 2026, needs more optimization.
6 882 0.827998488146 Henry Cohn, 2026, needs more optimization.
6 883 0.828017236402 Henry Cohn, 2026, needs more optimization.
6 884 0.828082755176 Henry Cohn, 2026, needs more optimization.
6 885 0.828312301010 Henry Cohn, 2026, needs more optimization.
6 886 0.828351533866 Henry Cohn, 2026, needs more optimization.
6 887 0.828416898167 Henry Cohn, 2026, needs more optimization.
6 888 0.828456233610 Henry Cohn, 2026, needs more optimization.
6 889 0.828554491084 Henry Cohn, 2026, needs more optimization.
6 890 0.828586246222 Henry Cohn, 2026, needs more optimization.
6 891 0.828610338687 Henry Cohn, 2026, needs more optimization.
6 892 0.828746783135 Henry Cohn, 2026, needs more optimization.
6 893 0.828777233457 Henry Cohn, 2026, needs more optimization.
6 894 0.828848913509 Henry Cohn, 2026, needs more optimization.
6 895 0.828850214370 Henry Cohn, 2026, needs more optimization.
6 896 0.828933332263 Henry Cohn, 2026, needs more optimization.
6 897 0.828968340290 Henry Cohn, 2026, needs more optimization.
6 898 0.829076964359 Henry Cohn, 2026, needs more optimization.
6 899 0.829083553904 Henry Cohn, 2026, needs more optimization.
6 900 0.829104133796 Henry Cohn, 2026, needs more optimization.
6 901 0.829304099250 Henry Cohn, 2026, needs more optimization.
6 902 0.829320783338 Henry Cohn, 2026, needs more optimization.
6 903 0.829431199111 Henry Cohn, 2026, needs more optimization.
6 904 0.829515684965 Henry Cohn, 2026, needs more optimization.
6 905 0.829604756605 Henry Cohn, 2026, needs more optimization.
6 906 0.829653026664 Henry Cohn, 2026, needs more optimization.
6 908 0.829782225097 Henry Cohn, 2026, needs more optimization.
6 909 0.829895525915 Henry Cohn, 2026, needs more optimization.
6 910 0.829940139325 Henry Cohn, 2026, needs more optimization.
6 911 0.829947323745 Henry Cohn, 2026, needs more optimization.
6 912 0.830008461618 Henry Cohn, 2026, needs more optimization.
6 913 0.830069146605 Henry Cohn, 2026, needs more optimization.
6 914 0.830151242659 Henry Cohn, 2026, needs more optimization.
6 916 0.830450166226 Henry Cohn, 2026, needs more optimization.
6 917 0.830454223396 Henry Cohn, 2026, needs more optimization.
6 918 0.830463209155 Henry Cohn, 2026, needs more optimization.
6 919 0.830487927069 Henry Cohn, 2026, needs more optimization.
6 920 0.830601381814 Henry Cohn, 2026, needs more optimization.
6 921 0.830622524231 Henry Cohn, 2026, needs more optimization.
6 922 0.830625293430 Henry Cohn, 2026, needs more optimization.
6 923 0.830742656325 Henry Cohn, 2026, needs more optimization.
6 924 0.830748785702 Henry Cohn, 2026, needs more optimization.
6 925 0.830773363755 Henry Cohn, 2026, needs more optimization.
6 926 0.830846129373 Henry Cohn, 2026, needs more optimization.
6 927 0.831055903070 Henry Cohn, 2026, needs more optimization.
6 928 0.831081793581 Henry Cohn, 2026, needs more optimization.
6 929 0.831184206661 Henry Cohn, 2026, needs more optimization.
6 930 0.831220289379 Henry Cohn, 2026, needs more optimization.
6 931 0.831282155385 Henry Cohn, 2026, needs more optimization.
6 932 0.831282237733 Henry Cohn, 2026, needs more optimization.
6 933 0.831290782401 Henry Cohn, 2026, needs more optimization.
6 934 0.831293093815 Henry Cohn, 2026, needs more optimization.
6 935 0.831326634223 Henry Cohn, 2026, needs more optimization.
6 936 0.831343225249 Henry Cohn, 2026, needs more optimization.
6 937 0.831404515812 Henry Cohn, 2026, needs more optimization.
6 938 0.831435861298 Henry Cohn, 2026, needs more optimization.
6 939 0.831688963259 Henry Cohn, 2026, needs more optimization.
6 940 0.831694362523 Henry Cohn, 2026, needs more optimization.
6 941 0.831697016339 Henry Cohn, 2026, needs more optimization.
6 942 0.831750546572 Henry Cohn, 2026, needs more optimization.
6 943 0.831774903503 Henry Cohn, 2026, needs more optimization.
6 945 0.831884757104 Henry Cohn, 2026, needs more optimization.
6 946 0.831907516523 Henry Cohn, 2026, needs more optimization.
6 947 0.831955028901 Henry Cohn, 2026, needs more optimization.
6 948 0.832013445188 Henry Cohn, 2026, needs more optimization.
6 949 0.832044640027 Henry Cohn, 2026, needs more optimization.
6 950 0.832054529413 Henry Cohn, 2026, needs more optimization.
6 951 0.832158518556 Henry Cohn, 2026, needs more optimization.
6 952 0.832192896422 Henry Cohn, 2026, needs more optimization.
6 953 0.832204867009 Henry Cohn, 2026, needs more optimization.
6 954 0.832224869527 Henry Cohn, 2026, needs more optimization.
6 955 0.832297768576 Henry Cohn, 2026, needs more optimization.
6 956 0.832309758483 Henry Cohn, 2026, needs more optimization.
6 957 0.832309822503 Henry Cohn, 2026, needs more optimization.
6 958 0.832324617575 Henry Cohn, 2026, needs more optimization.
6 959 0.832421474540 Henry Cohn, 2026, needs more optimization.
6 960 0.832466136662 Henry Cohn, 2026, needs more optimization.
6 961 0.832484117417 Henry Cohn, 2026, needs more optimization.
6 962 0.832513439778 Henry Cohn, 2026, needs more optimization.
6 963 0.832563224586 Henry Cohn, 2026, needs more optimization.
6 964 0.832623632710 Henry Cohn, 2026, needs more optimization.
6 965 0.832696333220 Henry Cohn, 2026, needs more optimization.
6 966 0.832724323178 Henry Cohn, 2026, needs more optimization.
6 967 0.832755662531 Henry Cohn, 2026, needs more optimization.
6 968 0.832820152412 Henry Cohn, 2026, needs more optimization.
6 969 0.832835317589 Henry Cohn, 2026, needs more optimization.
6 970 0.832865938394 Henry Cohn, 2026, needs more optimization.
6 971 0.832878133382 Henry Cohn, 2026, needs more optimization.
6 973 0.832885494479 Henry Cohn, 2026, needs more optimization.
6 974 0.832900829354 Henry Cohn, 2026, needs more optimization.
6 975 0.832990278007 Henry Cohn, 2026, needs more optimization.
6 976 0.833013698817 Henry Cohn, 2026, needs more optimization.
6 990 0.833333333334 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
6⁢x−5
6 1002 0.833333333334 Henry Cohn, 2026.
6⁢x−5
6 1003 0.835109209895 Henry Cohn, 2026, needs more optimization.
6 1004 0.836165329693 Henry Cohn, 2026, needs more optimization.
6 1005 0.836786742270 Henry Cohn, 2026, needs more optimization.
6 1006 0.837252368301 Henry Cohn, 2026, needs more optimization.
6 1007 0.837323111064 Henry Cohn, 2026, needs more optimization.
6 1008 0.837375765389 Henry Cohn, 2026, needs more optimization.
6 1009 0.837498856913 Henry Cohn, 2026, needs more optimization.
6 1010 0.837618364916 Henry Cohn, 2026, needs more optimization.
6 1011 0.837637098000 Henry Cohn, 2026, needs more optimization.
6 1012 0.837644626519 Henry Cohn, 2026, needs more optimization.
6 1013 0.837785140793 Henry Cohn, 2026, needs more optimization.
6 1014 0.837795131456 Henry Cohn, 2026, needs more optimization.
6 1015 0.837903804235 Henry Cohn, 2026, needs more optimization.
6 1016 0.837919921018 Henry Cohn, 2026, needs more optimization.
6 1017 0.837931372124 Henry Cohn, 2026, needs more optimization.
6 1018 0.838084883844 Henry Cohn, 2026, needs more optimization.
6 1019 0.838121767222 Henry Cohn, 2026, needs more optimization.
6 1020 0.838321766321 Henry Cohn, 2026, needs more optimization.
6 1021 0.838333047775 Henry Cohn, 2026, needs more optimization.
6 1022 0.838387762373 Henry Cohn, 2026, needs more optimization.
6 1023 0.838501910845 Henry Cohn, 2026, needs more optimization.
6 1024 0.838615228274 Henry Cohn, 2026, needs more optimization.
7 15 0.098701776273 P. G. Adams, A numerical approach to Tamme's problem in Euclidean n-space, Master of Science thesis, Oregon State University, 1997, https://hdl.handle.net/1957/33911.
175⁢x3−49⁢x2−7⁢x+1
7 16 0.113320879601 J. Wang, Finding and investigating exact spherical codes, Experiment. Math. 18 (2009), 249–256, https://projecteuclid.org/euclid.em/1259158434.
Minimal polynomial listed in plain text data
7 17 0.124841583816 H. Cohn, Small spherical and projective codes, data set, 2022, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
Minimal polynomial listed in plain text data
7 18 0.126131983623 P. G. Adams, A numerical approach to Tamme's problem in Euclidean n-space, Master of Science thesis, Oregon State University, 1997, https://hdl.handle.net/1957/33911.
47⁢x2+2⁢x−1
7 19 0.156597385418 J. Wang, Finding and investigating exact spherical codes, Experiment. Math. 18 (2009), 249–256, https://projecteuclid.org/euclid.em/1259158434.
1280⁢x6−352⁢x4−48⁢x3+37⁢x2+3⁢x−1
7 20 0.169520847199 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
23⁢x2+2⁢x−1
7 21 0.181523960801 J. Wang, Finding and investigating exact spherical codes, Experiment. Math. 18 (2009), 249–256, https://projecteuclid.org/euclid.em/1259158434.
7 22 0.182743997632 J. Wang, Finding and investigating exact spherical codes, Experiment. Math. 18 (2009), 249–256, https://projecteuclid.org/euclid.em/1259158434.
19⁢x2+2⁢x−1
7 23 0.182743997632 J. Wang, Finding and investigating exact spherical codes, Experiment. Math. 18 (2009), 249–256, https://projecteuclid.org/euclid.em/1259158434.
19⁢x2+2⁢x−1
7 24 0.182743997632 J. Wang, Finding and investigating exact spherical codes, Experiment. Math. 18 (2009), 249–256, https://projecteuclid.org/euclid.em/1259158434.
19⁢x2+2⁢x−1
7 25 0.214737233855 J. Wang, Finding and investigating exact spherical codes, Experiment. Math. 18 (2009), 249–256, https://projecteuclid.org/euclid.em/1259158434.
31⁢x2−2⁢x−1
7 26 0.231331430372 J. Wang, Finding and investigating exact spherical codes, Experiment. Math. 18 (2009), 249–256, https://projecteuclid.org/euclid.em/1259158434.
7 27 0.240549382010 H. Cohn, Small spherical and projective codes, data set, 2022, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
7 28 0.247356651208 H. Cohn, Small spherical and projective codes, data set, 2022, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
7 29 0.248893779344 H. Cohn, Small spherical and projective codes, data set, updated 2025, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
7 30 0.249468282003 H. Cohn, Small spherical and projective codes, data set, updated 2024, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
7 31 0.254502767515 H. Cohn, Small spherical and projective codes, data set, 2022, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
7 32 0.265595699432 H. Cohn, Small spherical and projective codes, data set, 2022, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
7 33 0.270023386002 Henry Cohn, 2024.
7 34 0.277696496789 J. Wang, Finding and investigating exact spherical codes, Experiment. Math. 18 (2009), 249–256, https://projecteuclid.org/euclid.em/1259158434.
7 35 0.289773019868 J. Wang, Finding and investigating exact spherical codes, Experiment. Math. 18 (2009), 249–256, https://projecteuclid.org/euclid.em/1259158434.
7 36 0.299959896814 Henry Cohn, 2023.
7 37 0.310451288111 Henry Cohn, 2026.
7 39 0.316279494687 Henry Cohn, 2023.
71⁢x2+6⁢x−9
7 40 0.323843153340 Henry Cohn, 2023.
7 41 0.325408592469 Henry Cohn, 2023.
32⁢x4+40⁢x3−23⁢x2−4⁢x+2
7 42 0.329083455200 Henry Cohn, 2025.
7 43 0.329665776133 Henry Cohn, 2023.
Minimal polynomial listed in plain text data
7 44 0.332131779753 Henry Cohn, 2025.
Minimal polynomial listed in plain text data
7 45 0.333226297127 Henry Cohn, 2026.
7 46 0.333312302683 Henry Cohn, 2026.
7 47 0.333332883018 Henry Cohn, 2026.
7 56* 0.333333333334 T. Gosset, On the regular and semi-regular figures in space of n dimensions, Messenger Math. 29 (1900), 43–48; V. I. Levenšteĭn, On bounds for packings in n-dimensional Euclidean space (Russian), Dokl. Akad. Nauk SSSR 245 (1979), 1299–1303, English translation in Soviet Math. Dokl. 20 (1979), 417–421.
3⁢x−1
7 57 0.389612708410 Henry Cohn, 2025.
7 58 0.393749423280 Henry Cohn, 2023.
7 59 0.403217495108 Henry Cohn, 2025.
7 60 0.407983464085 Henry Cohn, 2025.
7 61 0.412356098716 Henry Cohn, 2024.
7 62 0.414165742036 Henry Cohn, 2026.
7 63 0.415390831033 Henry Cohn, 2025.
7 64 0.420197073744 Henry Cohn, 2025.
7 67 0.421258543571 Henry Cohn, 2024.
622⁢x3−771⁢x2+288⁢x−31
7 68 0.427637413233 Henry Cohn, 2026.
7 69 0.428316243154 Henry Cohn, 2026.
7 70 0.428552368060 Henry Cohn, 2026.
7 78 0.428571428572 T. Ericson and V. Zinoviev, Spherical codes generated by binary partitions of symmetric pointsets, IEEE Trans. Inform. Theory 41 (1995), 107–129, doi:10.1109/18.370114.
7⁢x−3
7 79 0.452754163206 Henry Cohn, 2026.
7 80 0.453887992064 Henry Cohn, 2024.
7 81 0.458141126431 Henry Cohn, 2026.
7 82 0.459673068887 A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
7 83 0.460413485151 A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
7 84 0.464981341724 Henry Cohn, 2026, needs more optimization.
7 86 0.466580867327 Henry Cohn, 2025, needs more optimization.
7 87 0.469578821552 Henry Cohn, 2024.
7 88 0.471422440239 A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
7 89 0.474245162133 Henry Cohn, 2026, needs more optimization.
7 90 0.475294477919 Henry Cohn, 2024.
7 91 0.477365257014 Henry Cohn, 2026.
7 92 0.480306853225 Henry Cohn, 2025.
7 93 0.481807408321 Henry Cohn, 2026.
7 95 0.482130625709 Henry Cohn, 2026, needs more optimization.
7 96 0.482651330945 Henry Cohn, 2026.
7 97 0.486842071201 A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
7 98 0.489141129031 Henry Cohn, 2026.
7 99 0.493009413613 A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
7 100 0.494295597580 Henry Cohn, 2026, needs more optimization.
7 101 0.495171315420 A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
7 102 0.496162296397 Henry Cohn, 2026.
7 103 0.496798416963 Henry Cohn, 2026, needs more optimization.
7 104 0.497401637455 Henry Cohn, 2026, needs more optimization.
7 105 0.497982353835 Henry Cohn, 2026, needs more optimization.
7 106 0.498675447305 Henry Cohn, 2026.
7 107 0.499020848953 Henry Cohn, 2026, needs more optimization.
7 108 0.499492029355 Henry Cohn, 2026, needs more optimization.
7 109 0.499931101507 Henry Cohn, 2026, needs more optimization.
7 110 0.499969840621 Henry Cohn, 2026, needs more optimization.
7 111 0.499998590950 Henry Cohn, 2026, needs more optimization.
7 112 0.499999832934 Henry Cohn, 2026, needs more optimization.
7 126 0.5 A. Korkine and G. Zolotareff, Sur les formes quadratiques, Math. Ann. 6 (1873), 366–389, doi:10.1007/BF01442795; J. Leech, Six and seven dimensional non-lattice sphere packings, Canad. Math. Bull. 12 (1969), 151–155, doi:10.4153/CMB-1969-014-1; J. H. Conway and N. J. A. Sloane, What are all the best sphere packings in low dimensions?, Discrete Comput. Geom. 13 (1995), 383–403, doi:10.1007/BF02574051; H. Cohn, Y. Jiao, A. Kumar, and S. Torquato, Rigidity of spherical codes, Geom. Topol. 15 (2011), 2235–2273, doi:10.2140/gt.2011.15.2235, arXiv:1102.5060.
2⁢x−1
7 127 0.509952460664 A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
7 128 0.513834831907 Henry Cohn, 2026.
7 129 0.518758185595 Henry Cohn, 2026.
7 130 0.518780653650 Henry Cohn, 2026, needs more optimization.
7 133 0.519150244844 Henry Cohn, 2026, needs more optimization.
7 134 0.519150249448 Henry Cohn, 2026, needs more optimization.
7 135 0.519150255859 Henry Cohn, 2026, needs more optimization.
7 136 0.519153914324 Henry Cohn, 2026, needs more optimization.
7 137 0.519751518195 Henry Cohn, 2024.
7 138 0.527218738805 Henry Cohn, 2025.
7 139 0.530442894021 Henry Cohn, 2026, needs more optimization.
7 143 0.531592013892 Henry Cohn, 2026, needs more optimization.
7 144 0.531632269397 Henry Cohn, 2026, needs more optimization.
7 145 0.532533319720 Henry Cohn, 2026, needs more optimization.
7 146 0.532826481234 Henry Cohn, 2026, needs more optimization.
7 147 0.533479772596 Henry Cohn, 2024.
7 148 0.533995828316 Henry Cohn, 2026.
7 149 0.545945800422 Henry Cohn, 2026, needs more optimization.
7 150 0.545968828033 Henry Cohn, 2026, needs more optimization.
7 151 0.545970680607 Henry Cohn, 2026, needs more optimization.
7 152 0.546227197848 Henry Cohn, 2026, needs more optimization.
7 153 0.546231403910 Henry Cohn, 2026, needs more optimization.
7 154 0.546280407518 Henry Cohn, 2026, needs more optimization.
7 155 0.546473189225 Henry Cohn, 2026, needs more optimization.
7 156 0.552232059368 Henry Cohn, 2026, needs more optimization.
7 157 0.557005228514 Henry Cohn, 2026, needs more optimization.
7 158 0.558187412475 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
7 159 0.559254866910 Henry Cohn, 2026, needs more optimization.
7 160 0.559629487809 Henry Cohn, 2026, needs more optimization.
7 161 0.559629487822 Henry Cohn, 2026, needs more optimization.
7 162 0.559666725356 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
7 165 0.561660700022 Henry Cohn, 2026, needs more optimization.
7 168 0.561688600449 Henry Cohn, 2026, needs more optimization.
7 169 0.562559500091 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
7 170 0.563591813282 Henry Cohn, 2026, needs more optimization.
7 171 0.568958802433 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
7 172 0.569967220130 Henry Cohn, 2026, needs more optimization.
7 173 0.569967220168 Henry Cohn, 2026, needs more optimization.
7 174 0.569967822211 Henry Cohn, 2026, needs more optimization.
7 175 0.569967823281 Henry Cohn, 2026, needs more optimization.
7 176 0.570443305498 Henry Cohn, 2026, needs more optimization.
7 177 0.570453557788 Henry Cohn, 2026, needs more optimization.
7 178 0.570455567324 Henry Cohn, 2026, needs more optimization.
7 179 0.570548684102 Henry Cohn, 2026, needs more optimization.
7 180 0.570548702608 Henry Cohn, 2026, needs more optimization.
7 181 0.573146386876 Henry Cohn, 2026, needs more optimization.
7 182 0.577350269190 J. H. Conway, R. H. Hardin, and N. J. A. Sloane, Packing lines, planes, etc.: packings in Grassmannian spaces, Experiment. Math. 5 (1996), 139–159, https://projecteuclid.org/euclid.em/1047565645; B. Ballinger, G. Blekherman, H. Cohn, N. Giansiracusa, E. Kelly, and A. Schürmann, Experimental study of energy-minimizing point configurations on spheres, Experiment. Math. 18 (2009), 257–283, https://projecteuclid.org/euclid.em/1259158465.
3⁢x2−1
7 183 0.586919243616 Henry Cohn, 2026, needs more optimization.
7 184 0.589764306579 Henry Cohn, 2026, needs more optimization.
7 200 0.590112298788 Henry Cohn, 2026.
19⁢x3−9⁢x2−3⁢x+1
7 201 0.595100499739 Henry Cohn, 2026, needs more optimization.
7 202 0.598322408533 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
7 203 0.600574811824 Henry Cohn, 2026, needs more optimization.
7 204 0.601296346692 Henry Cohn, 2026, needs more optimization.
7 205 0.602637729064 Henry Cohn, 2026, needs more optimization.
7 206 0.603221072328 Henry Cohn, 2026, needs more optimization.
7 207 0.603909348132 Henry Cohn, 2026, needs more optimization.
7 208 0.606748586252 Henry Cohn, 2026, needs more optimization.
7 209 0.608544792589 Henry Cohn, 2026, needs more optimization.
7 210 0.610377583198 Henry Cohn, 2026, needs more optimization.
7 211 0.611215933412 Henry Cohn, 2026, needs more optimization.
7 212 0.612379041439 Henry Cohn, 2026, needs more optimization.
7 213 0.612935838189 Henry Cohn, 2026, needs more optimization.
7 214 0.613776590824 Henry Cohn, 2026, needs more optimization.
7 215 0.615174862325 Henry Cohn, 2026, needs more optimization.
7 216 0.615210534621 Henry Cohn, 2026, needs more optimization.
7 217 0.616416253734 Henry Cohn, 2026, needs more optimization.
7 218 0.617959361717 Henry Cohn, 2026, needs more optimization.
7 219 0.618773626741 Henry Cohn, 2026, needs more optimization.
7 220 0.618780648308 Henry Cohn, 2026, needs more optimization.
7 221 0.619615759972 Henry Cohn, 2026, needs more optimization.
7 222 0.619875245336 Henry Cohn, 2026, needs more optimization.
7 223 0.620004427691 Henry Cohn, 2026, needs more optimization.
7 224 0.623022635017 Henry Cohn, 2026, needs more optimization.
7 225 0.623054540881 Henry Cohn, 2026, needs more optimization.
7 226 0.623137563593 Henry Cohn, 2026, needs more optimization.
7 227 0.625163019184 Henry Cohn, 2026, needs more optimization.
7 228 0.625191082100 Henry Cohn, 2026, needs more optimization.
7 229 0.625803430005 Henry Cohn, 2026, needs more optimization.
7 230 0.626063443769 Henry Cohn, 2026, needs more optimization.
7 231 0.626309578850 Henry Cohn, 2026, needs more optimization.
7 232 0.627133597274 Henry Cohn, 2026, needs more optimization.
7 233 0.627561708337 Henry Cohn, 2026, needs more optimization.
7 234 0.627632655141 Henry Cohn, 2026, needs more optimization.
7 235 0.627716874874 Henry Cohn, 2026, needs more optimization.
7 236 0.628404918842 Henry Cohn, 2026, needs more optimization.
7 237 0.629685567831 Henry Cohn, 2026, needs more optimization.
7 238 0.629695173156 Henry Cohn, 2026, needs more optimization.
7 239 0.630338110573 Henry Cohn, 2026, needs more optimization.
7 240 0.630934248737 Henry Cohn, 2026, needs more optimization.
7 241 0.631242226442 Henry Cohn, 2026, needs more optimization.
7 242 0.633309713080 Henry Cohn, 2026, needs more optimization.
7 243 0.633557783425 Henry Cohn, 2026, needs more optimization.
7 244 0.633929113732 Henry Cohn, 2026, needs more optimization.
7 245 0.634447386247 Henry Cohn, 2026, needs more optimization.
7 246 0.634589034077 Henry Cohn, 2026, needs more optimization.
7 247 0.634826323148 Henry Cohn, 2026, needs more optimization.
7 248 0.634856487061 Henry Cohn, 2026, needs more optimization.
7 249 0.636496107317 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
7 250 0.636593026707 Henry Cohn, 2026, needs more optimization.
7 251 0.636625670362 Henry Cohn, 2026, needs more optimization.
7 252 0.637091812074 Henry Cohn, 2026, needs more optimization.
7 253 0.638298684868 Henry Cohn, 2026, needs more optimization.
7 254 0.638945447024 Henry Cohn, 2026, needs more optimization.
7 255 0.638946148909 Henry Cohn, 2026, needs more optimization.
7 256 0.639080183093 Henry Cohn, 2026, needs more optimization.
7 257 0.639816414016 Henry Cohn, 2026, needs more optimization.
7 258 0.640993582564 Henry Cohn, 2026, needs more optimization.
7 259 0.641101328593 Henry Cohn, 2026, needs more optimization.
7 260 0.641255381360 Henry Cohn, 2026, needs more optimization.
7 261 0.641546317885 Henry Cohn, 2026, needs more optimization.
7 262 0.642501832384 Henry Cohn, 2026, needs more optimization.
7 263 0.644822287142 Henry Cohn, 2026, needs more optimization.
7 264 0.645646991072 Henry Cohn, 2026, needs more optimization.
7 265 0.645810545984 Henry Cohn, 2026, needs more optimization.
7 266 0.646303210485 Henry Cohn, 2026, needs more optimization.
7 267 0.646964942216 Henry Cohn, 2026, needs more optimization.
7 268 0.647232419592 Henry Cohn, 2026, needs more optimization.
7 269 0.647812506178 Henry Cohn, 2026, needs more optimization.
7 270 0.648433997586 Henry Cohn, 2026, needs more optimization.
7 271 0.648619130045 Henry Cohn, 2026, needs more optimization.
7 272 0.649000173187 Henry Cohn, 2026, needs more optimization.
7 273 0.649490686035 Henry Cohn, 2026, needs more optimization.
7 274 0.649775453908 Henry Cohn, 2026, needs more optimization.
7 275 0.650332261444 Henry Cohn, 2026, needs more optimization.
7 276 0.650583453320 Henry Cohn, 2026, needs more optimization.
7 277 0.651291978538 Henry Cohn, 2026, needs more optimization.
7 278 0.651802413995 Henry Cohn, 2026, needs more optimization.
7 279 0.652267649771 Henry Cohn, 2026, needs more optimization.
7 280 0.652736826607 Henry Cohn, 2026, needs more optimization.
7 281 0.653339322901 Henry Cohn, 2026, needs more optimization.
7 282 0.653583660739 Henry Cohn, 2026, needs more optimization.
7 283 0.654058100379 Henry Cohn, 2026, needs more optimization.
7 284 0.654523381149 Henry Cohn, 2026, needs more optimization.
7 285 0.655131843915 Henry Cohn, 2026, needs more optimization.
7 286 0.655476610741 Henry Cohn, 2026, needs more optimization.
7 287 0.655809019433 Henry Cohn, 2026, needs more optimization.
7 288 0.656403355437 Henry Cohn, 2026, needs more optimization.
7 289 0.656861610890 Henry Cohn, 2026, needs more optimization.
7 290 0.657204781659 Henry Cohn, 2026, needs more optimization.
7 291 0.657460114727 Henry Cohn, 2026, needs more optimization.
7 292 0.658026386457 Henry Cohn, 2026, needs more optimization.
7 293 0.658403206318 Henry Cohn, 2026, needs more optimization.
7 294 0.658956528355 Henry Cohn, 2026, needs more optimization.
7 295 0.659122299970 Henry Cohn, 2026, needs more optimization.
7 296 0.659590716939 Henry Cohn, 2026, needs more optimization.
7 297 0.660007999656 Henry Cohn, 2026, needs more optimization.
7 298 0.660379816669 Henry Cohn, 2026, needs more optimization.
7 299 0.660982406034 Henry Cohn, 2026, needs more optimization.
7 300 0.661146169087 Henry Cohn, 2026, needs more optimization.
7 301 0.661602477909 Henry Cohn, 2026, needs more optimization.
7 302 0.661953970037 Henry Cohn, 2026, needs more optimization.
7 303 0.662611760783 Henry Cohn, 2026, needs more optimization.
7 304 0.663012161151 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
7 305 0.663349875959 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
7 317 0.663638178073 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
7 318 0.663871007993 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
7 319 0.664473191028 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
7 320 0.664759128799 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
7 322 0.665130469651 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
7 323 0.665323806596 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
7 324 0.665597950322 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
7 325 0.665932421263 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
7 331 0.666159937508 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
7 332 0.666179661568 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
7 333 0.666200099386 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
7 334 0.666330611299 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
7 335 0.666582929490 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
7 358 0.666666666667 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
3⁢x−2
7 359 0.668524326903 Henry Cohn, 2026, needs more optimization.
7 360 0.669362934454 Henry Cohn, 2026, needs more optimization.
7 361 0.669633423534 Henry Cohn, 2026, needs more optimization.
7 362 0.670192266698 Henry Cohn, 2026, needs more optimization.
7 363 0.670750854808 Henry Cohn, 2026, needs more optimization.
7 364 0.671294151256 Henry Cohn, 2026, needs more optimization.
7 365 0.671887914819 Henry Cohn, 2026, needs more optimization.
7 366 0.671934467982 Henry Cohn, 2026, needs more optimization.
7 367 0.672593553132 Henry Cohn, 2026, needs more optimization.
7 368 0.673276431317 Henry Cohn, 2026, needs more optimization.
7 369 0.673356851237 Henry Cohn, 2026, needs more optimization.
7 370 0.673506275826 Henry Cohn, 2026, needs more optimization.
7 371 0.673673235376 Henry Cohn, 2026, needs more optimization.
7 372 0.673937352186 Henry Cohn, 2026, needs more optimization.
7 373 0.675200736321 Henry Cohn, 2026, needs more optimization.
7 374 0.675806886522 Henry Cohn, 2026, needs more optimization.
7 375 0.676163660398 Henry Cohn, 2026, needs more optimization.
7 376 0.676760592707 Henry Cohn, 2026, needs more optimization.
7 377 0.676809608599 Henry Cohn, 2026, needs more optimization.
7 378 0.676962650280 Henry Cohn, 2026, needs more optimization.
7 379 0.676977902382 Henry Cohn, 2026, needs more optimization.
7 380 0.676998252678 Henry Cohn, 2026, needs more optimization.
7 381 0.677298292136 Henry Cohn, 2026, needs more optimization.
7 382 0.677313961837 Henry Cohn, 2026, needs more optimization.
7 383 0.677793975325 Henry Cohn, 2026, needs more optimization.
7 384 0.678284117476 Henry Cohn, 2026, needs more optimization.
7 385 0.678930053296 Henry Cohn, 2026, needs more optimization.
7 386 0.678973104605 Henry Cohn, 2026, needs more optimization.
7 387 0.679089823851 Henry Cohn, 2026, needs more optimization.
7 388 0.679579343842 Henry Cohn, 2026, needs more optimization.
7 389 0.679582785099 Henry Cohn, 2026, needs more optimization.
7 390 0.679898697993 Henry Cohn, 2026, needs more optimization.
7 391 0.680012075497 Henry Cohn, 2026, needs more optimization.
7 392 0.680112251936 Henry Cohn, 2026, needs more optimization.
7 393 0.680133869715 Henry Cohn, 2026, needs more optimization.
7 394 0.680145976056 Henry Cohn, 2026, needs more optimization.
7 395 0.680181943762 Henry Cohn, 2026, needs more optimization.
7 396 0.680430985281 Henry Cohn, 2026, needs more optimization.
7 397 0.680478074788 Henry Cohn, 2026, needs more optimization.
7 398 0.680540592144 Henry Cohn, 2026, needs more optimization.
7 399 0.681184384065 Henry Cohn, 2026, needs more optimization.
7 400 0.681382835472 Henry Cohn, 2026, needs more optimization.
7 401 0.681531294911 Henry Cohn, 2026, needs more optimization.
7 402 0.681925709228 Henry Cohn, 2026, needs more optimization.
7 403 0.681942722757 Henry Cohn, 2026, needs more optimization.
7 404 0.681944576172 Henry Cohn, 2026, needs more optimization.
7 405 0.683014355076 Henry Cohn, 2026, needs more optimization.
7 406 0.683122911717 Henry Cohn, 2026, needs more optimization.
7 407 0.683131889767 Henry Cohn, 2026, needs more optimization.
7 408 0.683324558743 Henry Cohn, 2026, needs more optimization.
7 409 0.683522563849 Henry Cohn, 2026, needs more optimization.
7 410 0.683564453737 Henry Cohn, 2026, needs more optimization.
7 411 0.683850126867 Henry Cohn, 2026, needs more optimization.
7 412 0.683974398230 Henry Cohn, 2026, needs more optimization.
7 413 0.684194302985 Henry Cohn, 2026, needs more optimization.
7 414 0.684215379852 Henry Cohn, 2026, needs more optimization.
7 415 0.684386975602 Henry Cohn, 2026, needs more optimization.
7 416 0.684415644831 Henry Cohn, 2026, needs more optimization.
7 417 0.684607910519 Henry Cohn, 2026, needs more optimization.
7 418 0.685261415247 Henry Cohn, 2026, needs more optimization.
7 419 0.686233220403 Henry Cohn, 2026, needs more optimization.
7 420 0.686400987840 Henry Cohn, 2026, needs more optimization.
7 421 0.686718066076 Henry Cohn, 2026, needs more optimization.
7 422 0.686962430420 Henry Cohn, 2026, needs more optimization.
7 423 0.687037857651 Henry Cohn, 2026, needs more optimization.
7 424 0.687898696693 Henry Cohn, 2026, needs more optimization.
7 425 0.688098483065 Henry Cohn, 2026, needs more optimization.
7 426 0.688867189582 Henry Cohn, 2026, needs more optimization.
7 427 0.690228210548 Henry Cohn, 2026, needs more optimization.
7 428 0.690512498853 Henry Cohn, 2026, needs more optimization.
7 429 0.691157592897 Henry Cohn, 2026, needs more optimization.
7 430 0.691234875468 Henry Cohn, 2026, needs more optimization.
7 431 0.691622823482 Henry Cohn, 2026, needs more optimization.
7 432 0.692316013565 Henry Cohn, 2026, needs more optimization.
7 433 0.692785364192 Henry Cohn, 2026, needs more optimization.
7 434 0.693144095516 Henry Cohn, 2026, needs more optimization.
7 435 0.693317159696 Henry Cohn, 2026, needs more optimization.
7 436 0.693606068806 Henry Cohn, 2026, needs more optimization.
7 437 0.693780989751 Henry Cohn, 2026, needs more optimization.
7 438 0.694193869810 Henry Cohn, 2026, needs more optimization.
7 439 0.694708629234 Henry Cohn, 2026, needs more optimization.
7 440 0.694966341333 Henry Cohn, 2026, needs more optimization.
7 441 0.695497445489 Henry Cohn, 2026, needs more optimization.
7 442 0.695855269381 Henry Cohn, 2026, needs more optimization.
7 443 0.696444008646 Henry Cohn, 2026, needs more optimization.
7 444 0.696495505221 Henry Cohn, 2026, needs more optimization.
7 445 0.696698695314 Henry Cohn, 2026, needs more optimization.
7 446 0.697147792071 Henry Cohn, 2026, needs more optimization.
7 447 0.697640162255 Henry Cohn, 2026, needs more optimization.
7 448 0.697706430517 Henry Cohn, 2026, needs more optimization.
7 449 0.698098872397 Henry Cohn, 2026, needs more optimization.
7 450 0.698801985717 Henry Cohn, 2026, needs more optimization.
7 451 0.699251286895 Henry Cohn, 2026, needs more optimization.
7 452 0.699351971029 Henry Cohn, 2026, needs more optimization.
7 453 0.699857211535 Henry Cohn, 2026, needs more optimization.
7 454 0.700493465313 Henry Cohn, 2026, needs more optimization.
7 455 0.700558461835 Henry Cohn, 2026, needs more optimization.
7 456 0.700652153915 Henry Cohn, 2026, needs more optimization.
7 457 0.700916626194 Henry Cohn, 2026, needs more optimization.
7 458 0.701284612188 Henry Cohn, 2026, needs more optimization.
7 459 0.701931689384 Henry Cohn, 2026, needs more optimization.
7 460 0.701984570679 Henry Cohn, 2026, needs more optimization.
7 461 0.702808776248 Henry Cohn, 2026, needs more optimization.
7 462 0.703366256347 Henry Cohn, 2026, needs more optimization.
7 463 0.703465407763 Henry Cohn, 2026, needs more optimization.
7 464 0.703890297078 Henry Cohn, 2026, needs more optimization.
7 465 0.704390331801 Henry Cohn, 2026, needs more optimization.
7 466 0.705191396460 Henry Cohn, 2026, needs more optimization.
7 467 0.705384604671 Henry Cohn, 2026, needs more optimization.
7 468 0.705696405538 Henry Cohn, 2026, needs more optimization.
7 469 0.705782722313 Henry Cohn, 2026, needs more optimization.
7 470 0.705921295367 Henry Cohn, 2026, needs more optimization.
7 471 0.706004701882 Henry Cohn, 2026, needs more optimization.
7 472 0.706072943599 Henry Cohn, 2026, needs more optimization.
7 473 0.706244259870 Henry Cohn, 2026, needs more optimization.
7 474 0.706519616782 Henry Cohn, 2026, needs more optimization.
7 475 0.706528776780 Henry Cohn, 2026, needs more optimization.
7 476 0.706666821255 Henry Cohn, 2026, needs more optimization.
7 477 0.706795715477 Henry Cohn, 2026, needs more optimization.
7 478 0.706880230853 Henry Cohn, 2026, needs more optimization.
7 479 0.706936423153 Henry Cohn, 2026, needs more optimization.
7 480 0.707050865122 Henry Cohn, 2026, needs more optimization.
7 481 0.707570435981 Henry Cohn, 2026, needs more optimization.
7 482 0.707629643609 Henry Cohn, 2026, needs more optimization.
7 483 0.707634289530 Henry Cohn, 2026, needs more optimization.
7 484 0.707637005315 Henry Cohn, 2026, needs more optimization.
7 485 0.707661866907 Henry Cohn, 2026, needs more optimization.
7 486 0.707715887074 Henry Cohn, 2026, needs more optimization.
7 487 0.707747171821 Henry Cohn, 2026, needs more optimization.
7 488 0.707829956962 Henry Cohn, 2026, needs more optimization.
7 489 0.707993718920 Henry Cohn, 2026, needs more optimization.
7 490 0.708046573854 Henry Cohn, 2026, needs more optimization.
7 491 0.708186322374 Henry Cohn, 2026, needs more optimization.
7 492 0.708188834945 Henry Cohn, 2026, needs more optimization.
7 493 0.708432526370 Henry Cohn, 2026, needs more optimization.
7 494 0.708855033052 Henry Cohn, 2026, needs more optimization.
7 495 0.709113739608 Henry Cohn, 2026, needs more optimization.
7 496 0.709116102520 Henry Cohn, 2026, needs more optimization.
7 497 0.709157745575 Henry Cohn, 2026, needs more optimization.
7 498 0.709273334443 Henry Cohn, 2026, needs more optimization.
7 500 0.709935789111 Henry Cohn, 2026, needs more optimization.
7 501 0.709936940114 Henry Cohn, 2026, needs more optimization.
7 502 0.710429090175 Henry Cohn, 2026, needs more optimization.
7 503 0.710492579368 Henry Cohn, 2026, needs more optimization.
7 504 0.710930565964 Henry Cohn, 2026, needs more optimization.
7 505 0.710931621745 Henry Cohn, 2026, needs more optimization.
7 506 0.710981468568 Henry Cohn, 2026, needs more optimization.
7 507 0.711080748912 Henry Cohn, 2026, needs more optimization.
7 508 0.711106286765 Henry Cohn, 2026, needs more optimization.
7 509 0.711201193804 Henry Cohn, 2026, needs more optimization.
7 510 0.711293614481 Henry Cohn, 2026, needs more optimization.
7 511 0.711363138156 Henry Cohn, 2026, needs more optimization.
7 512 0.711454751022 Henry Cohn, 2026, needs more optimization.
7 513 0.712172148167 Henry Cohn, 2026, needs more optimization.
7 514 0.712172858516 Henry Cohn, 2026, needs more optimization.
7 515 0.712174332932 Henry Cohn, 2026, needs more optimization.
7 516 0.712187605666 Henry Cohn, 2026, needs more optimization.
7 517 0.712210894377 Henry Cohn, 2026, needs more optimization.
7 518 0.712340678491 Henry Cohn, 2026, needs more optimization.
7 519 0.712372645069 Henry Cohn, 2026, needs more optimization.
7 520 0.712553554036 Henry Cohn, 2026, needs more optimization.
7 521 0.713126624328 Henry Cohn, 2026, needs more optimization.
7 522 0.713132305300 Henry Cohn, 2026, needs more optimization.
7 524 0.713132896741 Henry Cohn, 2026, needs more optimization.
7 525 0.713134779217 Henry Cohn, 2026, needs more optimization.
7 526 0.713136835087 Henry Cohn, 2026, needs more optimization.
7 527 0.713137350184 Henry Cohn, 2026, needs more optimization.
7 528 0.713143950997 Henry Cohn, 2026, needs more optimization.
7 529 0.713152366595 Henry Cohn, 2026, needs more optimization.
7 530 0.713308933799 Henry Cohn, 2026, needs more optimization.
7 531 0.713362812455 Henry Cohn, 2026, needs more optimization.
7 532 0.713415585593 Henry Cohn, 2026, needs more optimization.
7 533 0.713447851179 Henry Cohn, 2026, needs more optimization.
7 534 0.713451763297 Henry Cohn, 2026, needs more optimization.
7 535 0.713464596245 Henry Cohn, 2026, needs more optimization.
7 536 0.713491164389 Henry Cohn, 2026, needs more optimization.
7 537 0.713746154014 Henry Cohn, 2026, needs more optimization.
7 539 0.713788845727 Henry Cohn, 2026, needs more optimization.
7 540 0.713839038701 Henry Cohn, 2026, needs more optimization.
7 541 0.713901633998 Henry Cohn, 2026, needs more optimization.
7 542 0.713936687068 Henry Cohn, 2026, needs more optimization.
7 543 0.713972306627 Henry Cohn, 2026, needs more optimization.
7 544 0.714029273930 Henry Cohn, 2026, needs more optimization.
7 545 0.714047757773 Henry Cohn, 2026, needs more optimization.
7 546 0.714051910825 Henry Cohn, 2026, needs more optimization.
7 547 0.714053471320 Henry Cohn, 2026, needs more optimization.
7 548 0.714092438509 Henry Cohn, 2026, needs more optimization.
7 632 0.714285714286 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
7⁢x−5
7 633 0.718298267267 Henry Cohn, 2026, needs more optimization.
7 634 0.720002200382 Henry Cohn, 2026, needs more optimization.
7 635 0.721178151504 Henry Cohn, 2026, needs more optimization.
7 636 0.722117626408 Henry Cohn, 2026, needs more optimization.
7 637 0.722898526698 Henry Cohn, 2026, needs more optimization.
7 638 0.723678523364 Henry Cohn, 2026, needs more optimization.
7 639 0.724493655784 Henry Cohn, 2026, needs more optimization.
7 640 0.724992099175 Henry Cohn, 2026, needs more optimization.
7 641 0.725507835139 Henry Cohn, 2026, needs more optimization.
7 642 0.726057488486 Henry Cohn, 2026, needs more optimization.
7 643 0.726414329907 Henry Cohn, 2026, needs more optimization.
7 644 0.726762948360 Henry Cohn, 2026, needs more optimization.
7 645 0.727066173475 Henry Cohn, 2026, needs more optimization.
7 646 0.727511927558 Henry Cohn, 2026, needs more optimization.
7 647 0.727892829965 Henry Cohn, 2026, needs more optimization.
7 648 0.728306822468 Henry Cohn, 2026, needs more optimization.
7 649 0.728641434809 Henry Cohn, 2026, needs more optimization.
7 650 0.729053750309 Henry Cohn, 2026, needs more optimization.
7 651 0.729293304752 Henry Cohn, 2026, needs more optimization.
7 652 0.729541483668 Henry Cohn, 2026, needs more optimization.
7 653 0.729774984146 Henry Cohn, 2026, needs more optimization.
7 654 0.729975597506 Henry Cohn, 2026, needs more optimization.
7 655 0.730234409912 Henry Cohn, 2026, needs more optimization.
7 656 0.730552179793 Henry Cohn, 2026, needs more optimization.
7 657 0.730808205041 Henry Cohn, 2026, needs more optimization.
7 658 0.731114394228 Henry Cohn, 2026, needs more optimization.
7 659 0.731366920508 Henry Cohn, 2026, needs more optimization.
7 660 0.731486966907 Henry Cohn, 2026, needs more optimization.
7 661 0.731863844742 Henry Cohn, 2026, needs more optimization.
7 662 0.732087908448 Henry Cohn, 2026, needs more optimization.
7 663 0.732304909454 Henry Cohn, 2026, needs more optimization.
7 664 0.732496837853 Henry Cohn, 2026, needs more optimization.
7 665 0.732896068692 Henry Cohn, 2026, needs more optimization.
7 666 0.733212851171 Henry Cohn, 2026, needs more optimization.
7 667 0.733492079890 Henry Cohn, 2026, needs more optimization.
7 668 0.733758159494 Henry Cohn, 2026, needs more optimization.
7 669 0.734019369179 Henry Cohn, 2026, needs more optimization.
7 670 0.734308453025 Henry Cohn, 2026, needs more optimization.
7 671 0.734584924202 Henry Cohn, 2026, needs more optimization.
7 672 0.734847302605 Henry Cohn, 2026, needs more optimization.
7 673 0.735093146982 Henry Cohn, 2026, needs more optimization.
7 674 0.735512251064 Henry Cohn, 2026, needs more optimization.
7 675 0.735688762060 Henry Cohn, 2026, needs more optimization.
7 676 0.735874218556 Henry Cohn, 2026, needs more optimization.
7 677 0.736127950356 Henry Cohn, 2026, needs more optimization.
7 678 0.736345247240 Henry Cohn, 2026, needs more optimization.
7 679 0.736580921128 Henry Cohn, 2026, needs more optimization.
7 680 0.736864059165 Henry Cohn, 2026, needs more optimization.
7 681 0.737096385108 Henry Cohn, 2026, needs more optimization.
7 682 0.737349022300 Henry Cohn, 2026, needs more optimization.
7 683 0.737495491158 Henry Cohn, 2026, needs more optimization.
7 684 0.737632301274 Henry Cohn, 2026, needs more optimization.
7 685 0.737758345981 Henry Cohn, 2026, needs more optimization.
7 686 0.737989016417 Henry Cohn, 2026, needs more optimization.
7 688 0.737989951497 Henry Cohn, 2026, needs more optimization.
7 689 0.737991962928 Henry Cohn, 2026, needs more optimization.
7 691 0.738395197610 Henry Cohn, 2026, needs more optimization.
7 693 0.738395355564 Henry Cohn, 2026, needs more optimization.
7 694 0.738395413874 Henry Cohn, 2026, needs more optimization.
7 695 0.738395607664 Henry Cohn, 2026, needs more optimization.
7 696 0.738395677203 Henry Cohn, 2026, needs more optimization.
7 697 0.738395865402 Henry Cohn, 2026, needs more optimization.
7 699 0.738456115126 Henry Cohn, 2026, needs more optimization.
7 700 0.738654004337 Henry Cohn, 2026, needs more optimization.
7 701 0.739113594985 Henry Cohn, 2026, needs more optimization.
7 702 0.739266963736 Henry Cohn, 2026, needs more optimization.
7 703 0.739875175967 Henry Cohn, 2026, needs more optimization.
7 704 0.739899490843 Henry Cohn, 2026, needs more optimization.
7 705 0.739963753355 Henry Cohn, 2026, needs more optimization.
7 706 0.740009271381 Henry Cohn, 2026, needs more optimization.
7 707 0.740045549372 Henry Cohn, 2026, needs more optimization.
7 708 0.740059722230 Henry Cohn, 2026, needs more optimization.
7 709 0.740076922751 Numaro AI Autoresearch, 11,000+ New Verified Spherical-Code Records from AI Autoresearch, Numaro Research Report NUMARO-2026-015 (2026), https://numaro.tech/research/spherical-codes-2026/.
7 710 0.740181377611 Henry Cohn, 2026, needs more optimization.
7 711 0.740846308161 Henry Cohn, 2026, needs more optimization.
7 712 0.740846587614 Henry Cohn, 2026, needs more optimization.
7 713 0.740850252105 Henry Cohn, 2026, needs more optimization.
7 714 0.740855937549 Henry Cohn, 2026, needs more optimization.
7 733 0.744904412220 Henry Cohn, 2026, needs more optimization.
7 734 0.749190096013 Henry Cohn, 2026, needs more optimization.
7 735 0.749318376384 Henry Cohn, 2026, needs more optimization.
7 736 0.749503126972 Henry Cohn, 2026, needs more optimization.
7 737 0.749709123688 Henry Cohn, 2026, needs more optimization.
7 739 0.749838697083 Henry Cohn, 2026, needs more optimization.
7 740 0.749991793491 Henry Cohn, 2026, needs more optimization.
7 882 0.75 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
4⁢x−3
7 883 0.755753482894 Numaro AI Autoresearch, 11,000+ New Verified Spherical-Code Records from AI Autoresearch, Numaro Research Report NUMARO-2026-015 (2026), https://numaro.tech/research/spherical-codes-2026/.
7 884 0.766403667871 Henry Cohn, 2026, needs more optimization.
7 885 0.766503949399 Henry Cohn, 2026, needs more optimization.
7 886 0.766515797369 Henry Cohn, 2026, needs more optimization.
7 887 0.766833399074 Henry Cohn, 2026, needs more optimization.
7 888 0.766868178575 Henry Cohn, 2026, needs more optimization.
7 889 0.766869770381 Henry Cohn, 2026, needs more optimization.
7 890 0.766985366355 Henry Cohn, 2026, needs more optimization.
7 891 0.767019985987 Henry Cohn, 2026, needs more optimization.
7 893 0.767218317122 Henry Cohn, 2026, needs more optimization.
7 894 0.767234147504 Henry Cohn, 2026, needs more optimization.
7 895 0.767377575423 Henry Cohn, 2026, needs more optimization.
7 896 0.767393009928 Henry Cohn, 2026, needs more optimization.
7 897 0.767655605179 Henry Cohn, 2026, needs more optimization.
7 898 0.767719598031 Henry Cohn, 2026, needs more optimization.
7 899 0.767726215836 Henry Cohn, 2026, needs more optimization.
7 900 0.767761353429 Henry Cohn, 2026, needs more optimization.
7 901 0.767950576516 Henry Cohn, 2026, needs more optimization.
7 902 0.767962822017 Henry Cohn, 2026, needs more optimization.
7 903 0.768082739926 Henry Cohn, 2026, needs more optimization.
7 904 0.768127097499 Henry Cohn, 2026, needs more optimization.
7 905 0.768334718572 Henry Cohn, 2026, needs more optimization.
7 906 0.768375038473 Henry Cohn, 2026, needs more optimization.
7 907 0.768506317437 Henry Cohn, 2026, needs more optimization.
7 908 0.768561226536 Henry Cohn, 2026, needs more optimization.
7 909 0.768678675860 Henry Cohn, 2026, needs more optimization.
7 910 0.768710997688 Henry Cohn, 2026, needs more optimization.
7 911 0.768759423064 Henry Cohn, 2026, needs more optimization.
7 912 0.768901383815 Henry Cohn, 2026, needs more optimization.
7 913 0.768910403814 Henry Cohn, 2026, needs more optimization.
7 914 0.768913175132 Henry Cohn, 2026, needs more optimization.
7 915 0.769134615071 Henry Cohn, 2026, needs more optimization.
7 916 0.769165899544 Henry Cohn, 2026, needs more optimization.
7 917 0.769169809932 Henry Cohn, 2026, needs more optimization.
7 918 0.769514542786 Henry Cohn, 2026, needs more optimization.
7 919 0.769519225358 Henry Cohn, 2026, needs more optimization.
7 920 0.769538255807 Henry Cohn, 2026, needs more optimization.
7 921 0.769683167583 Henry Cohn, 2026, needs more optimization.
7 922 0.769867879767 Henry Cohn, 2026, needs more optimization.
7 923 0.769884556743 Henry Cohn, 2026, needs more optimization.
7 924 0.769912616093 Henry Cohn, 2026, needs more optimization.
7 925 0.769951179231 Henry Cohn, 2026, needs more optimization.
7 926 0.769985824487 Henry Cohn, 2026, needs more optimization.
7 927 0.770111462359 Henry Cohn, 2026, needs more optimization.
7 928 0.770208677205 Henry Cohn, 2026, needs more optimization.
7 929 0.770212325367 Henry Cohn, 2026, needs more optimization.
7 930 0.770252444565 Henry Cohn, 2026, needs more optimization.
7 931 0.770529119280 Henry Cohn, 2026, needs more optimization.
7 932 0.770546464880 Henry Cohn, 2026, needs more optimization.
7 933 0.770569399485 Henry Cohn, 2026, needs more optimization.
7 934 0.770613852703 Henry Cohn, 2026, needs more optimization.
7 935 0.770749958864 Henry Cohn, 2026, needs more optimization.
7 937 0.770888350416 Henry Cohn, 2026, needs more optimization.
7 938 0.771106973819 Henry Cohn, 2026, needs more optimization.
7 939 0.771135698571 Henry Cohn, 2026, needs more optimization.
7 940 0.771176789719 Henry Cohn, 2026, needs more optimization.
7 941 0.771204252438 Henry Cohn, 2026, needs more optimization.
7 943 0.771345993348 Henry Cohn, 2026, needs more optimization.
7 944 0.771489243036 Henry Cohn, 2026, needs more optimization.
7 945 0.771494361929 Henry Cohn, 2026, needs more optimization.
7 946 0.771683410352 Henry Cohn, 2026, needs more optimization.
7 947 0.771710772727 Henry Cohn, 2026, needs more optimization.
7 948 0.771738052814 Henry Cohn, 2026, needs more optimization.
7 949 0.771744287155 Henry Cohn, 2026, needs more optimization.
7 950 0.771847045078 Henry Cohn, 2026, needs more optimization.
7 951 0.772058147481 Henry Cohn, 2026, needs more optimization.
7 952 0.772196063541 Henry Cohn, 2026, needs more optimization.
7 953 0.772204908002 Henry Cohn, 2026, needs more optimization.
7 954 0.772220595876 Henry Cohn, 2026, needs more optimization.
7 955 0.772304275514 Henry Cohn, 2026, needs more optimization.
7 956 0.772574282259 Henry Cohn, 2026, needs more optimization.
7 957 0.772589319663 Henry Cohn, 2026, needs more optimization.
7 958 0.772688660881 Henry Cohn, 2026, needs more optimization.
7 959 0.772709982056 Henry Cohn, 2026, needs more optimization.
7 960 0.772787305766 Henry Cohn, 2026, needs more optimization.
7 961 0.772791677568 Henry Cohn, 2026, needs more optimization.
7 962 0.772892905282 Henry Cohn, 2026, needs more optimization.
7 963 0.773139643903 Henry Cohn, 2026, needs more optimization.
7 964 0.773163667810 Henry Cohn, 2026, needs more optimization.
7 965 0.773185231009 Henry Cohn, 2026, needs more optimization.
7 966 0.773199029035 Henry Cohn, 2026, needs more optimization.
7 967 0.773286609269 Henry Cohn, 2026, needs more optimization.
7 968 0.773504358055 Henry Cohn, 2026, needs more optimization.
7 969 0.773549198042 Henry Cohn, 2026, needs more optimization.
7 970 0.773568311109 Henry Cohn, 2026, needs more optimization.
7 971 0.773687438279 Henry Cohn, 2026, needs more optimization.
7 972 0.773806081196 Henry Cohn, 2026, needs more optimization.
7 973 0.773822117800 Henry Cohn, 2026, needs more optimization.
7 974 0.773892553944 Henry Cohn, 2026, needs more optimization.
7 975 0.774035870980 Henry Cohn, 2026, needs more optimization.
7 976 0.774155730431 Henry Cohn, 2026, needs more optimization.
7 977 0.774185002356 Henry Cohn, 2026, needs more optimization.
7 978 0.774191115604 Henry Cohn, 2026, needs more optimization.
7 979 0.774270256719 Henry Cohn, 2026, needs more optimization.
7 980 0.774281579149 Henry Cohn, 2026, needs more optimization.
7 981 0.774457384647 Henry Cohn, 2026, needs more optimization.
7 982 0.774479059052 Henry Cohn, 2026, needs more optimization.
7 983 0.774559436385 Henry Cohn, 2026, needs more optimization.
7 984 0.774731904293 Henry Cohn, 2026, needs more optimization.
7 985 0.774737540024 Henry Cohn, 2026, needs more optimization.
7 986 0.774764175241 Henry Cohn, 2026, needs more optimization.
7 987 0.774858399697 Henry Cohn, 2026, needs more optimization.
7 988 0.775025789637 Henry Cohn, 2026, needs more optimization.
7 989 0.775034837126 Henry Cohn, 2026, needs more optimization.
7 990 0.775211620503 Henry Cohn, 2026, needs more optimization.
7 991 0.775245133047 Henry Cohn, 2026, needs more optimization.
7 992 0.775406493636 Henry Cohn, 2026, needs more optimization.
7 993 0.775420509285 Henry Cohn, 2026, needs more optimization.
7 994 0.775433210900 Henry Cohn, 2026, needs more optimization.
7 995 0.775616839029 Henry Cohn, 2026, needs more optimization.
7 996 0.775654004625 Henry Cohn, 2026, needs more optimization.
7 997 0.775682729914 Henry Cohn, 2026, needs more optimization.
7 998 0.775735001908 Henry Cohn, 2026, needs more optimization.
7 999 0.775745947394 Henry Cohn, 2026, needs more optimization.
7 1000 0.775785168208 Henry Cohn, 2026, needs more optimization.
7 1001 0.775949167468 Henry Cohn, 2026, needs more optimization.
7 1002 0.775960223435 Henry Cohn, 2026, needs more optimization.
7 1003 0.776149990223 Henry Cohn, 2026, needs more optimization.
7 1004 0.776174949118 Henry Cohn, 2026, needs more optimization.
7 1005 0.776299673635 Henry Cohn, 2026, needs more optimization.
7 1006 0.776367867894 Henry Cohn, 2026, needs more optimization.
7 1007 0.776406449104 Henry Cohn, 2026, needs more optimization.
7 1008 0.776714638079 Henry Cohn, 2026, needs more optimization.
7 1009 0.776717156313 Henry Cohn, 2026, needs more optimization.
7 1010 0.776769676192 Henry Cohn, 2026, needs more optimization.
7 1011 0.776921257609 Henry Cohn, 2026, needs more optimization.
7 1012 0.776924506106 Henry Cohn, 2026, needs more optimization.
7 1013 0.777105347103 Henry Cohn, 2026, needs more optimization.
7 1014 0.777142296381 Henry Cohn, 2026, needs more optimization.
7 1015 0.777178068366 Henry Cohn, 2026, needs more optimization.
7 1016 0.777301098658 Henry Cohn, 2026, needs more optimization.
7 1017 0.777348365452 Henry Cohn, 2026, needs more optimization.
7 1018 0.777360719778 Henry Cohn, 2026, needs more optimization.
7 1019 0.777443855062 Henry Cohn, 2026, needs more optimization.
7 1020 0.777789903483 Henry Cohn, 2026, needs more optimization.
7 1021 0.777813632735 Henry Cohn, 2026, needs more optimization.
7 1022 0.777975416355 Henry Cohn, 2026, needs more optimization.
7 1023 0.777979072241 Henry Cohn, 2026, needs more optimization.
7 1024 0.777993825278 Henry Cohn, 2026, needs more optimization.
8 17 0.087733463324 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
288⁢x3−64⁢x2−8⁢x+1
8 18 0.099469572709 J. Wang, Finding and investigating exact spherical codes, Experiment. Math. 18 (2009), 249–256, https://projecteuclid.org/euclid.em/1259158434.
8 19 0.111409975027 J. Wang, Finding and investigating exact spherical codes, Experiment. Math. 18 (2009), 249–256, https://projecteuclid.org/euclid.em/1259158434.
Minimal polynomial listed in plain text data
8 20 0.119496866688 J. Wang, Finding and investigating exact spherical codes, Experiment. Math. 18 (2009), 249–256, https://projecteuclid.org/euclid.em/1259158434.
224⁢x3+60⁢x2−2⁢x−1
8 21 0.130601937482 J. Wang, Finding and investigating exact spherical codes, Experiment. Math. 18 (2009), 249–256, https://projecteuclid.org/euclid.em/1259158434.
28⁢x2+4⁢x−1
8 22 0.130601937482 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
28⁢x2+4⁢x−1
8 23 0.157169941990 J. Wang, Finding and investigating exact spherical codes, Experiment. Math. 18 (2009), 249–256, https://projecteuclid.org/euclid.em/1259158434.
Minimal polynomial listed in plain text data
8 24 0.157692144940 J. Wang, Finding and investigating exact spherical codes, Experiment. Math. 18 (2009), 249–256, https://projecteuclid.org/euclid.em/1259158434.
4⁢x4−4⁢x3−27⁢x2−2⁢x+1
8 25 0.164334174126 H. Cohn, Small spherical and projective codes, data set, 2022, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
Minimal polynomial listed in plain text data
8 26 0.172652095036 H. Cohn, Small spherical and projective codes, data set, 2022, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
Minimal polynomial listed in plain text data
8 27 0.179856457059 H. Cohn, Small spherical and projective codes, data set, 2022, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
Minimal polynomial listed in plain text data
8 28 0.181158420022 H. Cohn, Small spherical and projective codes, data set, 2022, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
36⁢x4+24⁢x3−36⁢x2+1
8 29 0.187922490077 H. Cohn, Small spherical and projective codes, data set, updated 2024, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
8 30 0.203916279404 H. Cohn, Small spherical and projective codes, data set, 2022, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
8 31 0.219706528517 H. Cohn, Small spherical and projective codes, data set, updated 2024, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
8 32 0.227325452024 H. Cohn, Small spherical and projective codes, data set, updated 2023, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
95⁢x2−4⁢x−4
8 33 0.227325452024 Henry Cohn, 2023.
95⁢x2−4⁢x−4
8 34 0.233864616950 Henry Cohn, 2023.
26887680⁢x6+11003904⁢x5−444096⁢x4−594432⁢x3−55800⁢x2−480⁢x−1
8 35 0.236461100794 Henry Cohn, 2023.
4⁢x4+8⁢x3−20⁢x2+1
8 38 0.239920745566 Henry Cohn, 2023.
1088⁢x4−80⁢x2+1
8 39 0.243600150512 Henry Cohn, 2023.
1183744⁢x8+122880⁢x7−575488⁢x6−138240⁢x5+53632⁢x4+14976⁢x3−1568⁢x2−720⁢x+81
8 40 0.265121155593 Henry Cohn, 2025.
8 41 0.269588854450 Henry Cohn, 2025.
8 42 0.276791074187 Henry Cohn, 2023.
8 43 0.285155668748 Henry Cohn, 2025.
8 44 0.288883351523 Henry Cohn, 2026.
8 45 0.293504048474 Henry Cohn, 2025.
8 46 0.298271343353 Henry Cohn, 2025.
8 47 0.301070997037 Henry Cohn, 2025.
8 48 0.306796780995 Henry Cohn, 2025.
8 49 0.310558546149 Henry Cohn, 2025.
8 50 0.314033492890 Henry Cohn, 2026.
8 51 0.316443462389 Henry Cohn, 2026.
8 52 0.317147531407 Henry Cohn, 2025.
8 53 0.323010527708 Henry Cohn, 2025.
8 54 0.326002020004 Henry Cohn, 2025.
8 55 0.328647326389 Henry Cohn, 2025.
8 56 0.330635803908 Henry Cohn, 2024.
8 57 0.332158951387 Henry Cohn, 2025.
8 58 0.332676598414 Henry Cohn, 2025.
8 59 0.333047687244 Henry Cohn, 2025.
8 60 0.333177612425 Henry Cohn, 2025.
8 61 0.333249870325 Henry Cohn, 2025.
8 62 0.333256273907 Henry Cohn, 2025.
8 63 0.333327460019 Henry Cohn, 2025.
8 64 0.333333333334 T. Ericson and V. Zinoviev, Spherical codes generated by binary partitions of symmetric pointsets, IEEE Trans. Inform. Theory 41 (1995), 107–129, doi:10.1109/18.370114.
3⁢x−1
8 65 0.340292894900 Henry Cohn, 2025.
8 66 0.348776902230 Henry Cohn, 2025.
8 67 0.350755730045 Henry Cohn, 2025.
8 68 0.352461904199 Henry Cohn, 2025.
8 71 0.353553390594 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
8⁢x2−1
8 72 0.357142857143 J. H. Conway, R. H. Hardin, and N. J. A. Sloane, Packing lines, planes, etc.: packings in Grassmannian spaces, Experiment. Math. 5 (1996), 139–159, https://projecteuclid.org/euclid.em/1047565645.
14⁢x−5
8 73 0.374351529308 A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
8 74 0.375030122030 Henry Cohn, 2025.
8 75 0.380121614172 Henry Cohn, 2026.
8 76 0.383280469013 Henry Cohn, 2023.
8 77 0.386305789989 Henry Cohn, 2025.
8 78 0.387879817423 Henry Cohn, 2025.
8 79 0.395049514668 Henry Cohn, 2024.
8 80 0.396541503332 Henry Cohn, 2026, needs more optimization.
8 83 0.4 A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
5⁢x−2
8 84 0.401846838467 A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
8 85 0.404581540848 A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
8 86 0.405334578003 A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
8 87 0.409324629428 A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
8 88 0.414496555473 A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
8 89 0.418879541456 A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
8 90 0.421656007707 Henry Cohn, 2026, needs more optimization.
8 91 0.422013535027 Henry Cohn, 2026.
8 92 0.422534257743 A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
8 93 0.423439618648 Henry Cohn, 2026.
8 94 0.425228129624 A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
8 95 0.426308373208 Henry Cohn, 2026.
8 96 0.426582964791 Henry Cohn, 2026.
8 97 0.427518817396 Henry Cohn, 2026.
8 98 0.428413697861 Henry Cohn, 2026.
8 99 0.428528982794 A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
8 100 0.428556416307 Henry Cohn, 2026, needs more optimization.
8 101 0.428570628728 A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
8 114 0.428571428572 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
7⁢x−3
8 115 0.447550493892 Henry Cohn, 2026, needs more optimization.
8 116 0.448006674268 Henry Cohn, 2026.
8 117 0.451120553073 Henry Cohn, 2026, needs more optimization.
8 118 0.455245746618 Henry Cohn, 2026, needs more optimization.
8 119 0.460486481289 Henry Cohn, 2026.
8 120 0.461570019406 Henry Cohn, 2026.
8 121 0.461664940349 Henry Cohn, 2026, needs more optimization.
8 122 0.461856796769 Henry Cohn, 2026.
8 123 0.462062366159 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
8 124 0.462073184368 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
8 125 0.462391754669 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
8 136 0.462585942982 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
68⁢x2−12⁢x−9
8 137 0.466199226032 Henry Cohn, 2025.
8 138 0.467414924363 Henry Cohn, 2026, needs more optimization.
8 139 0.468643119766 Henry Cohn, 2026, needs more optimization.
8 140 0.470794044358 Henry Cohn, 2026, needs more optimization.
8 141 0.472524014496 Henry Cohn, 2026, needs more optimization.
8 142 0.475934084553 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
8 143 0.476461017781 Henry Cohn, 2026, needs more optimization.
8 144 0.482497830264 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
8 145 0.484049782458 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
8 146 0.484342502723 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
8 147 0.485629021325 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
8 148 0.487345967860 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
8 149 0.488370745688 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
8 150 0.489648778915 Henry Cohn, 2026, needs more optimization.
8 151 0.490514920467 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
8 152 0.491018836925 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
8 153 0.491634112970 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
8 154 0.492164973608 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
8 155 0.492546117506 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
8 156 0.493356625884 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
8 157 0.493592843164 Henry Cohn, 2026, needs more optimization.
8 158 0.493973024529 Henry Cohn, 2026, needs more optimization.
8 159 0.494092911671 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
8 160 0.494736830969 Henry Cohn, 2026, needs more optimization.
8 161 0.495478240482 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
8 162 0.495696105505 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
8 163 0.496348270898 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
8 164 0.496405095086 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
8 165 0.496940175906 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
8 166 0.497162216855 Henry Cohn, 2026, needs more optimization.
8 167 0.497721332130 Henry Cohn, 2026, needs more optimization.
8 168 0.498088479818 Henry Cohn, 2026, needs more optimization.
8 169 0.498223265158 Henry Cohn, 2026, needs more optimization.
8 170 0.498762986187 Henry Cohn, 2026, needs more optimization.
8 171 0.498914115868 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
8 172 0.499128465310 Henry Cohn, 2026, needs more optimization.
8 173 0.499375203486 Henry Cohn, 2026, needs more optimization.
8 174 0.499610514813 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
8 175 0.499803727376 Henry Cohn, 2026, needs more optimization.
8 176 0.499906111937 Henry Cohn, 2026, needs more optimization.
8 177 0.499931955747 Henry Cohn, 2026, needs more optimization.
8 178 0.499932794301 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
8 179 0.499940784018 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
8 240* 0.5 A. Korkine and G. Zolotareff, Sur les formes quadratiques, Math. Ann. 6 (1873), 366–389, doi:10.1007/BF01442795; V. I. Levenšteĭn, On bounds for packings in n-dimensional Euclidean space (Russian), Dokl. Akad. Nauk SSSR 245 (1979), 1299–1303, English translation in Soviet Math. Dokl. 20 (1979), 417–421; A. M. Odlyzko and N. J. A. Sloane, New bounds on the number of unit spheres that can touch a unit sphere in n dimensions, J. Combin. Theory Ser. A 26 (1979), 210–214, doi:10.1016/0097-3165(79)90074-8.
2⁢x−1
8 241 0.539501901248 Henry Cohn, 2024, needs more optimization.
8 242 0.544042192920 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
8 243 0.547251707822 Henry Cohn, 2026, needs more optimization.
8 244 0.549350578104 Henry Cohn, 2026, needs more optimization.
8 245 0.551498748553 Henry Cohn, 2026, needs more optimization.
8 246 0.553416987925 Henry Cohn, 2026, needs more optimization.
8 247 0.555266096638 Henry Cohn, 2026, needs more optimization.
8 248 0.557093069689 Henry Cohn, 2026, needs more optimization.
8 249 0.559106188621 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
8 250 0.560484971119 Henry Cohn, 2026, needs more optimization.
8 251 0.561370577120 Henry Cohn, 2026, needs more optimization.
8 252 0.562684715689 Henry Cohn, 2026, needs more optimization.
8 253 0.564030186495 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
8 254 0.564218395870 Henry Cohn, 2026, needs more optimization.
8 255 0.564229248938 Henry Cohn, 2026, needs more optimization.
8 256 0.564562475847 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
8 257 0.564958246328 Henry Cohn, 2026, needs more optimization.
8 258 0.566626006714 Henry Cohn, 2026, needs more optimization.
8 259 0.568538732572 Henry Cohn, 2026, needs more optimization.
8 260 0.568554258957 Henry Cohn, 2026, needs more optimization.
8 261 0.569474412994 Henry Cohn, 2026, needs more optimization.
8 262 0.569986354892 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
8 263 0.571060177659 Henry Cohn, 2026, needs more optimization.
8 264 0.571387637535 Henry Cohn, 2026, needs more optimization.
8 265 0.571634376585 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
8 266 0.572560459171 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
8 267 0.573025002155 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
8 268 0.573583849050 Henry Cohn, 2026, needs more optimization.
8 269 0.573870262427 Henry Cohn, 2026, needs more optimization.
8 270 0.574627466701 Henry Cohn, 2026, needs more optimization.
8 271 0.575183375633 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
8 272 0.575733015557 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
8 273 0.576057960059 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
8 274 0.577116672865 Henry Cohn, 2026, needs more optimization.
8 275 0.577880233307 Henry Cohn, 2026, needs more optimization.
8 276 0.578734877468 Henry Cohn, 2026, needs more optimization.
8 277 0.579482565249 Henry Cohn, 2026, needs more optimization.
8 279 0.579817983127 Henry Cohn, 2026, needs more optimization.
8 280 0.579829936547 Henry Cohn, 2026, needs more optimization.
8 281 0.579837641111 Henry Cohn, 2026, needs more optimization.
8 283 0.579878928030 Henry Cohn, 2026, needs more optimization.
8 284 0.580580117500 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
8 285 0.580884103471 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
8 286 0.581854299142 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
8 287 0.582978386015 Henry Cohn, 2026, needs more optimization.
8 288 0.584430106567 Henry Cohn, 2026, needs more optimization.
8 289 0.584766934684 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
8 290 0.585253696921 Henry Cohn, 2026, needs more optimization.
8 291 0.585264543699 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
8 292 0.585664608742 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
8 293 0.585736507984 Henry Cohn, 2026, needs more optimization.
8 294 0.586495980094 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
8 295 0.586901002767 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
8 296 0.588178347277 Henry Cohn, 2026, needs more optimization.
8 297 0.588671194029 Henry Cohn, 2026, needs more optimization.
8 298 0.588671380646 Henry Cohn, 2026, needs more optimization.
8 299 0.588679215560 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
8 300 0.588685892032 Henry Cohn, 2026, needs more optimization.
8 301 0.588687128598 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
8 302 0.588694051230 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
8 303 0.590576764339 Henry Cohn, 2026, needs more optimization.
8 304 0.590590010414 Henry Cohn, 2026, needs more optimization.
8 305 0.590642335600 Henry Cohn, 2026, needs more optimization.
8 306 0.590690107237 Henry Cohn, 2026, needs more optimization.
8 307 0.590768910737 Henry Cohn, 2026, needs more optimization.
8 308 0.590975246189 Henry Cohn, 2026, needs more optimization.
8 309 0.590975835369 Henry Cohn, 2026, needs more optimization.
8 310 0.591748494092 Henry Cohn, 2026, needs more optimization.
8 311 0.592694080866 Henry Cohn, 2026, needs more optimization.
8 312 0.593711560108 Henry Cohn, 2026, needs more optimization.
8 313 0.594290936103 Henry Cohn, 2026, needs more optimization.
8 314 0.594416382510 Henry Cohn, 2026, needs more optimization.
8 315 0.594746132939 Henry Cohn, 2026, needs more optimization.
8 316 0.594774104343 Henry Cohn, 2026, needs more optimization.
8 317 0.595127698465 Henry Cohn, 2026, needs more optimization.
8 318 0.595158259597 Henry Cohn, 2026, needs more optimization.
8 319 0.595272996668 Henry Cohn, 2026, needs more optimization.
8 320 0.595799620137 Henry Cohn, 2026, needs more optimization.
8 321 0.596348376090 Henry Cohn, 2026, needs more optimization.
8 322 0.597009193983 Henry Cohn, 2026, needs more optimization.
8 323 0.597585521531 Henry Cohn, 2026, needs more optimization.
8 324 0.598032769529 Henry Cohn, 2026, needs more optimization.
8 325 0.598633111133 Henry Cohn, 2026, needs more optimization.
8 326 0.599027363368 Henry Cohn, 2026, needs more optimization.
8 327 0.599940934149 Henry Cohn, 2026, needs more optimization.
8 328 0.600347098495 Henry Cohn, 2026, needs more optimization.
8 329 0.600630007965 Henry Cohn, 2026, needs more optimization.
8 330 0.600673973046 Henry Cohn, 2026, needs more optimization.
8 331 0.600899142072 Henry Cohn, 2026, needs more optimization.
8 332 0.600914147794 Henry Cohn, 2026, needs more optimization.
8 333 0.601572958657 Henry Cohn, 2026, needs more optimization.
8 334 0.601881591264 Henry Cohn, 2026, needs more optimization.
8 335 0.602154266592 Henry Cohn, 2026, needs more optimization.
8 336 0.602595151547 Henry Cohn, 2026, needs more optimization.
8 337 0.602727139686 Henry Cohn, 2026, needs more optimization.
8 338 0.602862451292 Henry Cohn, 2026, needs more optimization.
8 339 0.602940137504 Henry Cohn, 2026, needs more optimization.
8 340 0.603052528786 Henry Cohn, 2026, needs more optimization.
8 341 0.603111043930 Henry Cohn, 2026, needs more optimization.
8 342 0.603120715559 Henry Cohn, 2026, needs more optimization.
8 343 0.604241183695 Henry Cohn, 2026, needs more optimization.
8 344 0.604315159720 Henry Cohn, 2026, needs more optimization.
8 345 0.604440074471 Henry Cohn, 2026, needs more optimization.
8 346 0.604486159249 Henry Cohn, 2026, needs more optimization.
8 347 0.604487730075 Henry Cohn, 2026, needs more optimization.
8 348 0.604496639421 Henry Cohn, 2026, needs more optimization.
8 349 0.604498128902 Henry Cohn, 2026, needs more optimization.
8 350 0.604516407588 Henry Cohn, 2026, needs more optimization.
8 351 0.604525373965 Henry Cohn, 2026, needs more optimization.
8 352 0.604543457256 Henry Cohn, 2026, needs more optimization.
8 353 0.604548727949 Henry Cohn, 2026, needs more optimization.
8 354 0.604552653988 Henry Cohn, 2026, needs more optimization.
8 355 0.604683509183 Henry Cohn, 2026, needs more optimization.
8 356 0.606373932200 Henry Cohn, 2026, needs more optimization.
8 357 0.606594124945 Henry Cohn, 2026, needs more optimization.
8 358 0.606814110203 Henry Cohn, 2026, needs more optimization.
8 359 0.606910189080 Henry Cohn, 2026, needs more optimization.
8 360 0.606975914964 Henry Cohn, 2026, needs more optimization.
8 361 0.611019509418 Henry Cohn, 2026, needs more optimization.
8 362 0.611378602037 Henry Cohn, 2026, needs more optimization.
8 363 0.611405093464 Henry Cohn, 2026, needs more optimization.
8 364 0.611604557073 Henry Cohn, 2026, needs more optimization.
8 365 0.611771036235 Henry Cohn, 2026, needs more optimization.
8 366 0.612111608158 Henry Cohn, 2026, needs more optimization.
8 367 0.612209884221 Henry Cohn, 2026, needs more optimization.
8 368 0.612272510343 Henry Cohn, 2026, needs more optimization.
8 369 0.612330742933 Henry Cohn, 2026, needs more optimization.
8 370 0.614280900915 Henry Cohn, 2026, needs more optimization.
8 371 0.614458177435 Henry Cohn, 2026, needs more optimization.
8 372 0.615194699728 Henry Cohn, 2026, needs more optimization.
8 373 0.616551329088 Henry Cohn, 2026, needs more optimization.
8 374 0.617361192966 Henry Cohn, 2026, needs more optimization.
8 375 0.618182537197 Henry Cohn, 2026, needs more optimization.
8 376 0.618243297642 Henry Cohn, 2026, needs more optimization.
8 377 0.618664711822 Henry Cohn, 2026, needs more optimization.
8 378 0.621609538450 Henry Cohn, 2026, needs more optimization.
8 379 0.622000809104 Henry Cohn, 2026, needs more optimization.
8 380 0.622736223453 Henry Cohn, 2026, needs more optimization.
8 381 0.624159639106 Henry Cohn, 2026, needs more optimization.
8 382 0.624716330804 Henry Cohn, 2026, needs more optimization.
8 383 0.624850620711 Henry Cohn, 2026, needs more optimization.
8 384 0.625022765875 Henry Cohn, 2026, needs more optimization.
8 385 0.625386020215 Henry Cohn, 2026, needs more optimization.
8 386 0.625607724160 Henry Cohn, 2026, needs more optimization.
8 387 0.625886189962 Henry Cohn, 2026, needs more optimization.
8 388 0.626417404197 Henry Cohn, 2026, needs more optimization.
8 389 0.626817955582 Henry Cohn, 2026, needs more optimization.
8 390 0.627040767692 Henry Cohn, 2026, needs more optimization.
8 391 0.627501874978 Henry Cohn, 2026, needs more optimization.
8 392 0.627762259159 Henry Cohn, 2026, needs more optimization.
8 393 0.628160397957 Henry Cohn, 2026, needs more optimization.
8 394 0.628311253987 Henry Cohn, 2026, needs more optimization.
8 395 0.628582779094 Henry Cohn, 2026, needs more optimization.
8 396 0.629014746040 Henry Cohn, 2026, needs more optimization.
8 397 0.629116972440 Henry Cohn, 2026, needs more optimization.
8 398 0.629495159125 Henry Cohn, 2026, needs more optimization.
8 399 0.629812766094 Henry Cohn, 2026, needs more optimization.
8 400 0.630147279093 Henry Cohn, 2026, needs more optimization.
8 401 0.630340517930 Henry Cohn, 2026, needs more optimization.
8 402 0.630556440744 Henry Cohn, 2026, needs more optimization.
8 403 0.630793914166 Henry Cohn, 2026, needs more optimization.
8 404 0.631433260905 Henry Cohn, 2026, needs more optimization.
8 405 0.631947907009 Henry Cohn, 2026, needs more optimization.
8 406 0.632027930958 Henry Cohn, 2026, needs more optimization.
8 407 0.632312669504 Henry Cohn, 2026, needs more optimization.
8 408 0.632576421518 Henry Cohn, 2026, needs more optimization.
8 409 0.632756923570 Henry Cohn, 2026, needs more optimization.
8 410 0.633016483791 Henry Cohn, 2026, needs more optimization.
8 411 0.633300020588 Henry Cohn, 2026, needs more optimization.
8 412 0.633610927946 Henry Cohn, 2026, needs more optimization.
8 413 0.633861390629 Henry Cohn, 2026, needs more optimization.
8 414 0.634118291067 Henry Cohn, 2026, needs more optimization.
8 415 0.634352865964 Henry Cohn, 2026, needs more optimization.
8 416 0.634657586482 Henry Cohn, 2026, needs more optimization.
8 417 0.634754352405 Henry Cohn, 2026, needs more optimization.
8 418 0.634825543223 Henry Cohn, 2026, needs more optimization.
8 419 0.634978866731 Henry Cohn, 2026, needs more optimization.
8 420 0.635004804157 Henry Cohn, 2026, needs more optimization.
8 421 0.635205684917 Henry Cohn, 2026, needs more optimization.
8 422 0.635656172055 Henry Cohn, 2026, needs more optimization.
8 423 0.635749833637 Henry Cohn, 2026, needs more optimization.
8 424 0.635846139455 Henry Cohn, 2026, needs more optimization.
8 425 0.635997987104 Henry Cohn, 2026, needs more optimization.
8 426 0.636148122798 Henry Cohn, 2026, needs more optimization.
8 427 0.636376429834 Henry Cohn, 2026, needs more optimization.
8 428 0.636521221198 Henry Cohn, 2026, needs more optimization.
8 429 0.636723681236 Henry Cohn, 2026, needs more optimization.
8 430 0.636855327515 Henry Cohn, 2026, needs more optimization.
8 431 0.637177044534 Henry Cohn, 2026, needs more optimization.
8 432 0.637254289873 Henry Cohn, 2026, needs more optimization.
8 433 0.637676318005 Henry Cohn, 2026, needs more optimization.
8 434 0.637832402830 Henry Cohn, 2026, needs more optimization.
8 435 0.637897129131 Henry Cohn, 2026, needs more optimization.
8 436 0.638123992510 Henry Cohn, 2026, needs more optimization.
8 437 0.638687588975 Henry Cohn, 2026, needs more optimization.
8 438 0.639251748850 Henry Cohn, 2026, needs more optimization.
8 439 0.639340834260 Henry Cohn, 2026, needs more optimization.
8 440 0.639454117309 Henry Cohn, 2026, needs more optimization.
8 441 0.639715861318 Henry Cohn, 2026, needs more optimization.
8 442 0.639896014065 Henry Cohn, 2026, needs more optimization.
8 443 0.639935194648 Henry Cohn, 2026, needs more optimization.
8 444 0.640165531313 Henry Cohn, 2026, needs more optimization.
8 445 0.640356193211 Henry Cohn, 2026, needs more optimization.
8 446 0.640583382881 Henry Cohn, 2026, needs more optimization.
8 447 0.640896137734 Henry Cohn, 2026, needs more optimization.
8 448 0.641210160572 Henry Cohn, 2026, needs more optimization.
8 449 0.641499640032 Henry Cohn, 2026, needs more optimization.
8 450 0.641527675003 Henry Cohn, 2026, needs more optimization.
8 451 0.641552810470 Henry Cohn, 2026, needs more optimization.
8 452 0.641572063588 Henry Cohn, 2026, needs more optimization.
8 453 0.641646626049 Henry Cohn, 2026, needs more optimization.
8 454 0.641685157118 Henry Cohn, 2026, needs more optimization.
8 455 0.641741845619 Henry Cohn, 2026, needs more optimization.
8 456 0.641840724778 Henry Cohn, 2026, needs more optimization.
8 457 0.641886239772 Henry Cohn, 2026, needs more optimization.
8 458 0.641915306504 Henry Cohn, 2026, needs more optimization.
8 459 0.641953900145 Henry Cohn, 2026, needs more optimization.
8 460 0.642073202655 Henry Cohn, 2026, needs more optimization.
8 461 0.642127883847 Henry Cohn, 2026, needs more optimization.
8 462 0.642155257569 Henry Cohn, 2026, needs more optimization.
8 463 0.642260833571 Henry Cohn, 2026, needs more optimization.
8 464 0.642306748644 Henry Cohn, 2026, needs more optimization.
8 465 0.642343098311 Henry Cohn, 2026, needs more optimization.
8 466 0.642539261523 Henry Cohn, 2026, needs more optimization.
8 467 0.642685864497 Henry Cohn, 2026, needs more optimization.
8 468 0.642926166545 Henry Cohn, 2026, needs more optimization.
8 469 0.643119590378 Henry Cohn, 2026, needs more optimization.
8 470 0.643284970042 Henry Cohn, 2026, needs more optimization.
8 471 0.643437800686 Henry Cohn, 2026, needs more optimization.
8 472 0.643636340848 Henry Cohn, 2026, needs more optimization.
8 473 0.643809792523 Henry Cohn, 2026, needs more optimization.
8 474 0.643833015336 Henry Cohn, 2026, needs more optimization.
8 475 0.644049748672 Henry Cohn, 2026, needs more optimization.
8 476 0.644194914296 Henry Cohn, 2026, needs more optimization.
8 477 0.644345506565 Henry Cohn, 2026, needs more optimization.
8 478 0.644642718331 Henry Cohn, 2026, needs more optimization.
8 479 0.644770751218 Henry Cohn, 2026, needs more optimization.
8 480 0.645222710568 Henry Cohn, 2026, needs more optimization.
8 481 0.645331843906 Henry Cohn, 2026, needs more optimization.
8 482 0.645545406367 Henry Cohn, 2026, needs more optimization.
8 483 0.645624493579 Henry Cohn, 2026, needs more optimization.
8 484 0.646158517897 Henry Cohn, 2026, needs more optimization.
8 485 0.646385618854 Henry Cohn, 2026, needs more optimization.
8 486 0.646805472923 Henry Cohn, 2026, needs more optimization.
8 487 0.647253216387 Henry Cohn, 2026, needs more optimization.
8 488 0.647379338535 Henry Cohn, 2026, needs more optimization.
8 489 0.647400679296 Henry Cohn, 2026, needs more optimization.
8 490 0.647720981105 Henry Cohn, 2026, needs more optimization.
8 491 0.647998952833 Henry Cohn, 2026, needs more optimization.
8 492 0.648389658438 Henry Cohn, 2026, needs more optimization.
8 493 0.648765659695 Henry Cohn, 2026, needs more optimization.
8 494 0.648972961261 Henry Cohn, 2026, needs more optimization.
8 495 0.649004586296 Henry Cohn, 2026, needs more optimization.
8 497 0.649040740986 Henry Cohn, 2026, needs more optimization.
8 498 0.649064175709 Henry Cohn, 2026, needs more optimization.
8 499 0.649368032779 Henry Cohn, 2026, needs more optimization.
8 500 0.649487709556 Henry Cohn, 2026, needs more optimization.
8 501 0.649605936279 Henry Cohn, 2026, needs more optimization.
8 502 0.649819491123 Henry Cohn, 2026, needs more optimization.
8 503 0.650148200757 Henry Cohn, 2026, needs more optimization.
8 504 0.650330034251 Henry Cohn, 2026, needs more optimization.
8 505 0.650401056282 Henry Cohn, 2026, needs more optimization.
8 506 0.651003373593 Henry Cohn, 2026, needs more optimization.
8 507 0.651467057239 Henry Cohn, 2026, needs more optimization.
8 508 0.651575893146 Henry Cohn, 2026, needs more optimization.
8 509 0.651787245357 Henry Cohn, 2026, needs more optimization.
8 510 0.652093746495 Henry Cohn, 2026, needs more optimization.
8 513 0.652124600989 Henry Cohn, 2026, needs more optimization.
8 514 0.652358598050 Henry Cohn, 2026, needs more optimization.
8 515 0.652418790948 Henry Cohn, 2026, needs more optimization.
8 516 0.652683432965 Henry Cohn, 2026, needs more optimization.
8 517 0.652808631235 Henry Cohn, 2026, needs more optimization.
8 518 0.653034111533 Henry Cohn, 2026, needs more optimization.
8 519 0.653292746339 Henry Cohn, 2026, needs more optimization.
8 520 0.653649737531 Henry Cohn, 2026, needs more optimization.
8 521 0.653780271671 Henry Cohn, 2026, needs more optimization.
8 522 0.654165789203 Henry Cohn, 2026, needs more optimization.
8 523 0.654187229577 Henry Cohn, 2026, needs more optimization.
8 524 0.654281978209 Henry Cohn, 2026, needs more optimization.
8 525 0.654394234594 Henry Cohn, 2026, needs more optimization.
8 526 0.654540154079 Henry Cohn, 2026, needs more optimization.
8 527 0.654611224335 Henry Cohn, 2026, needs more optimization.
8 528 0.654701364820 Henry Cohn, 2026, needs more optimization.
8 529 0.655016689839 Henry Cohn, 2026, needs more optimization.
8 530 0.655235074646 Henry Cohn, 2026, needs more optimization.
8 531 0.655715168102 Henry Cohn, 2026, needs more optimization.
8 532 0.655791550465 Henry Cohn, 2026, needs more optimization.
8 533 0.655991758770 Henry Cohn, 2026, needs more optimization.
8 534 0.656154781979 Henry Cohn, 2026, needs more optimization.
8 535 0.656436251212 Henry Cohn, 2026, needs more optimization.
8 536 0.656701904170 Henry Cohn, 2026, needs more optimization.
8 537 0.657017394409 Henry Cohn, 2026, needs more optimization.
8 538 0.657333349433 Henry Cohn, 2026, needs more optimization.
8 539 0.657507500348 Henry Cohn, 2026, needs more optimization.
8 540 0.657688115124 Henry Cohn, 2026, needs more optimization.
8 541 0.657785711175 Henry Cohn, 2026, needs more optimization.
8 542 0.658020422074 Henry Cohn, 2026, needs more optimization.
8 543 0.658310428913 Henry Cohn, 2026, needs more optimization.
8 544 0.658636021775 Henry Cohn, 2026, needs more optimization.
8 545 0.658861083537 Henry Cohn, 2026, needs more optimization.
8 546 0.659011112284 Henry Cohn, 2026, needs more optimization.
8 547 0.659328901755 Henry Cohn, 2026, needs more optimization.
8 548 0.659530575421 Henry Cohn, 2026, needs more optimization.
8 549 0.659611195100 Henry Cohn, 2026, needs more optimization.
8 550 0.659625284781 Henry Cohn, 2026, needs more optimization.
8 551 0.659962734533 Henry Cohn, 2026, needs more optimization.
8 552 0.660489039247 Henry Cohn, 2026, needs more optimization.
8 553 0.660621126485 Henry Cohn, 2026, needs more optimization.
8 554 0.660757882480 Henry Cohn, 2026, needs more optimization.
8 555 0.660856752208 Henry Cohn, 2026, needs more optimization.
8 556 0.661108821247 Henry Cohn, 2026, needs more optimization.
8 557 0.661255072069 Henry Cohn, 2026, needs more optimization.
8 558 0.661399841684 Henry Cohn, 2026, needs more optimization.
8 559 0.661739684354 Henry Cohn, 2026, needs more optimization.
8 560 0.661903640126 Henry Cohn, 2026, needs more optimization.
8 561 0.662019635313 Henry Cohn, 2026, needs more optimization.
8 562 0.662288409714 Henry Cohn, 2026, needs more optimization.
8 563 0.662426944948 Henry Cohn, 2026, needs more optimization.
8 564 0.662575927155 Henry Cohn, 2026, needs more optimization.
8 565 0.662674253598 Henry Cohn, 2026, needs more optimization.
8 566 0.662749356541 Henry Cohn, 2026, needs more optimization.
8 567 0.662782643184 Henry Cohn, 2026, needs more optimization.
8 568 0.662911656880 Henry Cohn, 2026, needs more optimization.
8 569 0.663083008359 Henry Cohn, 2026, needs more optimization.
8 570 0.663126150144 Henry Cohn, 2026, needs more optimization.
8 571 0.663286779122 Henry Cohn, 2026, needs more optimization.
8 572 0.663464580841 Henry Cohn, 2026, needs more optimization.
8 573 0.663512155499 Henry Cohn, 2026, needs more optimization.
8 574 0.663793229936 Henry Cohn, 2026, needs more optimization.
8 575 0.663929025996 Henry Cohn, 2026, needs more optimization.
8 576 0.663997353869 Henry Cohn, 2026, needs more optimization.
8 577 0.664085130260 Henry Cohn, 2026, needs more optimization.
8 578 0.664190211637 Henry Cohn, 2026, needs more optimization.
8 579 0.664343371350 Henry Cohn, 2026, needs more optimization.
8 580 0.664397181016 Henry Cohn, 2026, needs more optimization.
8 581 0.664512511717 Henry Cohn, 2026, needs more optimization.
8 582 0.664533563531 Henry Cohn, 2026, needs more optimization.
8 583 0.664740748095 Henry Cohn, 2026, needs more optimization.
8 585 0.664754488702 Henry Cohn, 2026, needs more optimization.
8 586 0.664857542562 Henry Cohn, 2026, needs more optimization.
8 587 0.664937708028 Henry Cohn, 2026, needs more optimization.
8 588 0.665026111869 Henry Cohn, 2026, needs more optimization.
8 589 0.665199284068 Henry Cohn, 2026, needs more optimization.
8 590 0.665220860722 Henry Cohn, 2026, needs more optimization.
8 591 0.665221153451 Henry Cohn, 2026, needs more optimization.
8 592 0.665237954464 Henry Cohn, 2026, needs more optimization.
8 593 0.665250968581 Henry Cohn, 2026, needs more optimization.
8 594 0.665272330149 Henry Cohn, 2026, needs more optimization.
8 595 0.665281279696 Henry Cohn, 2026, needs more optimization.
8 596 0.665281280559 Henry Cohn, 2026, needs more optimization.
8 598 0.665314893705 Henry Cohn, 2026, needs more optimization.
8 599 0.665326225383 Henry Cohn, 2026, needs more optimization.
8 600 0.665352476024 Henry Cohn, 2026, needs more optimization.
8 601 0.665357264769 Henry Cohn, 2026, needs more optimization.
8 602 0.665375981515 Henry Cohn, 2026, needs more optimization.
8 604 0.665423924086 Henry Cohn, 2026, needs more optimization.
8 605 0.665446026612 Henry Cohn, 2026, needs more optimization.
8 606 0.665516149129 Henry Cohn, 2026, needs more optimization.
8 607 0.665530347342 Henry Cohn, 2026, needs more optimization.
8 608 0.665572856472 Henry Cohn, 2026, needs more optimization.
8 609 0.665607995204 Henry Cohn, 2026, needs more optimization.
8 610 0.665624368896 Henry Cohn, 2026, needs more optimization.
8 611 0.665634785911 Henry Cohn, 2026, needs more optimization.
8 612 0.665653993650 Henry Cohn, 2026, needs more optimization.
8 613 0.665659338738 Henry Cohn, 2026, needs more optimization.
8 614 0.665679340715 Henry Cohn, 2026, needs more optimization.
8 615 0.665717470676 Henry Cohn, 2026, needs more optimization.
8 617 0.665728219322 Henry Cohn, 2026, needs more optimization.
8 618 0.665750684637 Henry Cohn, 2026, needs more optimization.
8 619 0.665884611026 Henry Cohn, 2026, needs more optimization.
8 620 0.665945460855 Henry Cohn, 2026, needs more optimization.
8 621 0.665986957515 Henry Cohn, 2026, needs more optimization.
8 622 0.665997258145 Henry Cohn, 2026, needs more optimization.
8 623 0.666018179457 Henry Cohn, 2026, needs more optimization.
8 624 0.666021770569 Henry Cohn, 2026, needs more optimization.
8 628 0.666067266746 Henry Cohn, 2026, needs more optimization.
8 629 0.666080905347 Henry Cohn, 2026, needs more optimization.
8 630 0.666123751442 Henry Cohn, 2026, needs more optimization.
8 631 0.666168370841 Henry Cohn, 2026, needs more optimization.
8 632 0.666175586047 Henry Cohn, 2026, needs more optimization.
8 634 0.666198423078 Henry Cohn, 2026, needs more optimization.
8 635 0.666205270882 Henry Cohn, 2026, needs more optimization.
8 636 0.666298703941 Henry Cohn, 2026, needs more optimization.
8 637 0.666308460437 Henry Cohn, 2026, needs more optimization.
8 638 0.666333120315 Henry Cohn, 2026, needs more optimization.
8 639 0.666347591469 Henry Cohn, 2026, needs more optimization.
8 640 0.666362769783 Henry Cohn, 2026, needs more optimization.
8 644 0.666452185400 Henry Cohn, 2026, needs more optimization.
8 645 0.666472049166 Henry Cohn, 2026, needs more optimization.
8 646 0.666518928940 Henry Cohn, 2026, needs more optimization.
8 647 0.666520155493 Henry Cohn, 2026, needs more optimization.
8 648 0.666525441302 Henry Cohn, 2026, needs more optimization.
8 649 0.666530913994 Henry Cohn, 2026, needs more optimization.
8 650 0.666541471024 Henry Cohn, 2026, needs more optimization.
8 651 0.666558648353 Henry Cohn, 2026, needs more optimization.
8 652 0.666571951706 Henry Cohn, 2026, needs more optimization.
8 653 0.666586829735 Henry Cohn, 2026, needs more optimization.
8 654 0.666587585749 Henry Cohn, 2026, needs more optimization.
8 655 0.666587895988 Henry Cohn, 2026, needs more optimization.
8 656 0.666588253908 Henry Cohn, 2026, needs more optimization.
8 658 0.666589822785 Henry Cohn, 2026, needs more optimization.
8 659 0.666593744008 Henry Cohn, 2026, needs more optimization.
8 660 0.666734051471 Henry Cohn, 2026, needs more optimization.
8 661 0.667059557205 Henry Cohn, 2026, needs more optimization.
8 662 0.667266812287 Henry Cohn, 2026, needs more optimization.
8 663 0.668189420532 Henry Cohn, 2026, needs more optimization.
8 664 0.668388533877 Henry Cohn, 2026, needs more optimization.
8 665 0.668667308515 Henry Cohn, 2026, needs more optimization.
8 666 0.668685067830 Henry Cohn, 2026, needs more optimization.
8 667 0.668689361255 Henry Cohn, 2026, needs more optimization.
8 668 0.668755836012 Henry Cohn, 2026, needs more optimization.
8 669 0.668759815844 A. Kravatsky, V. Khrulkov, and I. Oseledets, ImprovEvolve: basin-hopping meets LLM-guided evolutionary search, ICML 2026 AI4Math Workshop Poster, https://openreview.net/forum?id=nE1q0gRDNr, arXiv:2602.10233, after some further optimization.
8 670 0.669180126171 Henry Cohn, 2026, needs more optimization.
8 671 0.669708221834 Henry Cohn, 2026, needs more optimization.
8 672 0.669884995471 Henry Cohn, 2026, needs more optimization.
8 673 0.670145639921 Henry Cohn, 2026, needs more optimization.
8 674 0.670497088947 Henry Cohn, 2026, needs more optimization.
8 675 0.670784218358 Henry Cohn, 2026, needs more optimization.
8 676 0.671136271804 Henry Cohn, 2026, needs more optimization.
8 677 0.671548378052 Henry Cohn, 2026, needs more optimization.
8 678 0.671995810195 Henry Cohn, 2026, needs more optimization.
8 679 0.673148791588 Henry Cohn, 2026, needs more optimization.
8 680 0.673409642002 Henry Cohn, 2026, needs more optimization.
8 681 0.673441590670 Henry Cohn, 2026, needs more optimization.
8 682 0.673480034152 Henry Cohn, 2026, needs more optimization.
8 683 0.673483270979 Henry Cohn, 2026, needs more optimization.
8 684 0.673537408049 Henry Cohn, 2026, needs more optimization.
8 685 0.674072288522 Henry Cohn, 2026, needs more optimization.
8 686 0.674212597417 Henry Cohn, 2026, needs more optimization.
8 687 0.674551336718 Henry Cohn, 2026, needs more optimization.
8 688 0.674938295084 Henry Cohn, 2026, needs more optimization.
8 689 0.675169798861 Henry Cohn, 2026, needs more optimization.
8 690 0.675522724462 Henry Cohn, 2026, needs more optimization.
8 691 0.676056187152 Henry Cohn, 2026, needs more optimization.
8 692 0.676435510098 Henry Cohn, 2026, needs more optimization.
8 693 0.676908415030 Henry Cohn, 2026, needs more optimization.
8 694 0.677369428483 Henry Cohn, 2026, needs more optimization.
8 695 0.677450069985 Henry Cohn, 2026, needs more optimization.
8 696 0.677681791857 Henry Cohn, 2026, needs more optimization.
8 697 0.677810009434 Henry Cohn, 2026, needs more optimization.
8 698 0.678219417670 Henry Cohn, 2026, needs more optimization.
8 699 0.678433617867 Henry Cohn, 2026, needs more optimization.
8 700 0.678621367520 Henry Cohn, 2026, needs more optimization.
8 701 0.679067367872 Henry Cohn, 2026, needs more optimization.
8 702 0.679291865525 Henry Cohn, 2026, needs more optimization.
8 703 0.679783562154 Henry Cohn, 2026, needs more optimization.
8 704 0.680144936870 Henry Cohn, 2026, needs more optimization.
8 705 0.680251247714 Henry Cohn, 2026, needs more optimization.
8 706 0.680421041284 Henry Cohn, 2026, needs more optimization.
8 707 0.680529382018 Henry Cohn, 2026, needs more optimization.
8 708 0.680603367281 Henry Cohn, 2026, needs more optimization.
8 709 0.680917656168 Henry Cohn, 2026, needs more optimization.
8 710 0.681407341367 Henry Cohn, 2026, needs more optimization.
8 711 0.681570154052 Henry Cohn, 2026, needs more optimization.
8 712 0.681898472793 Henry Cohn, 2026, needs more optimization.
8 713 0.682062589932 Henry Cohn, 2026, needs more optimization.
8 714 0.682450105562 Henry Cohn, 2026, needs more optimization.
8 715 0.682455975389 Henry Cohn, 2026, needs more optimization.
8 716 0.682927915314 Henry Cohn, 2026, needs more optimization.
8 717 0.683250995223 Henry Cohn, 2026, needs more optimization.
8 718 0.683505170878 Henry Cohn, 2026, needs more optimization.
8 719 0.683536202064 Henry Cohn, 2026, needs more optimization.
8 720 0.683900141450 Henry Cohn, 2026, needs more optimization.
8 721 0.683988574592 Henry Cohn, 2026, needs more optimization.
8 722 0.684082234595 Henry Cohn, 2026, needs more optimization.
8 723 0.684327548063 Henry Cohn, 2026, needs more optimization.
8 724 0.684572024670 Henry Cohn, 2026, needs more optimization.
8 725 0.684992630075 Henry Cohn, 2026, needs more optimization.
8 726 0.685139487668 Henry Cohn, 2026, needs more optimization.
8 727 0.685417175392 Henry Cohn, 2026, needs more optimization.
8 728 0.685493824678 Henry Cohn, 2026, needs more optimization.
8 729 0.685800750358 Henry Cohn, 2026, needs more optimization.
8 730 0.686122767784 Henry Cohn, 2026, needs more optimization.
8 731 0.686238293498 Henry Cohn, 2026, needs more optimization.
8 732 0.686363545542 Henry Cohn, 2026, needs more optimization.
8 733 0.686431742157 Henry Cohn, 2026, needs more optimization.
8 734 0.686768554422 Henry Cohn, 2026, needs more optimization.
8 735 0.686834302912 Henry Cohn, 2026, needs more optimization.
8 736 0.687498998984 Henry Cohn, 2026, needs more optimization.
8 737 0.687550875671 Henry Cohn, 2026, needs more optimization.
8 738 0.687683482864 Henry Cohn, 2026, needs more optimization.
8 739 0.687767527083 Henry Cohn, 2026, needs more optimization.
8 740 0.687921195711 Henry Cohn, 2026, needs more optimization.
8 741 0.688124294312 Henry Cohn, 2026, needs more optimization.
8 742 0.688248713159 Henry Cohn, 2026, needs more optimization.
8 744 0.688503505435 Henry Cohn, 2026, needs more optimization.
8 745 0.688695128957 Henry Cohn, 2026, needs more optimization.
8 746 0.688880179096 Henry Cohn, 2026, needs more optimization.
8 747 0.688930619300 Henry Cohn, 2026, needs more optimization.
8 748 0.689151548655 Henry Cohn, 2026, needs more optimization.
8 749 0.689287042770 Henry Cohn, 2026, needs more optimization.
8 750 0.689288141702 Henry Cohn, 2026, needs more optimization.
8 751 0.689460174164 Henry Cohn, 2026, needs more optimization.
8 752 0.689823955445 Henry Cohn, 2026, needs more optimization.
8 753 0.689960241317 Henry Cohn, 2026, needs more optimization.
8 754 0.690100260171 Henry Cohn, 2026, needs more optimization.
8 755 0.690114415828 Henry Cohn, 2026, needs more optimization.
8 756 0.690114907482 Henry Cohn, 2026, needs more optimization.
8 757 0.690116219466 Henry Cohn, 2026, needs more optimization.
8 758 0.690122999268 Henry Cohn, 2026, needs more optimization.
8 759 0.690123854201 Henry Cohn, 2026, needs more optimization.
8 760 0.690135076341 Henry Cohn, 2026, needs more optimization.
8 761 0.690141766885 Henry Cohn, 2026, needs more optimization.
8 762 0.690160200040 Henry Cohn, 2026, needs more optimization.
8 763 0.690167768109 Henry Cohn, 2026, needs more optimization.
8 764 0.690913824401 Henry Cohn, 2026, needs more optimization.
8 765 0.690992966422 Henry Cohn, 2026, needs more optimization.
8 766 0.691020774889 Henry Cohn, 2026, needs more optimization.
8 767 0.691147928364 Henry Cohn, 2026, needs more optimization.
8 768 0.691267490650 Henry Cohn, 2026, needs more optimization.
8 769 0.691300519871 Henry Cohn, 2026, needs more optimization.
8 770 0.691509851220 Henry Cohn, 2026, needs more optimization.
8 772 0.691654184434 Henry Cohn, 2026, needs more optimization.
8 773 0.691666212277 Henry Cohn, 2026, needs more optimization.
8 774 0.691756111292 Henry Cohn, 2026, needs more optimization.
8 775 0.691782871122 Henry Cohn, 2026, needs more optimization.
8 776 0.692234022117 Henry Cohn, 2026, needs more optimization.
8 777 0.692355902700 Henry Cohn, 2026, needs more optimization.
8 778 0.692449523111 Henry Cohn, 2026, needs more optimization.
8 779 0.692455040413 Henry Cohn, 2026, needs more optimization.
8 780 0.692525030524 Henry Cohn, 2026, needs more optimization.
8 781 0.692550299794 Henry Cohn, 2026, needs more optimization.
8 782 0.692593285971 Henry Cohn, 2026, needs more optimization.
8 783 0.692706269961 Henry Cohn, 2026, needs more optimization.
8 784 0.692778928021 Henry Cohn, 2026, needs more optimization.
8 785 0.693257813840 Henry Cohn, 2026, needs more optimization.
8 786 0.693484821630 Henry Cohn, 2026, needs more optimization.
8 787 0.693718279298 Henry Cohn, 2026, needs more optimization.
8 788 0.693764242927 Henry Cohn, 2026, needs more optimization.
8 789 0.694024856785 Henry Cohn, 2026, needs more optimization.
8 790 0.694166351634 Henry Cohn, 2026, needs more optimization.
8 791 0.694175853478 Henry Cohn, 2026, needs more optimization.
8 792 0.694200975542 Henry Cohn, 2026, needs more optimization.
8 793 0.694574892758 Henry Cohn, 2026, needs more optimization.
8 794 0.694575917974 Henry Cohn, 2026, needs more optimization.
8 795 0.694610806721 Henry Cohn, 2026, needs more optimization.
8 797 0.694616461550 Henry Cohn, 2026, needs more optimization.
8 798 0.694818547663 Henry Cohn, 2026, needs more optimization.
8 799 0.694857484167 Henry Cohn, 2026, needs more optimization.
8 800 0.695061439169 Henry Cohn, 2026, needs more optimization.
8 801 0.695304433515 Henry Cohn, 2026, needs more optimization.
8 802 0.695555458680 Henry Cohn, 2026, needs more optimization.
8 803 0.695615816088 Henry Cohn, 2026, needs more optimization.
8 804 0.695862248288 Henry Cohn, 2026, needs more optimization.
8 805 0.696113625150 Henry Cohn, 2026, needs more optimization.
8 806 0.696185954942 Henry Cohn, 2026, needs more optimization.
8 807 0.696223672161 Henry Cohn, 2026, needs more optimization.
8 808 0.696225028665 Henry Cohn, 2026, needs more optimization.
8 809 0.696281056563 Henry Cohn, 2026, needs more optimization.
8 810 0.696283094420 Henry Cohn, 2026, needs more optimization.
8 811 0.696657658453 Henry Cohn, 2026, needs more optimization.
8 812 0.696674433242 Henry Cohn, 2026, needs more optimization.
8 813 0.696812182344 Henry Cohn, 2026, needs more optimization.
8 814 0.697481464886 Henry Cohn, 2026, needs more optimization.
8 815 0.697483352759 Henry Cohn, 2026, needs more optimization.
8 816 0.697523432592 Henry Cohn, 2026, needs more optimization.
8 817 0.697525689662 Henry Cohn, 2026, needs more optimization.
8 818 0.697548304432 Henry Cohn, 2026, needs more optimization.
8 819 0.697583050185 Henry Cohn, 2026, needs more optimization.
8 820 0.697594807773 Henry Cohn, 2026, needs more optimization.
8 821 0.697663821271 Henry Cohn, 2026, needs more optimization.
8 822 0.697873896314 Henry Cohn, 2026, needs more optimization.
8 823 0.697925257984 Henry Cohn, 2026, needs more optimization.
8 824 0.697960629300 Henry Cohn, 2026, needs more optimization.
8 825 0.697970144343 Henry Cohn, 2026, needs more optimization.
8 826 0.698100482435 Henry Cohn, 2026, needs more optimization.
8 827 0.698590151291 Henry Cohn, 2026, needs more optimization.
8 828 0.698591738767 Henry Cohn, 2026, needs more optimization.
8 829 0.698601868969 Henry Cohn, 2026, needs more optimization.
8 834 0.698864537961 Henry Cohn, 2026, needs more optimization.
8 835 0.698865115281 Henry Cohn, 2026, needs more optimization.
8 836 0.699603381823 Henry Cohn, 2026, needs more optimization.
8 837 0.699603527866 Henry Cohn, 2026, needs more optimization.
8 838 0.699611626124 Henry Cohn, 2026, needs more optimization.
8 839 0.699629745242 Henry Cohn, 2026, needs more optimization.
8 840 0.699985211070 Henry Cohn, 2026, needs more optimization.
8 841 0.700469880787 Henry Cohn, 2026, needs more optimization.
8 842 0.700472228750 Henry Cohn, 2026, needs more optimization.
8 843 0.700499543206 Henry Cohn, 2026, needs more optimization.
8 844 0.700503547474 Henry Cohn, 2026, needs more optimization.
8 845 0.700522956014 Henry Cohn, 2026, needs more optimization.
8 846 0.700523050600 Henry Cohn, 2026, needs more optimization.
8 847 0.700534017186 Henry Cohn, 2026, needs more optimization.
8 848 0.700572062997 Henry Cohn, 2026, needs more optimization.
8 849 0.701122605859 Henry Cohn, 2026, needs more optimization.
8 850 0.701127098044 Henry Cohn, 2026, needs more optimization.
8 851 0.701131257945 Henry Cohn, 2026, needs more optimization.
8 852 0.701213736332 Henry Cohn, 2026, needs more optimization.
8 853 0.701511214696 Henry Cohn, 2026, needs more optimization.
8 854 0.701522461791 Henry Cohn, 2026, needs more optimization.
8 855 0.702080052808 Henry Cohn, 2026, needs more optimization.
8 856 0.702083854258 Henry Cohn, 2026, needs more optimization.
8 858 0.702084625947 Henry Cohn, 2026, needs more optimization.
8 859 0.702245820835 Henry Cohn, 2026, needs more optimization.
8 860 0.702249351299 Henry Cohn, 2026, needs more optimization.
8 861 0.702295979969 Henry Cohn, 2026, needs more optimization.
8 862 0.702296771008 Henry Cohn, 2026, needs more optimization.
8 863 0.702365575210 Henry Cohn, 2026, needs more optimization.
8 864 0.702383902868 Henry Cohn, 2026, needs more optimization.
8 865 0.702385445288 Henry Cohn, 2026, needs more optimization.
8 867 0.702397123562 Henry Cohn, 2026, needs more optimization.
8 868 0.702408609353 Henry Cohn, 2026, needs more optimization.
8 869 0.702429818893 Henry Cohn, 2026, needs more optimization.
8 870 0.702473192988 Henry Cohn, 2026, needs more optimization.
8 871 0.702551582662 Henry Cohn, 2026, needs more optimization.
8 872 0.702552292207 Numaro AI Autoresearch, 11,000+ New Verified Spherical-Code Records from AI Autoresearch, Numaro Research Report NUMARO-2026-015 (2026), https://numaro.tech/research/spherical-codes-2026/.
8 873 0.702552518575 Numaro AI Autoresearch, 11,000+ New Verified Spherical-Code Records from AI Autoresearch, Numaro Research Report NUMARO-2026-015 (2026), https://numaro.tech/research/spherical-codes-2026/.
8 874 0.703831084022 Henry Cohn, 2026, needs more optimization.
8 875 0.703833479586 Henry Cohn, 2026, needs more optimization.
8 876 0.703838430659 Henry Cohn, 2026, needs more optimization.
8 877 0.704317475980 Henry Cohn, 2026, needs more optimization.
8 880 0.704337398696 Henry Cohn, 2026, needs more optimization.
8 881 0.704344606077 Henry Cohn, 2026, needs more optimization.
8 882 0.704360745621 Henry Cohn, 2026, needs more optimization.
8 883 0.704508684389 Henry Cohn, 2026, needs more optimization.
8 884 0.704525379184 Henry Cohn, 2026, needs more optimization.
8 885 0.704530105656 Henry Cohn, 2026, needs more optimization.
8 886 0.704967507312 Henry Cohn, 2026, needs more optimization.
8 887 0.704975099685 Henry Cohn, 2026, needs more optimization.
8 888 0.704975397755 Henry Cohn, 2026, needs more optimization.
8 889 0.705001440178 Henry Cohn, 2026, needs more optimization.
8 890 0.705020064769 Henry Cohn, 2026, needs more optimization.
8 891 0.705380291375 Henry Cohn, 2026, needs more optimization.
8 892 0.705578305277 Henry Cohn, 2026, needs more optimization.
8 893 0.705611476420 Henry Cohn, 2026, needs more optimization.
8 894 0.705629132266 Henry Cohn, 2026, needs more optimization.
8 895 0.705629484230 Henry Cohn, 2026, needs more optimization.
8 896 0.705636198079 Henry Cohn, 2026, needs more optimization.
8 898 0.705645646014 Henry Cohn, 2026, needs more optimization.
8 899 0.705645706889 Henry Cohn, 2026, needs more optimization.
8 901 0.705679591207 Henry Cohn, 2026, needs more optimization.
8 902 0.705679736946 Henry Cohn, 2026, needs more optimization.
8 903 0.705686397484 Henry Cohn, 2026, needs more optimization.
8 905 0.705968256150 Henry Cohn, 2026, needs more optimization.
8 908 0.706399378544 Henry Cohn, 2026, needs more optimization.
8 909 0.706410382011 Henry Cohn, 2026, needs more optimization.
8 910 0.706411015906 Henry Cohn, 2026, needs more optimization.
8 911 0.706420753295 Henry Cohn, 2026, needs more optimization.
8 912 0.706436986802 Henry Cohn, 2026, needs more optimization.
8 913 0.706457092125 Henry Cohn, 2026, needs more optimization.
8 914 0.706504347886 Henry Cohn, 2026, needs more optimization.
8 915 0.706833147330 Henry Cohn, 2026, needs more optimization.
8 916 0.706855875538 Henry Cohn, 2026, needs more optimization.
8 917 0.706863913772 Henry Cohn, 2026, needs more optimization.
8 918 0.707059191808 Henry Cohn, 2026, needs more optimization.
8 919 0.707061557063 Henry Cohn, 2026, needs more optimization.
8 920 0.707063787048 Henry Cohn, 2026, needs more optimization.
8 922 0.707521864130 Henry Cohn, 2026, needs more optimization.
8 923 0.707522431897 Henry Cohn, 2026, needs more optimization.
8 924 0.707528219550 Henry Cohn, 2026, needs more optimization.
8 925 0.707530782302 Henry Cohn, 2026, needs more optimization.
8 926 0.707629541393 Henry Cohn, 2026, needs more optimization.
8 927 0.707921629256 Henry Cohn, 2026, needs more optimization.
8 928 0.707924239201 Henry Cohn, 2026, needs more optimization.
8 930 0.707937660644 Henry Cohn, 2026, needs more optimization.
8 931 0.707959372745 Henry Cohn, 2026, needs more optimization.
8 932 0.708007131461 Henry Cohn, 2026, needs more optimization.
8 933 0.708011039766 Henry Cohn, 2026, needs more optimization.
8 934 0.708300927727 Henry Cohn, 2026, needs more optimization.
8 935 0.708304960984 Henry Cohn, 2026, needs more optimization.
8 936 0.708305820721 Henry Cohn, 2026, needs more optimization.
8 937 0.708308339972 Henry Cohn, 2026, needs more optimization.
8 938 0.708312554990 Henry Cohn, 2026, needs more optimization.
8 939 0.708865690264 Henry Cohn, 2026, needs more optimization.
8 940 0.708883997492 Henry Cohn, 2026, needs more optimization.
8 942 0.708890590702 Henry Cohn, 2026, needs more optimization.
8 943 0.708946620290 Henry Cohn, 2026, needs more optimization.
8 944 0.708964112201 Henry Cohn, 2026, needs more optimization.
8 945 0.709112029335 Henry Cohn, 2026, needs more optimization.
8 947 0.709112637893 Henry Cohn, 2026, needs more optimization.
8 949 0.709501174969 Henry Cohn, 2026, needs more optimization.
8 950 0.709503372635 Henry Cohn, 2026, needs more optimization.
8 952 0.709508481283 Henry Cohn, 2026, needs more optimization.
8 953 0.709509229753 Henry Cohn, 2026, needs more optimization.
8 954 0.709513713949 Henry Cohn, 2026, needs more optimization.
8 955 0.709886285896 Henry Cohn, 2026, needs more optimization.
8 956 0.709897891473 Henry Cohn, 2026, needs more optimization.
8 957 0.709964639994 Henry Cohn, 2026, needs more optimization.
8 958 0.709973038688 Henry Cohn, 2026, needs more optimization.
8 960 0.710147380704 Numaro AI Autoresearch, 11,000+ New Verified Spherical-Code Records from AI Autoresearch, Numaro Research Report NUMARO-2026-015 (2026), https://numaro.tech/research/spherical-codes-2026/.
8 961 0.710158811271 Henry Cohn, 2026, needs more optimization.
8 962 0.710628575372 Henry Cohn, 2026, needs more optimization.
8 963 0.710648050480 Henry Cohn, 2026, needs more optimization.
8 965 0.710726632255 Henry Cohn, 2026, needs more optimization.
8 966 0.710746177280 Henry Cohn, 2026, needs more optimization.
8 968 0.710756465503 Henry Cohn, 2026, needs more optimization.
8 969 0.710775728715 Henry Cohn, 2026, needs more optimization.
8 970 0.710847051963 Henry Cohn, 2026, needs more optimization.
8 971 0.711350558718 Henry Cohn, 2026, needs more optimization.
8 973 0.711410271207 Henry Cohn, 2026, needs more optimization.
8 974 0.711448229209 Henry Cohn, 2026, needs more optimization.
8 977 0.711456296832 Henry Cohn, 2026, needs more optimization.
8 978 0.711467125010 Henry Cohn, 2026, needs more optimization.
8 979 0.711868123840 Henry Cohn, 2026, needs more optimization.
8 980 0.711880937389 Numaro AI Autoresearch, 11,000+ New Verified Spherical-Code Records from AI Autoresearch, Numaro Research Report NUMARO-2026-015 (2026), https://numaro.tech/research/spherical-codes-2026/.
8 981 0.711912858191 Numaro AI Autoresearch, 11,000+ New Verified Spherical-Code Records from AI Autoresearch, Numaro Research Report NUMARO-2026-015 (2026), https://numaro.tech/research/spherical-codes-2026/.
8 982 0.711936483489 Henry Cohn, 2026, needs more optimization.
8 983 0.711965177015 Henry Cohn, 2026, needs more optimization.
8 984 0.711973239459 Henry Cohn, 2026, needs more optimization.
8 985 0.712236082913 Henry Cohn, 2026, needs more optimization.
8 986 0.712284718069 Henry Cohn, 2026, needs more optimization.
8 987 0.712301328587 Numaro AI Autoresearch, 11,000+ New Verified Spherical-Code Records from AI Autoresearch, Numaro Research Report NUMARO-2026-015 (2026), https://numaro.tech/research/spherical-codes-2026/.
8 988 0.712314426025 Henry Cohn, 2026, needs more optimization.
8 989 0.712553070373 Henry Cohn, 2026, needs more optimization.
8 990 0.712933317720 Henry Cohn, 2026, needs more optimization.
8 992 0.712941734601 Henry Cohn, 2026, needs more optimization.
8 993 0.712956123011 Henry Cohn, 2026, needs more optimization.
8 995 0.712957474969 Henry Cohn, 2026, needs more optimization.
8 996 0.712959704807 Henry Cohn, 2026, needs more optimization.
8 997 0.713013757239 Henry Cohn, 2026, needs more optimization.
8 998 0.713043212880 Henry Cohn, 2026, needs more optimization.
8 999 0.713096194068 Henry Cohn, 2026, needs more optimization.
8 1000 0.713098626788 Henry Cohn, 2026, needs more optimization.
8 1001 0.713158809405 Henry Cohn, 2026, needs more optimization.
8 1002 0.713215630015 Henry Cohn, 2026, needs more optimization.
8 1003 0.713235261092 Henry Cohn, 2026, needs more optimization.
8 1004 0.713270610291 Henry Cohn, 2026, needs more optimization.
8 1005 0.713354072023 Henry Cohn, 2026, needs more optimization.
8 1006 0.713359220896 Henry Cohn, 2026, needs more optimization.
8 1007 0.713455278822 Henry Cohn, 2026, needs more optimization.
8 1008 0.713526474986 Henry Cohn, 2026, needs more optimization.
8 1010 0.713579362093 Henry Cohn, 2026, needs more optimization.
8 1011 0.713623934623 Henry Cohn, 2026, needs more optimization.
8 1012 0.713663647953 Henry Cohn, 2026, needs more optimization.
8 1013 0.713676332691 Henry Cohn, 2026, needs more optimization.
8 1014 0.713690388283 Henry Cohn, 2026, needs more optimization.
8 1015 0.713701634133 Henry Cohn, 2026, needs more optimization.
8 1016 0.713731117549 Henry Cohn, 2026, needs more optimization.
8 1017 0.713765260179 Henry Cohn, 2026, needs more optimization.
8 1018 0.713802412200 Henry Cohn, 2026, needs more optimization.
8 1019 0.713816564697 Henry Cohn, 2026, needs more optimization.
8 1020 0.713821612542 Henry Cohn, 2026, needs more optimization.
8 1021 0.713862252795 Henry Cohn, 2026, needs more optimization.
8 1022 0.713871532851 Henry Cohn, 2026, needs more optimization.
8 1023 0.713876896216 Henry Cohn, 2026, needs more optimization.
8 1024 0.713972790894 Numaro AI Autoresearch, 11,000+ New Verified Spherical-Code Records from AI Autoresearch, Numaro Research Report NUMARO-2026-015 (2026), https://numaro.tech/research/spherical-codes-2026/.
9 19 0.079067151218 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
441⁢x3−81⁢x2−9⁢x+1
9 20 0.087067958322 H. Cohn, Small spherical and projective codes, data set, 2022, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
63⁢x2+6⁢x−1
9 21 0.087067958322 H. Cohn, Small spherical and projective codes, data set, 2022, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
63⁢x2+6⁢x−1
9 22 0.109015375240 H. Cohn, Small spherical and projective codes, data set, 2022, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
662⁢x4+23⁢x3−67⁢x2−3⁢x+1
9 23 0.114272369686 H. Cohn, Small spherical and projective codes, data set, 2022, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
Minimal polynomial listed in plain text data
9 24 0.127138702332 H. Cohn, Small spherical and projective codes, data set, 2022, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
9 25 0.135451570712 H. Cohn, Small spherical and projective codes, data set, updated 2023, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
9 26 0.146662063556 H. Cohn, Small spherical and projective codes, data set, 2022, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
9 27 0.149913487586 H. Cohn, Small spherical and projective codes, data set, updated 2025, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
9 28 0.150185176423 H. Cohn, Small spherical and projective codes, data set, updated 2024, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
9 29 0.150221104823 H. Cohn, Small spherical and projective codes, data set, 2022, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
31⁢x2+2⁢x−1
9 30 0.150221104823 H. Cohn, Small spherical and projective codes, data set, 2022, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
31⁢x2+2⁢x−1
9 31 0.150221104823 H. Cohn, Small spherical and projective codes, data set, 2022, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
31⁢x2+2⁢x−1
9 32 0.150221104823 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
31⁢x2+2⁢x−1
9 33 0.180525091271 Henry Cohn, 2023.
9 34 0.183408724272 Henry Cohn, 2023.
9 35 0.195176120873 Henry Cohn, 2024.
9 36 0.199856614456 Valentin Khrulkov, 2026, using the program of A. Kravatsky, V. Khrulkov, and I. Oseledets, ImprovEvolve: basin-hopping meets LLM-guided evolutionary search, ICML 2026 AI4Math Workshop Poster, https://openreview.net/forum?id=nE1q0gRDNr, arXiv:2602.10233.
9 37 0.213781170696 Henry Cohn, 2025.
9 38 0.216954638443 A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
Minimal polynomial listed in plain text data
9 39 0.222837046412 Henry Cohn, 2023.
9 40 0.225659998291 Henry Cohn, 2025.
9 42 0.226907255686 Henry Cohn, 2025.
190336⁢x6+377632⁢x5−322153⁢x4−82188⁢x3+48762⁢x2−972⁢x−729
9 43 0.231201190091 Henry Cohn, 2023.
9 44 0.233554527157 Henry Cohn, 2025.
Minimal polynomial listed in plain text data
9 47 0.238172399483 Henry Cohn, 2023.
335⁢x2−42⁢x−9
9 48 0.254741665820 Henry Cohn, 2025.
9 50 0.256477368938 Henry Cohn, 2026.
23⁢x2−2⁢x−1
9 51 0.266033138128 Henry Cohn, 2026.
9 52 0.267191024627 Henry Cohn, 2023.
71⁢x2−4⁢x−4
9 53 0.269834758170 Henry Cohn, 2023.
Minimal polynomial listed in plain text data
9 54 0.271671378177 Henry Cohn, 2025.
9 56 0.272133267170 Henry Cohn, 2025.
9 57 0.282916244589 Henry Cohn, 2026.
9 58 0.288070633971 Henry Cohn, 2026.
9 59 0.293943006572 Henry Cohn, 2025.
9 60 0.294882506582 Henry Cohn, 2026.
9 61 0.297699008547 Henry Cohn, 2026.
9 62 0.299403421072 Henry Cohn, 2026, needs more optimization.
9 63 0.302685227391 Henry Cohn, 2025.
9 64 0.306653313780 Henry Cohn, 2023.
9 65 0.310475871050 Henry Cohn, 2026.
9 66 0.313645759189 Henry Cohn, 2026.
9 67 0.317743907015 Henry Cohn, 2026.
9 68 0.322050465427 Henry Cohn, 2025.
9 69 0.324666182383 Henry Cohn, 2025.
9 70 0.327710258396 Henry Cohn, 2026.
9 71 0.328977728606 Henry Cohn, 2026.
9 72 0.329462395516 Henry Cohn, 2026, needs more optimization.
9 74 0.329478113244 A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
9 77 0.329568177750 Henry Cohn, 2026.
9 78 0.330101895521 Henry Cohn, 2025.
9 79 0.330918543665 Henry Cohn, 2024.
9 80 0.332977706545 Henry Cohn, 2025.
9 96 0.333333333334 T. Ericson and V. Zinoviev, Spherical codes generated by binary partitions of symmetric pointsets, IEEE Trans. Inform. Theory 41 (1995), 107–129, doi:10.1109/18.370114.
3⁢x−1
9 97 0.371099110252 Henry Cohn, 2024.
9 98 0.372095101498 Henry Cohn, 2025.
9 101 0.375074698542 Henry Cohn, 2025.
3191⁢x4+68⁢x3−350⁢x2−44⁢x−1
9 102 0.378388662601 A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
9 103 0.378849371703 Henry Cohn, 2026, needs more optimization.
9 104 0.379090673532 A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
9 105 0.391186576796 A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
9 106 0.394987130628 A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
9 107 0.397604188479 Henry Cohn, 2026, needs more optimization.
9 108 0.399008208476 A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
9 109 0.401769349098 Henry Cohn, 2026, needs more optimization.
9 110 0.404779316037 A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
9 111 0.406315844175 Henry Cohn, 2026, needs more optimization.
9 112 0.408809354652 Henry Cohn, 2026, needs more optimization.
9 113 0.410377412245 Henry Cohn, 2026, needs more optimization.
9 114 0.411211045215 Henry Cohn, 2026, needs more optimization.
9 115 0.412580097180 Henry Cohn, 2026, needs more optimization.
9 116 0.413817761243 Henry Cohn, 2026, needs more optimization.
9 117 0.414582258230 Henry Cohn, 2026, needs more optimization.
9 118 0.415620595367 Henry Cohn, 2026, needs more optimization.
9 119 0.416041502843 A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
9 120 0.416495806056 Henry Cohn, 2026, needs more optimization.
9 121 0.416963250261 Henry Cohn, 2026, needs more optimization.
9 122 0.418282170106 Henry Cohn, 2026.
9 123 0.419103980438 Henry Cohn, 2026, needs more optimization.
9 124 0.419753748412 Henry Cohn, 2026, needs more optimization.
9 126 0.419821271705 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
11⁢x2−7⁢x+1
9 127 0.420798443080 Henry Cohn, 2026, needs more optimization.
9 128 0.421924268897 Henry Cohn, 2026, needs more optimization.
9 129 0.422328036854 Henry Cohn, 2026, needs more optimization.
9 130 0.422354936715 Henry Cohn, 2026, needs more optimization.
9 131 0.422480787968 Henry Cohn, 2026, needs more optimization.
9 132 0.426176700405 Henry Cohn, 2026, needs more optimization.
9 133 0.427220992691 Henry Cohn, 2026, needs more optimization.
9 134 0.428560129298 Henry Cohn, 2026, needs more optimization.
9 146 0.428571428572 M. Ganzhinov and P. R. J. Östergård, Spherical codes with prescribed signed permutation automorphisms inside shells of low-dimensional integer lattices, IEEE Trans. Inform. Theory 70 (2024), 8669–8674, doi:10.1109/tit.2024.3462593, arXiv:2403.04330.
7⁢x−3
9 147 0.441557533284 Henry Cohn, 2026, needs more optimization.
9 148 0.444821514980 Henry Cohn, 2026, needs more optimization.
9 149 0.447315325073 Henry Cohn, 2026, needs more optimization.
9 150 0.449515109655 Henry Cohn, 2026, needs more optimization.
9 151 0.449961750335 Henry Cohn, 2026, needs more optimization.
9 152 0.451335383742 Henry Cohn, 2026, needs more optimization.
9 153 0.453775580485 Henry Cohn, 2026, needs more optimization.
9 165 0.454545454546 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
11⁢x−5
9 168 0.454545454546 Henry Cohn, 2026.
11⁢x−5
9 171 0.454545454546 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
11⁢x−5
9 172 0.454957421011 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
9 173 0.455018137625 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
9 174 0.455357822235 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
9 175 0.459556172123 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
9 176 0.461292480151 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
9 177 0.461573261130 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
9 178 0.462117811360 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
9 179 0.462342896984 Henry Cohn, 2026, needs more optimization.
9 180 0.462395912009 Henry Cohn, 2026, needs more optimization.
9 181 0.462508208693 Henry Cohn, 2026, needs more optimization.
9 182 0.462732221054 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
9 183 0.463287984078 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
9 184 0.465115672969 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
9 185 0.467204760305 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
9 186 0.470064330442 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
9 187 0.471348636813 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
9 188 0.471653547287 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
9 189 0.473670491722 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
9 209 0.475156558223 Henry Cohn, 2026.
103⁢x2−30⁢x−9
9 210 0.475233276896 Henry Cohn, 2026, needs more optimization.
9 211 0.478983398769 Henry Cohn, 2026, needs more optimization.
9 212 0.481582508861 Henry Cohn, 2026, needs more optimization.
9 213 0.483367964064 Henry Cohn, 2026, needs more optimization.
9 214 0.484883886449 Henry Cohn, 2026, needs more optimization.
9 215 0.485412775808 Henry Cohn, 2026, needs more optimization.
9 216 0.485998504243 Henry Cohn, 2026, needs more optimization.
9 217 0.486671258272 Henry Cohn, 2026, needs more optimization.
9 218 0.492804963179 Henry Cohn, 2026, needs more optimization.
9 219 0.492955542035 Henry Cohn, 2026, needs more optimization.
9 220 0.495572296401 Henry Cohn, 2026, needs more optimization.
9 221 0.496134698803 Henry Cohn, 2026, needs more optimization.
9 222 0.496670174636 Henry Cohn, 2026, needs more optimization.
9 223 0.496814486878 Henry Cohn, 2026, needs more optimization.
9 224 0.496926847587 Henry Cohn, 2026, needs more optimization.
9 225 0.497084456039 Henry Cohn, 2026, needs more optimization.
9 226 0.497519235655 Henry Cohn, 2026, needs more optimization.
9 227 0.497548191114 Henry Cohn, 2026, needs more optimization.
9 228 0.498094948967 Henry Cohn, 2026, needs more optimization.
9 229 0.498287395784 Henry Cohn, 2026, needs more optimization.
9 230 0.498479843456 Henry Cohn, 2026, needs more optimization.
9 231 0.498564023611 Henry Cohn, 2026, needs more optimization.
9 232 0.498592843255 Henry Cohn, 2026, needs more optimization.
9 233 0.498782649996 Henry Cohn, 2026, needs more optimization.
9 234 0.499011651012 Henry Cohn, 2026, needs more optimization.
9 235 0.499135035636 Henry Cohn, 2026, needs more optimization.
9 236 0.499135403347 Henry Cohn, 2026, needs more optimization.
9 237 0.499189819130 Henry Cohn, 2026, needs more optimization.
9 238 0.499254951846 Henry Cohn, 2026, needs more optimization.
9 239 0.499337108362 Henry Cohn, 2026, needs more optimization.
9 240 0.499480424858 Henry Cohn, 2026, needs more optimization.
9 241 0.499538008060 Henry Cohn, 2026, needs more optimization.
9 242 0.499561100227 Henry Cohn, 2026, needs more optimization.
9 243 0.499577141906 Henry Cohn, 2026, needs more optimization.
9 244 0.499612883475 Henry Cohn, 2026, needs more optimization.
9 245 0.499705104070 Henry Cohn, 2026, needs more optimization.
9 246 0.499836894116 Henry Cohn, 2026, needs more optimization.
9 247 0.499876227869 Henry Cohn, 2026, needs more optimization.
9 248 0.499944280677 Henry Cohn, 2026, needs more optimization.
9 249 0.499966295346 Henry Cohn, 2026, needs more optimization.
9 306 0.5 J. Leech and N. J. A. Sloane, Sphere packings and error-correcting codes, Canadian J. Math. 23 (1971), 718–745, doi:10.4153/CJM-1971-081-3; H. Cohn and I. Rajagopal, Variations on five-dimensional sphere packings, preprint, 2024, arXiv:2412.00937.
2⁢x−1
9 307 0.517020006376 Henry Cohn, 2026, needs more optimization.
9 308 0.518911020501 Henry Cohn, 2026, needs more optimization.
9 309 0.520835148079 Henry Cohn, 2026, needs more optimization.
9 310 0.521829161479 Henry Cohn, 2026, needs more optimization.
9 311 0.521840732694 Henry Cohn, 2026, needs more optimization.
9 312 0.521845423776 Henry Cohn, 2026, needs more optimization.
9 313 0.522200619152 Henry Cohn, 2026, needs more optimization.
9 330 0.523809523810 Henry Cohn and Ilmari Vahteristo (independently), 2026.
21⁢x−11
9 331 0.528486973796 Henry Cohn, 2026, needs more optimization.
9 332 0.530011486582 Henry Cohn, 2026, needs more optimization.
9 333 0.533317479777 Henry Cohn, 2026, needs more optimization.
9 334 0.534880501029 Henry Cohn, 2026, needs more optimization.
9 335 0.536073163685 Henry Cohn, 2026, needs more optimization.
9 336 0.536191435188 Henry Cohn, 2026, needs more optimization.
9 337 0.536435633791 Henry Cohn, 2026, needs more optimization.
9 338 0.536441576637 Henry Cohn, 2026, needs more optimization.
9 339 0.537017557534 Henry Cohn, 2026, needs more optimization.
9 340 0.538002447067 Henry Cohn, 2026, needs more optimization.
9 341 0.538056434706 Henry Cohn, 2026, needs more optimization.
9 342 0.539405267259 Henry Cohn, 2026, needs more optimization.
9 343 0.540088308685 Henry Cohn, 2026, needs more optimization.
9 344 0.540165093065 Henry Cohn, 2026, needs more optimization.
9 345 0.540668367698 Henry Cohn, 2026, needs more optimization.
9 346 0.541056179355 Henry Cohn, 2026, needs more optimization.
9 347 0.541586860369 Henry Cohn, 2026, needs more optimization.
9 348 0.542525870436 Henry Cohn, 2026, needs more optimization.
9 349 0.543233881535 Henry Cohn, 2026, needs more optimization.
9 350 0.543337505237 Henry Cohn, 2026, needs more optimization.
9 351 0.543634058326 Henry Cohn, 2026, needs more optimization.
9 352 0.543836419842 Henry Cohn, 2026, needs more optimization.
9 353 0.543919733502 Henry Cohn, 2026, needs more optimization.
9 354 0.543988993615 Henry Cohn, 2026, needs more optimization.
9 355 0.544036060116 Henry Cohn, 2026, needs more optimization.
9 356 0.544183215856 Henry Cohn, 2026, needs more optimization.
9 357 0.544707550799 Henry Cohn, 2026, needs more optimization.
9 358 0.544843171827 Henry Cohn, 2026, needs more optimization.
9 359 0.545945208958 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
9 360 0.546522386214 Henry Cohn, 2026, needs more optimization.
9 361 0.546736309254 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
9 482 0.546918160679 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
7⁢x2−2⁢x−1
9 483 0.555131086100 Henry Cohn, 2026, needs more optimization.
9 484 0.556740696957 Henry Cohn, 2026, needs more optimization.
9 485 0.562156243476 Henry Cohn, 2026, needs more optimization.
9 486 0.565394637504 Henry Cohn, 2026, needs more optimization.
9 487 0.568200798897 Henry Cohn, 2026, needs more optimization.
9 488 0.569244061493 Henry Cohn, 2026, needs more optimization.
9 489 0.570781288936 Henry Cohn, 2026, needs more optimization.
9 490 0.572422283995 Henry Cohn, 2026, needs more optimization.
9 491 0.574075087841 Henry Cohn, 2026, needs more optimization.
9 492 0.574928622693 Henry Cohn, 2026, needs more optimization.
9 493 0.576322163126 Henry Cohn, 2026, needs more optimization.
9 494 0.577910205845 Henry Cohn, 2026, needs more optimization.
9 495 0.578749902869 Henry Cohn, 2026, needs more optimization.
9 496 0.580066368685 Henry Cohn, 2026, needs more optimization.
9 497 0.580561930308 Henry Cohn, 2026, needs more optimization.
9 498 0.581667168999 Henry Cohn, 2026, needs more optimization.
9 499 0.582980383305 Henry Cohn, 2026, needs more optimization.
9 500 0.583854478902 Henry Cohn, 2026, needs more optimization.
9 501 0.584637563741 Henry Cohn, 2026, needs more optimization.
9 502 0.585602287416 Henry Cohn, 2026, needs more optimization.
9 503 0.586187162317 Henry Cohn, 2026, needs more optimization.
9 504 0.586661652201 Henry Cohn, 2026, needs more optimization.
9 505 0.587085107885 Henry Cohn, 2026, needs more optimization.
9 506 0.588068244510 Henry Cohn, 2026, needs more optimization.
9 507 0.588215485331 Henry Cohn, 2026, needs more optimization.
9 508 0.589090891057 Henry Cohn, 2026, needs more optimization.
9 509 0.589558925093 Henry Cohn, 2026, needs more optimization.
9 510 0.589564453019 Henry Cohn, 2026, needs more optimization.
9 511 0.589572824790 Henry Cohn, 2026, needs more optimization.
9 512 0.589586260342 Henry Cohn, 2026, needs more optimization.
9 513 0.589788458064 Henry Cohn, 2026, needs more optimization.
9 514 0.589801365294 Henry Cohn, 2026, needs more optimization.
9 515 0.589810162025 Henry Cohn, 2026, needs more optimization.
9 516 0.589818497105 Henry Cohn, 2026, needs more optimization.
9 517 0.589831570992 Henry Cohn, 2026, needs more optimization.
9 518 0.589848904731 Henry Cohn, 2026, needs more optimization.
9 519 0.589886168140 Henry Cohn, 2026, needs more optimization.
9 520 0.589889828555 Henry Cohn, 2026, needs more optimization.
9 521 0.589894037724 A. Kravatsky, V. Khrulkov, and I. Oseledets, ImprovEvolve: basin-hopping meets LLM-guided evolutionary search, ICML 2026 AI4Math Workshop Poster, https://openreview.net/forum?id=nE1q0gRDNr, arXiv:2602.10233, after some further optimization.
9 522 0.589905827862 Henry Cohn, 2026, needs more optimization.
9 523 0.589909801233 Henry Cohn, 2026, needs more optimization.
9 524 0.589915327031 Henry Cohn, 2026, needs more optimization.
9 525 0.590355099480 Henry Cohn, 2026, needs more optimization.
9 526 0.591418930421 Henry Cohn, 2026, needs more optimization.
9 527 0.593589111405 Henry Cohn, 2026, needs more optimization.
9 528 0.594370199339 Henry Cohn, 2026, needs more optimization.
9 529 0.595167863103 Henry Cohn, 2026, needs more optimization.
9 530 0.595851112299 Henry Cohn, 2026, needs more optimization.
9 531 0.596429630524 Henry Cohn, 2026, needs more optimization.
9 532 0.596829158554 Henry Cohn, 2026, needs more optimization.
9 533 0.596958058829 Henry Cohn, 2026, needs more optimization.
9 534 0.597601064141 Henry Cohn, 2026, needs more optimization.
9 535 0.597916522425 Henry Cohn, 2026, needs more optimization.
9 536 0.598621708953 Henry Cohn, 2026, needs more optimization.
9 537 0.598789702993 Henry Cohn, 2026, needs more optimization.
9 538 0.598994748687 Henry Cohn, 2026, needs more optimization.
9 539 0.599422005113 Henry Cohn, 2026, needs more optimization.
9 540 0.599733464770 Henry Cohn, 2026, needs more optimization.
9 541 0.599873219660 Henry Cohn, 2026, needs more optimization.
9 542 0.599968490183 Henry Cohn, 2026, needs more optimization.
9 610 0.6 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
5⁢x−3
9 612 0.6 M. Ganzhinov and P. R. J. Östergård, Spherical codes with prescribed signed permutation automorphisms inside shells of low-dimensional integer lattices, IEEE Trans. Inform. Theory 70 (2024), 8669–8674, doi:10.1109/tit.2024.3462593, arXiv:2403.04330.
5⁢x−3
9 613 0.605088440846 Henry Cohn, 2026, needs more optimization.
9 614 0.606325591123 Henry Cohn, 2026, needs more optimization.
9 615 0.606815290817 Henry Cohn, 2026, needs more optimization.
9 616 0.607944337733 Henry Cohn, 2026, needs more optimization.
9 617 0.608242609400 Henry Cohn, 2026, needs more optimization.
9 618 0.608318679064 Henry Cohn, 2026, needs more optimization.
9 619 0.608425316027 Henry Cohn, 2026, needs more optimization.
9 620 0.613520023806 Henry Cohn, 2026, needs more optimization.
9 621 0.613559531766 Henry Cohn, 2026, needs more optimization.
9 622 0.613588227822 Henry Cohn, 2026, needs more optimization.
9 623 0.613624951242 Henry Cohn, 2026, needs more optimization.
9 624 0.613705974838 Henry Cohn, 2026, needs more optimization.
9 625 0.613722729093 Henry Cohn, 2026, needs more optimization.
9 626 0.613825304318 Henry Cohn, 2026, needs more optimization.
9 627 0.614357024359 Henry Cohn, 2026, needs more optimization.
9 628 0.614795967734 Henry Cohn, 2026, needs more optimization.
9 629 0.615187198209 Henry Cohn, 2026, needs more optimization.
9 630 0.615581131335 Henry Cohn, 2026, needs more optimization.
9 631 0.615984807016 Henry Cohn, 2026, needs more optimization.
9 632 0.617563322021 Henry Cohn, 2026, needs more optimization.
9 633 0.617725809555 Henry Cohn, 2026, needs more optimization.
9 636 0.618033022014 Henry Cohn, 2026, needs more optimization.
9 637 0.618033194702 Henry Cohn, 2026, needs more optimization.
9 639 0.618033458638 Henry Cohn, 2026, needs more optimization.
9 642 0.618033508794 Henry Cohn, 2026, needs more optimization.
9 643 0.618033531240 Henry Cohn, 2026, needs more optimization.
9 644 0.618033987482 Henry Cohn, 2026, needs more optimization.
9 645 0.618033987526 Henry Cohn, 2026, needs more optimization.
9 722 0.618033988750 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
x2+x−1
9 723 0.624150426062 Henry Cohn, 2026, needs more optimization.
9 724 0.642721560289 Henry Cohn, 2026, needs more optimization.
9 725 0.642927485092 Henry Cohn, 2026, needs more optimization.
9 726 0.643184786115 Henry Cohn, 2026, needs more optimization.
9 727 0.643231883292 Henry Cohn, 2026, needs more optimization.
9 728 0.643354657418 Henry Cohn, 2026, needs more optimization.
9 729 0.643385603684 Henry Cohn, 2026, needs more optimization.
9 730 0.643665751311 Henry Cohn, 2026, needs more optimization.
9 731 0.643689559046 Henry Cohn, 2026, needs more optimization.
9 732 0.643699534107 Henry Cohn, 2026, needs more optimization.
9 733 0.643813753265 Henry Cohn, 2026, needs more optimization.
9 734 0.644253278983 Henry Cohn, 2026, needs more optimization.
9 735 0.644261705976 Henry Cohn, 2026, needs more optimization.
9 736 0.644480278480 Henry Cohn, 2026, needs more optimization.
9 737 0.644548821887 Henry Cohn, 2026, needs more optimization.
9 738 0.644553237764 Henry Cohn, 2026, needs more optimization.
9 739 0.644818881418 Henry Cohn, 2026, needs more optimization.
9 740 0.645076590083 Henry Cohn, 2026, needs more optimization.
9 741 0.645091777530 Henry Cohn, 2026, needs more optimization.
9 742 0.645154959069 Henry Cohn, 2026, needs more optimization.
9 743 0.645211315551 Henry Cohn, 2026, needs more optimization.
9 744 0.645310865487 Henry Cohn, 2026, needs more optimization.
9 745 0.645556409988 Henry Cohn, 2026, needs more optimization.
9 746 0.645572213375 Henry Cohn, 2026, needs more optimization.
9 748 0.645598656076 Henry Cohn, 2026, needs more optimization.
9 749 0.645604199108 Henry Cohn, 2026, needs more optimization.
9 750 0.645604199109 A. Kravatsky, V. Khrulkov, and I. Oseledets, ImprovEvolve: basin-hopping meets LLM-guided evolutionary search, ICML 2026 AI4Math Workshop Poster, https://openreview.net/forum?id=nE1q0gRDNr, arXiv:2602.10233, after some further optimization.
9 751 0.646101413995 Henry Cohn, 2026, needs more optimization.
9 752 0.646422600330 Henry Cohn, 2026, needs more optimization.
9 753 0.646606524330 Henry Cohn, 2026, needs more optimization.
9 754 0.646623609923 Henry Cohn, 2026, needs more optimization.
9 755 0.646634849801 Henry Cohn, 2026, needs more optimization.
9 756 0.646792067762 Henry Cohn, 2026, needs more optimization.
9 757 0.646987096413 Henry Cohn, 2026, needs more optimization.
9 758 0.647155957106 Henry Cohn, 2026, needs more optimization.
9 760 0.647388747232 Henry Cohn, 2026, needs more optimization.
9 761 0.647426604226 Henry Cohn, 2026, needs more optimization.
9 762 0.647473643069 Henry Cohn, 2026, needs more optimization.
9 763 0.647857777728 Henry Cohn, 2026, needs more optimization.
9 764 0.647877831712 Henry Cohn, 2026, needs more optimization.
9 765 0.647987366378 Henry Cohn, 2026, needs more optimization.
9 766 0.648003950956 Henry Cohn, 2026, needs more optimization.
9 767 0.648187226152 Henry Cohn, 2026, needs more optimization.
9 768 0.648261071245 Henry Cohn, 2026, needs more optimization.
9 769 0.648382280144 Henry Cohn, 2026, needs more optimization.
9 770 0.648403964750 Henry Cohn, 2026, needs more optimization.
9 771 0.648939121593 Henry Cohn, 2026, needs more optimization.
9 772 0.648955472806 Henry Cohn, 2026, needs more optimization.
9 773 0.648959902389 Henry Cohn, 2026, needs more optimization.
9 774 0.649035264532 Henry Cohn, 2026, needs more optimization.
9 775 0.649278548648 Henry Cohn, 2026, needs more optimization.
9 776 0.649281111642 Henry Cohn, 2026, needs more optimization.
9 777 0.649349557884 Henry Cohn, 2026, needs more optimization.
9 778 0.649374430744 Henry Cohn, 2026, needs more optimization.
9 779 0.649774292889 Henry Cohn, 2026, needs more optimization.
9 780 0.649790515659 Henry Cohn, 2026, needs more optimization.
9 781 0.649812053326 Henry Cohn, 2026, needs more optimization.
9 782 0.649824333783 Henry Cohn, 2026, needs more optimization.
9 783 0.649830170704 Henry Cohn, 2026, needs more optimization.
9 784 0.649832827855 Henry Cohn, 2026, needs more optimization.
9 785 0.649836443819 Henry Cohn, 2026, needs more optimization.
9 786 0.649845567424 Henry Cohn, 2026, needs more optimization.
9 787 0.650694641366 Henry Cohn, 2026, needs more optimization.
9 788 0.650720862977 Henry Cohn, 2026, needs more optimization.
9 789 0.650803483813 Henry Cohn, 2026, needs more optimization.
9 790 0.651025072784 Henry Cohn, 2026, needs more optimization.
9 791 0.651271968969 Henry Cohn, 2026, needs more optimization.
9 792 0.651289304987 Henry Cohn, 2026, needs more optimization.
9 793 0.651366797888 Henry Cohn, 2026, needs more optimization.
9 794 0.651509838219 Henry Cohn, 2026, needs more optimization.
9 795 0.651637334271 Henry Cohn, 2026, needs more optimization.
9 796 0.651645693347 Henry Cohn, 2026, needs more optimization.
9 797 0.651669348573 Henry Cohn, 2026, needs more optimization.
9 798 0.651848620818 Henry Cohn, 2026, needs more optimization.
9 799 0.652135186476 Henry Cohn, 2026, needs more optimization.
9 800 0.652146255882 Henry Cohn, 2026, needs more optimization.
9 801 0.652204302043 Henry Cohn, 2026, needs more optimization.
9 802 0.652260814562 Henry Cohn, 2026, needs more optimization.
9 803 0.652502322012 Henry Cohn, 2026, needs more optimization.
9 804 0.652530464075 Henry Cohn, 2026, needs more optimization.
9 805 0.652542824610 Henry Cohn, 2026, needs more optimization.
9 806 0.652684833429 Henry Cohn, 2026, needs more optimization.
9 807 0.652898823052 Henry Cohn, 2026, needs more optimization.
9 808 0.652936150300 Henry Cohn, 2026, needs more optimization.
9 809 0.653140355308 Henry Cohn, 2026, needs more optimization.
9 810 0.653153337645 Henry Cohn, 2026, needs more optimization.
9 811 0.653206935054 Henry Cohn, 2026, needs more optimization.
9 812 0.653342032034 Henry Cohn, 2026, needs more optimization.
9 813 0.653405755005 Henry Cohn, 2026, needs more optimization.
9 814 0.653661144038 Henry Cohn, 2026, needs more optimization.
9 815 0.653751090289 Henry Cohn, 2026, needs more optimization.
9 816 0.653804443137 Henry Cohn, 2026, needs more optimization.
9 817 0.653831271323 Henry Cohn, 2026, needs more optimization.
9 818 0.653902949771 Henry Cohn, 2026, needs more optimization.
9 819 0.654105764524 Henry Cohn, 2026, needs more optimization.
9 820 0.654112354917 Henry Cohn, 2026, needs more optimization.
9 821 0.654197824215 Henry Cohn, 2026, needs more optimization.
9 822 0.654225455243 Henry Cohn, 2026, needs more optimization.
9 823 0.654353944407 Henry Cohn, 2026, needs more optimization.
9 824 0.654457227661 Henry Cohn, 2026, needs more optimization.
9 825 0.654598861149 Henry Cohn, 2026, needs more optimization.
9 826 0.654786945437 Henry Cohn, 2026, needs more optimization.
9 827 0.654972589029 Henry Cohn, 2026, needs more optimization.
9 828 0.654989500670 Henry Cohn, 2026, needs more optimization.
9 829 0.655125280660 Henry Cohn, 2026, needs more optimization.
9 830 0.655136358218 Henry Cohn, 2026, needs more optimization.
9 831 0.655438475090 Henry Cohn, 2026, needs more optimization.
9 832 0.655440390554 Henry Cohn, 2026, needs more optimization.
9 833 0.655628704989 Henry Cohn, 2026, needs more optimization.
9 834 0.655667602003 Henry Cohn, 2026, needs more optimization.
9 835 0.655711019276 Henry Cohn, 2026, needs more optimization.
9 836 0.655716650323 Henry Cohn, 2026, needs more optimization.
9 837 0.655719681396 Henry Cohn, 2026, needs more optimization.
9 838 0.655721095970 Henry Cohn, 2026, needs more optimization.
9 839 0.656321531617 Henry Cohn, 2026, needs more optimization.
9 840 0.656386669815 Henry Cohn, 2026, needs more optimization.
9 841 0.656785021817 Henry Cohn, 2026, needs more optimization.
9 842 0.656789772890 Henry Cohn, 2026, needs more optimization.
9 843 0.657066220406 Henry Cohn, 2026, needs more optimization.
9 844 0.657082810719 Henry Cohn, 2026, needs more optimization.
9 845 0.657121395833 Henry Cohn, 2026, needs more optimization.
9 846 0.657373078563 Henry Cohn, 2026, needs more optimization.
9 847 0.657402922209 Henry Cohn, 2026, needs more optimization.
9 848 0.657405778254 Henry Cohn, 2026, needs more optimization.
9 849 0.657435048883 Henry Cohn, 2026, needs more optimization.
9 850 0.657500756593 Henry Cohn, 2026, needs more optimization.
9 851 0.657736062641 Henry Cohn, 2026, needs more optimization.
9 852 0.657773460655 Henry Cohn, 2026, needs more optimization.
9 853 0.657782515473 Henry Cohn, 2026, needs more optimization.
9 854 0.657796352915 Henry Cohn, 2026, needs more optimization.
9 855 0.657979581959 Henry Cohn, 2026, needs more optimization.
9 856 0.658300533514 Henry Cohn, 2026, needs more optimization.
9 857 0.658349956628 Henry Cohn, 2026, needs more optimization.
9 858 0.658537663106 Henry Cohn, 2026, needs more optimization.
9 859 0.658589303721 Henry Cohn, 2026, needs more optimization.
9 860 0.658757155945 Henry Cohn, 2026, needs more optimization.
9 861 0.658810497836 Henry Cohn, 2026, needs more optimization.
9 862 0.658978584705 Henry Cohn, 2026, needs more optimization.
9 863 0.658993813654 Henry Cohn, 2026, needs more optimization.
9 864 0.659004546802 Henry Cohn, 2026, needs more optimization.
9 865 0.659013593117 Henry Cohn, 2026, needs more optimization.
9 866 0.659015260821 Henry Cohn, 2026, needs more optimization.
9 867 0.659044054984 Henry Cohn, 2026, needs more optimization.
9 868 0.659053193901 Henry Cohn, 2026, needs more optimization.
9 869 0.659054429661 Henry Cohn, 2026, needs more optimization.
9 870 0.659678104795 Henry Cohn, 2026, needs more optimization.
9 871 0.659689264983 Henry Cohn, 2026, needs more optimization.
9 872 0.659696830239 Henry Cohn, 2026, needs more optimization.
9 873 0.660054033987 Henry Cohn, 2026, needs more optimization.
9 874 0.660063029155 Henry Cohn, 2026, needs more optimization.
9 875 0.660107858288 Henry Cohn, 2026, needs more optimization.
9 876 0.660143279412 Henry Cohn, 2026, needs more optimization.
9 877 0.660145083865 Henry Cohn, 2026, needs more optimization.
9 878 0.660162603089 Henry Cohn, 2026, needs more optimization.
9 879 0.660172570849 Henry Cohn, 2026, needs more optimization.
9 880 0.660177015016 Henry Cohn, 2026, needs more optimization.
9 881 0.660721576246 Henry Cohn, 2026, needs more optimization.
9 882 0.660729566577 Henry Cohn, 2026, needs more optimization.
9 883 0.660742414400 Henry Cohn, 2026, needs more optimization.
9 884 0.660755108924 Henry Cohn, 2026, needs more optimization.
9 885 0.660756326036 Henry Cohn, 2026, needs more optimization.
9 886 0.660758414425 Henry Cohn, 2026, needs more optimization.
9 887 0.661268302093 Henry Cohn, 2026, needs more optimization.
9 888 0.661633302851 Henry Cohn, 2026, needs more optimization.
9 889 0.661680644286 Henry Cohn, 2026, needs more optimization.
9 890 0.661721285020 Henry Cohn, 2026, needs more optimization.
9 891 0.661726957817 Henry Cohn, 2026, needs more optimization.
9 892 0.661920034044 Henry Cohn, 2026, needs more optimization.
9 893 0.661977750135 Henry Cohn, 2026, needs more optimization.
9 894 0.662019762803 Henry Cohn, 2026, needs more optimization.
9 895 0.662235834702 Henry Cohn, 2026, needs more optimization.
9 896 0.662260568460 Henry Cohn, 2026, needs more optimization.
9 897 0.662288571365 Henry Cohn, 2026, needs more optimization.
9 898 0.662503808464 Henry Cohn, 2026, needs more optimization.
9 899 0.662526713907 Henry Cohn, 2026, needs more optimization.
9 900 0.662622903436 Henry Cohn, 2026, needs more optimization.
9 901 0.662630421236 Henry Cohn, 2026, needs more optimization.
9 902 0.662789088003 Henry Cohn, 2026, needs more optimization.
9 903 0.663109930456 Henry Cohn, 2026, needs more optimization.
9 904 0.663115743654 Henry Cohn, 2026, needs more optimization.
9 905 0.663170163713 Henry Cohn, 2026, needs more optimization.
9 906 0.663309853639 Henry Cohn, 2026, needs more optimization.
9 907 0.663359673377 Henry Cohn, 2026, needs more optimization.
9 908 0.663367431645 Henry Cohn, 2026, needs more optimization.
9 909 0.663563709395 Henry Cohn, 2026, needs more optimization.
9 910 0.663608883338 Henry Cohn, 2026, needs more optimization.
9 911 0.663710162914 Henry Cohn, 2026, needs more optimization.
9 912 0.663843234808 Henry Cohn, 2026, needs more optimization.
9 913 0.663863554935 Henry Cohn, 2026, needs more optimization.
9 914 0.663882581758 Henry Cohn, 2026, needs more optimization.
9 915 0.663926037313 Henry Cohn, 2026, needs more optimization.
9 916 0.664189579448 Henry Cohn, 2026, needs more optimization.
9 917 0.664197947595 Henry Cohn, 2026, needs more optimization.
9 918 0.664301015937 Henry Cohn, 2026, needs more optimization.
9 919 0.664661885545 Henry Cohn, 2026, needs more optimization.
9 920 0.664691021901 Henry Cohn, 2026, needs more optimization.
9 921 0.664714723432 Henry Cohn, 2026, needs more optimization.
9 922 0.664739801855 Henry Cohn, 2026, needs more optimization.
9 923 0.665016988510 Henry Cohn, 2026, needs more optimization.
9 924 0.665063582704 Henry Cohn, 2026, needs more optimization.
9 925 0.665317048532 Henry Cohn, 2026, needs more optimization.
9 926 0.665340570898 Henry Cohn, 2026, needs more optimization.
9 927 0.665363992103 Henry Cohn, 2026, needs more optimization.
9 928 0.665634551000 Henry Cohn, 2026, needs more optimization.
9 929 0.665636751065 Henry Cohn, 2026, needs more optimization.
9 930 0.665714377923 Henry Cohn, 2026, needs more optimization.
9 931 0.665762025287 Henry Cohn, 2026, needs more optimization.
9 932 0.665811256623 Henry Cohn, 2026, needs more optimization.
9 933 0.665832545509 Henry Cohn, 2026, needs more optimization.
9 934 0.666169370598 Henry Cohn, 2026, needs more optimization.
9 935 0.666177092111 Henry Cohn, 2026, needs more optimization.
9 936 0.666333729577 Henry Cohn, 2026, needs more optimization.
9 937 0.666434617927 Henry Cohn, 2026, needs more optimization.
9 938 0.666522238951 Henry Cohn, 2026, needs more optimization.
9 939 0.666626705676 Henry Cohn, 2026, needs more optimization.
9 1008 0.666666666667 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
3⁢x−2
9 1024 0.666666666667 Subcode of a code of size 1056 from M. Ganzhinov and P. R. J. Östergård, Spherical codes with prescribed signed permutation automorphisms inside shells of low-dimensional integer lattices, IEEE Trans. Inform. Theory 70 (2024), 8669–8674, doi:10.1109/tit.2024.3462593, arXiv:2403.04330.
3⁢x−2
10 21 0.072033139843 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
640⁢x3−100⁢x2−10⁢x+1
10 22 0.083956154719 H. Cohn, Small spherical and projective codes, data set, 2022, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
10 23 0.086853938956 H. Cohn, Small spherical and projective codes, data set, updated 2024, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
10 24 0.098710133500 H. Cohn, Small spherical and projective codes, data set, 2022, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
613376⁢x8−228096⁢x7+40432⁢x6+16416⁢x5−8016⁢x4−216⁢x3+184⁢x2−1
10 25 0.104476374556 H. Cohn, Small spherical and projective codes, data set, 2022, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
10 26 0.104477652124 H. Cohn, Small spherical and projective codes, data set, 2022, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
10 27 0.124212414191 H. Cohn, Small spherical and projective codes, data set, 2022, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
10 28 0.128238684469 H. Cohn, Small spherical and projective codes, data set, 2022, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
92⁢x2−4⁢x−1
10 29 0.130634295944 H. Cohn, Small spherical and projective codes, data set, 2022, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
Minimal polynomial listed in plain text data
10 30 0.138418790027 H. Cohn, Small spherical and projective codes, data set, updated 2024, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
10 31 0.144114939804 H. Cohn, Small spherical and projective codes, data set, 2022, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
Minimal polynomial listed in plain text data
10 32 0.146959243017 H. Cohn, Small spherical and projective codes, data set, 2022, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
279⁢x4−420⁢x3+102⁢x2−1
10 33 0.150071241046 Henry Cohn, 2025.
10 34 0.150182198338 Henry Cohn, 2025.
10 35 0.157397110567 Henry Cohn, 2025.
10 36 0.164041833761 Henry Cohn, 2023.
10 40 0.166666666667 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
6⁢x−1
10 41 0.176776695297 Henry Cohn, 2023.
32⁢x2−1
10 42 0.196163849637 Henry Cohn, 2026.
10 43 0.205622503031 Henry Cohn, 2025.
10 44 0.209906238690 A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
10 45 0.210496566837 Henry Cohn, 2026.
10 46 0.210715021825 A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
10 50 0.210852996458 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
71⁢x2+4⁢x−4
10 51 0.216689708737 Henry Cohn, 2025.
10 52 0.230823073590 Henry Cohn, 2026.
10 57 0.231237647788 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
36⁢x2−4⁢x−1
10 58 0.25 Henry Cohn, 2024.
4⁢x−1
10 59 0.252499828074 A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
10 60 0.252845078510 Henry Cohn, 2026.
10 61 0.255558009804 Henry Cohn, 2026.
10 62 0.257763357141 A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
10 63 0.257944905339 Henry Cohn, 2025.
10 64 0.260558293949 Henry Cohn, 2026.
10 65 0.264885834877 Henry Cohn, 2025.
10 66 0.265168946762 Henry Cohn, 2025.
10 67 0.268064425530 Henry Cohn, 2025.
10 68 0.268886163794 Henry Cohn, 2026, needs more optimization.
10 69 0.269687676246 Henry Cohn, 2026, needs more optimization.
10 70 0.271728059137 Henry Cohn, 2026, needs more optimization.
10 71 0.271905044079 Henry Cohn, 2026.
10 72 0.274447908374 Henry Cohn, 2026.
10 73 0.275987133320 Henry Cohn, 2025.
10 74 0.279604372367 Henry Cohn, 2026, needs more optimization.
10 75 0.283455182208 Henry Cohn, 2026.
10 76 0.284096667917 Henry Cohn, 2025.
10 77 0.284910960402 Henry Cohn, 2025.
10 78 0.289669890099 Henry Cohn, 2026, needs more optimization.
10 79 0.295238353835 Henry Cohn, 2026, needs more optimization.
10 80 0.299105344231 Henry Cohn, 2026, needs more optimization.
10 81 0.301757578659 Henry Cohn, 2026, needs more optimization.
10 82 0.304386285241 Henry Cohn, 2026, needs more optimization.
10 83 0.307850500669 Henry Cohn, 2026, needs more optimization.
10 84 0.310845409715 Henry Cohn, 2026, needs more optimization.
10 85 0.318197566143 Henry Cohn, 2026, needs more optimization.
10 86 0.322133293315 Henry Cohn, 2026.
10 87 0.323321961159 Henry Cohn, 2026.
10 88 0.324088773612 Henry Cohn, 2026, needs more optimization.
10 89 0.324767468389 Henry Cohn, 2026, needs more optimization.
10 90 0.325381372953 Henry Cohn, 2026, needs more optimization.
10 91 0.326253805113 Henry Cohn, 2026, needs more optimization.
10 92 0.327937279523 Henry Cohn, 2026, needs more optimization.
10 93 0.328575897849 Henry Cohn, 2026, needs more optimization.
10 94 0.329287496203 Henry Cohn, 2026, needs more optimization.
10 95 0.329852072737 Henry Cohn, 2026, needs more optimization.
10 96 0.330229861877 Henry Cohn, 2026, needs more optimization.
10 97 0.330427146443 Henry Cohn, 2026, needs more optimization.
10 98 0.330427149808 Henry Cohn, 2026, needs more optimization.
10 99 0.330654923978 Henry Cohn, 2026.
10 100 0.330959507706 Henry Cohn, 2026, needs more optimization.
10 101 0.331169613949 Henry Cohn, 2026, needs more optimization.
10 102 0.331364193607 Henry Cohn, 2026, needs more optimization.
10 103 0.333133200802 Henry Cohn, 2026, needs more optimization.
10 104 0.333225786947 Henry Cohn, 2026, needs more optimization.
10 105 0.333254051255 Henry Cohn, 2026, needs more optimization.
10 106 0.333281877714 Henry Cohn, 2026, needs more optimization.
10 107 0.333303202448 Henry Cohn, 2026, needs more optimization.
10 108 0.333303602351 Henry Cohn, 2026, needs more optimization.
10 109 0.335265624981 Henry Cohn, 2026, needs more optimization.
10 110 0.339290566040 A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
10 111 0.342150835629 Henry Cohn, 2026, needs more optimization.
10 112 0.344823388603 Henry Cohn, 2026, needs more optimization.
10 113 0.347102526263 A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
10 114 0.348284889017 Numaro AI Autoresearch, 11,000+ New Verified Spherical-Code Records from AI Autoresearch, Numaro Research Report NUMARO-2026-015 (2026), https://numaro.tech/research/spherical-codes-2026/.
10 115 0.352515784788 Henry Cohn, 2026, needs more optimization.
10 116 0.353509999293 Henry Cohn, 2026, needs more optimization.
10 117 0.358339648482 Henry Cohn, 2026, needs more optimization.
10 118 0.361651491445 Henry Cohn, 2026, needs more optimization.
10 119 0.363761710067 Henry Cohn, 2026, needs more optimization.
10 120 0.364662417502 Henry Cohn, 2026, needs more optimization.
10 121 0.365191096657 Henry Cohn, 2026.
10 122 0.365459215843 Henry Cohn, 2026, needs more optimization.
10 123 0.365549237535 Henry Cohn, 2026, needs more optimization.
10 124 0.365549529689 Henry Cohn, 2026, needs more optimization.
10 125 0.365549585532 Henry Cohn, 2026, needs more optimization.
10 126 0.365549593044 Henry Cohn, 2026, needs more optimization.
10 127 0.366035053027 Henry Cohn, 2024.
10 128 0.367843329086 Henry Cohn, 2026, needs more optimization.
10 129 0.370352757621 Henry Cohn, 2026, needs more optimization.
10 130 0.371246122112 Henry Cohn, 2026, needs more optimization.
10 131 0.371286600423 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
10 132 0.371409893582 Henry Cohn, 2026, needs more optimization.
10 133 0.384950576549 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
10 134 0.389728253422 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
10 135 0.392340580382 Henry Cohn, 2026, needs more optimization.
10 136 0.392922374482 Henry Cohn, 2026, needs more optimization.
10 137 0.396210893031 Henry Cohn, 2026, needs more optimization.
10 138 0.398648215668 Henry Cohn, 2026, needs more optimization.
10 139 0.400187109545 Henry Cohn, 2026, needs more optimization.
10 140 0.401786079598 Henry Cohn, 2026, needs more optimization.
10 141 0.403135635222 Henry Cohn, 2026, needs more optimization.
10 142 0.404394572823 Henry Cohn, 2026, needs more optimization.
10 156 0.405827419558 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
11⁢x2−2⁢x−1
10 157 0.413095134945 Henry Cohn, 2026, needs more optimization.
10 158 0.414010278214 Henry Cohn, 2026, needs more optimization.
10 159 0.414516421918 Henry Cohn, 2026, needs more optimization.
10 160 0.414818422222 Henry Cohn, 2026, needs more optimization.
10 161 0.415973100701 Henry Cohn, 2026, needs more optimization.
10 162 0.416875406071 Henry Cohn, 2026, needs more optimization.
10 163 0.419201643498 Henry Cohn, 2026, needs more optimization.
10 164 0.420591580362 Henry Cohn, 2026, needs more optimization.
10 165 0.421674879470 Henry Cohn, 2026, needs more optimization.
10 166 0.422482723925 Henry Cohn, 2026, needs more optimization.
10 167 0.423422355515 Henry Cohn, 2026, needs more optimization.
10 168 0.424374959358 Henry Cohn, 2026, needs more optimization.
10 169 0.425515856893 Henry Cohn, 2026, needs more optimization.
10 170 0.425990211490 Henry Cohn, 2026, needs more optimization.
10 171 0.427020432877 Henry Cohn, 2026, needs more optimization.
10 172 0.428113782467 Henry Cohn, 2026, needs more optimization.
10 194 0.428571428572 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
7⁢x−3
10 195 0.438691046790 Henry Cohn, 2026, needs more optimization.
10 196 0.441223756568 Henry Cohn, 2026, needs more optimization.
10 197 0.443292131876 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
10 198 0.445359293971 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
10 199 0.447037312953 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
10 200 0.448180876705 Henry Cohn, 2026, needs more optimization.
10 201 0.449219199688 Henry Cohn, 2026, needs more optimization.
10 202 0.450485068274 Henry Cohn, 2026, needs more optimization.
10 203 0.451662263520 Henry Cohn, 2026, needs more optimization.
10 204 0.452579690892 Henry Cohn, 2026, needs more optimization.
10 205 0.453658761189 Henry Cohn, 2026, needs more optimization.
10 206 0.454652189860 Henry Cohn, 2026, needs more optimization.
10 207 0.454688164058 Henry Cohn, 2026, needs more optimization.
10 208 0.454706173477 Henry Cohn, 2026, needs more optimization.
10 209 0.454734287430 Henry Cohn, 2026, needs more optimization.
10 212 0.454882998577 Henry Cohn, 2026, needs more optimization.
10 213 0.454894624055 Henry Cohn, 2026, needs more optimization.
10 214 0.454903457830 Henry Cohn, 2026, needs more optimization.
10 215 0.454906479232 Henry Cohn, 2026, needs more optimization.
10 216 0.454922536540 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
10 218 0.454984600560 Henry Cohn, 2026, needs more optimization.
10 219 0.454985186570 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
10 220 0.454998720466 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
10 221 0.455047463068 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
10 224 0.455055766989 Henry Cohn, 2026, needs more optimization.
10 225 0.455117296729 Henry Cohn, 2026, needs more optimization.
10 226 0.455143701601 Henry Cohn, 2026, needs more optimization.
10 227 0.455150796312 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
10 228 0.455163561650 Henry Cohn, 2026, needs more optimization.
10 229 0.455163739968 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
10 230 0.455213852651 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
10 231 0.455305429775 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
10 238 0.455341801262 Henry Cohn, 2026.
18⁢x2−6⁢x−1
10 239 0.455408702429 Henry Cohn, 2026, needs more optimization.
10 240 0.455664293649 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
10 241 0.455995382070 Henry Cohn, 2026, needs more optimization.
10 242 0.456233022207 Henry Cohn, 2026, needs more optimization.
10 243 0.456311080811 Henry Cohn, 2026, needs more optimization.
10 244 0.456311357991 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
10 245 0.457690113819 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
10 246 0.458722272597 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
10 247 0.462298054529 Henry Cohn, 2026, needs more optimization.
10 248 0.464406202452 Henry Cohn, 2026, needs more optimization.
10 249 0.464406202687 Henry Cohn, 2026, needs more optimization.
10 250 0.464749675477 Henry Cohn, 2026, needs more optimization.
10 251 0.465138545117 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
10 252 0.465574187238 Henry Cohn, 2026, needs more optimization.
10 253 0.466529765538 Henry Cohn, 2026, needs more optimization.
10 254 0.467474598224 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
10 255 0.469117680257 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
10 256 0.470340310693 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
10 257 0.471321783184 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
10 258 0.472029986182 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
10 259 0.473097500103 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
10 260 0.474064288244 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
10 261 0.474934262312 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
10 262 0.475878535613 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
10 263 0.476583455393 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
10 264 0.477128035060 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
10 265 0.477938351790 Henry Cohn, 2026, needs more optimization.
10 266 0.477954324747 Henry Cohn, 2026, needs more optimization.
10 267 0.478068292731 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
10 268 0.478166314905 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
10 269 0.478312873265 Henry Cohn, 2026, needs more optimization.
10 270 0.478493487051 Henry Cohn, 2026, needs more optimization.
10 271 0.478514956362 Henry Cohn, 2026, needs more optimization.
10 272 0.478917151498 Henry Cohn, 2026, needs more optimization.
10 273 0.479280422634 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
10 274 0.479876664782 Henry Cohn, 2026, needs more optimization.
10 275 0.480414997729 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
10 276 0.480953472380 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
10 277 0.481312615113 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
10 278 0.481860983731 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
10 279 0.482470091734 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
10 280 0.482905236363 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
10 281 0.483430296310 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
10 282 0.483905806893 Henry Cohn, 2026, needs more optimization.
10 283 0.483905991848 Henry Cohn, 2026, needs more optimization.
10 284 0.483906517416 Henry Cohn, 2026, needs more optimization.
10 285 0.483906563362 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
10 286 0.484201475833 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
10 287 0.484552264837 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
10 288 0.484774432369 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
10 289 0.484907546917 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
10 290 0.485053820861 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
10 291 0.485376276351 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
10 292 0.485614923186 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
10 293 0.485869697804 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
10 294 0.486140680016 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
10 295 0.486488690017 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
10 296 0.486812723391 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
10 297 0.487126742057 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
10 298 0.487603275683 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
10 299 0.488618806990 Henry Cohn, 2026, needs more optimization.
10 300 0.489051735169 Henry Cohn, 2026, needs more optimization.
10 301 0.489344159188 Henry Cohn, 2026, needs more optimization.
10 302 0.489509798836 Henry Cohn, 2026, needs more optimization.
10 303 0.489654044251 Henry Cohn, 2026, needs more optimization.
10 304 0.490035135291 Henry Cohn, 2026, needs more optimization.
10 305 0.490234940006 Henry Cohn, 2026, needs more optimization.
10 308 0.490780537236 Henry Cohn, 2026, needs more optimization.
10 309 0.490891845546 Henry Cohn, 2026, needs more optimization.
10 310 0.490991762658 Henry Cohn, 2026, needs more optimization.
10 311 0.491042444886 Henry Cohn, 2026, needs more optimization.
10 312 0.491076777721 Henry Cohn, 2026, needs more optimization.
10 313 0.491231555731 Henry Cohn, 2026, needs more optimization.
10 314 0.491265161773 Henry Cohn, 2026, needs more optimization.
10 315 0.491757762109 Henry Cohn, 2026, needs more optimization.
10 316 0.491770917207 Henry Cohn, 2026, needs more optimization.
10 317 0.491808051676 Henry Cohn, 2026, needs more optimization.
10 318 0.492033043316 Henry Cohn, 2026, needs more optimization.
10 319 0.492123007422 Henry Cohn, 2026, needs more optimization.
10 320 0.492429423383 Henry Cohn, 2026, needs more optimization.
10 321 0.492980299593 Henry Cohn, 2026, needs more optimization.
10 322 0.493346297304 Henry Cohn, 2026, needs more optimization.
10 323 0.493410020006 Henry Cohn, 2026, needs more optimization.
10 324 0.493589614030 Henry Cohn, 2026, needs more optimization.
10 325 0.494146563605 Henry Cohn, 2026, needs more optimization.
10 326 0.494238764561 Henry Cohn, 2026, needs more optimization.
10 327 0.494529351600 Henry Cohn, 2026, needs more optimization.
10 328 0.494880059327 Henry Cohn, 2026, needs more optimization.
10 329 0.495011306803 Henry Cohn, 2026, needs more optimization.
10 330 0.495072609764 Henry Cohn, 2026, needs more optimization.
10 331 0.495280053487 Henry Cohn, 2026, needs more optimization.
10 332 0.495436051848 Henry Cohn, 2026, needs more optimization.
10 333 0.495543093661 Henry Cohn, 2026, needs more optimization.
10 334 0.496248260082 Henry Cohn, 2026, needs more optimization.
10 335 0.496349754282 Henry Cohn, 2026, needs more optimization.
10 336 0.496542311827 Henry Cohn, 2026, needs more optimization.
10 337 0.496745457997 Henry Cohn, 2026, needs more optimization.
10 338 0.496892075028 Henry Cohn, 2026, needs more optimization.
10 339 0.496989076095 Henry Cohn, 2026, needs more optimization.
10 340 0.497144297181 Henry Cohn, 2026, needs more optimization.
10 341 0.497200713345 Henry Cohn, 2026, needs more optimization.
10 342 0.497249987165 Henry Cohn, 2026, needs more optimization.
10 343 0.497344751392 Henry Cohn, 2026, needs more optimization.
10 344 0.497437086376 Henry Cohn, 2026, needs more optimization.
10 345 0.497529391212 Henry Cohn, 2026, needs more optimization.
10 346 0.498117459613 Henry Cohn, 2026, needs more optimization.
10 347 0.498209450353 Henry Cohn, 2026, needs more optimization.
10 348 0.498296929024 Henry Cohn, 2026, needs more optimization.
10 349 0.498367447322 Henry Cohn, 2026, needs more optimization.
10 350 0.498415413091 Henry Cohn, 2026, needs more optimization.
10 351 0.498469565026 Henry Cohn, 2026, needs more optimization.
10 352 0.498482039654 Henry Cohn, 2026, needs more optimization.
10 353 0.498582985165 Henry Cohn, 2026, needs more optimization.
10 354 0.498586283139 Henry Cohn, 2026, needs more optimization.
10 355 0.498745489091 Henry Cohn, 2026, needs more optimization.
10 356 0.498786849568 Henry Cohn, 2026, needs more optimization.
10 358 0.498834255096 Henry Cohn, 2026, needs more optimization.
10 360 0.498892979708 Henry Cohn, 2026, needs more optimization.
10 361 0.498911658551 Henry Cohn, 2026, needs more optimization.
10 363 0.498941593529 Henry Cohn, 2026, needs more optimization.
10 365 0.498997215654 Henry Cohn, 2026, needs more optimization.
10 366 0.499002311530 Henry Cohn, 2026, needs more optimization.
10 368 0.499253169099 Henry Cohn, 2026, needs more optimization.
10 369 0.499262516928 Henry Cohn, 2026, needs more optimization.
10 370 0.499284005095 Henry Cohn, 2026, needs more optimization.
10 371 0.499409623072 Henry Cohn, 2026, needs more optimization.
10 372 0.499528045277 Henry Cohn, 2026, needs more optimization.
10 373 0.499545407915 Henry Cohn, 2026, needs more optimization.
10 374 0.499556123192 Henry Cohn, 2026, needs more optimization.
10 375 0.499632429060 Henry Cohn, 2026, needs more optimization.
10 500 0.5 J. Leech and N. J. A. Sloane, Sphere packings and error-correcting codes, Canadian J. Math. 23 (1971), 718–745, doi:10.4153/CJM-1971-081-3.
2⁢x−1
10 510 0.5 M. Ganzhinov, Highly symmetric lines, Linear Algebra Appl. 722 (2025), 12–37, doi:10.1016/j.laa.2025.05.002.
2⁢x−1
10 511 0.526700843530 Henry Cohn, 2026, needs more optimization.
10 512 0.529968272398 Henry Cohn, 2026, needs more optimization.
10 513 0.532736170813 Henry Cohn, 2026, needs more optimization.
10 514 0.533829637767 Henry Cohn, 2026, needs more optimization.
10 515 0.535003141560 Henry Cohn, 2026, needs more optimization.
10 516 0.536921721120 Henry Cohn, 2026, needs more optimization.
10 517 0.538153453225 Henry Cohn, 2026, needs more optimization.
10 518 0.538840381350 Henry Cohn, 2026, needs more optimization.
10 519 0.540276034156 Henry Cohn, 2026, needs more optimization.
10 520 0.541047257346 Henry Cohn, 2026, needs more optimization.
10 521 0.542194287050 Henry Cohn, 2026, needs more optimization.
10 522 0.542988119072 Henry Cohn, 2026, needs more optimization.
10 523 0.543621198156 Henry Cohn, 2026, needs more optimization.
10 524 0.544339656905 Henry Cohn, 2026, needs more optimization.
10 525 0.545204195917 Henry Cohn, 2026, needs more optimization.
10 526 0.545962924895 Henry Cohn, 2026, needs more optimization.
10 527 0.546307325892 Henry Cohn, 2026, needs more optimization.
10 528 0.547355995912 Henry Cohn, 2026, needs more optimization.
10 529 0.548002860397 Henry Cohn, 2026, needs more optimization.
10 530 0.548729340461 Henry Cohn, 2026, needs more optimization.
10 531 0.549323112916 Henry Cohn, 2026, needs more optimization.
10 532 0.549611999581 Henry Cohn, 2026, needs more optimization.
10 533 0.550218266840 Henry Cohn, 2026, needs more optimization.
10 534 0.550797452912 Henry Cohn, 2026, needs more optimization.
10 535 0.551309336286 Henry Cohn, 2026, needs more optimization.
10 536 0.552015030521 Henry Cohn, 2026, needs more optimization.
10 537 0.552488856714 Henry Cohn, 2026, needs more optimization.
10 538 0.553340297309 Henry Cohn, 2026, needs more optimization.
10 539 0.553478729808 Henry Cohn, 2026, needs more optimization.
10 540 0.553993393852 Henry Cohn, 2026, needs more optimization.
10 541 0.554445384435 Henry Cohn, 2026, needs more optimization.
10 542 0.554862258407 Henry Cohn, 2026, needs more optimization.
10 543 0.555232889432 Henry Cohn, 2026, needs more optimization.
10 596 0.555555555556 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
9⁢x−5
10 608 0.555555555556 Henry Cohn, 2026, by enlarging a code from T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
9⁢x−5
10 740 0.564577451054 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
92⁢x2−36⁢x−9
10 771 0.564577451054 Henry Cohn, 2026, by enlarging a code from T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
92⁢x2−36⁢x−9
10 772 0.567862778412 Henry Cohn, 2026, needs more optimization.
10 773 0.569692585270 Henry Cohn, 2026, needs more optimization.
10 774 0.570752236329 Henry Cohn, 2026, needs more optimization.
10 775 0.571372288729 Henry Cohn, 2026, needs more optimization.
10 776 0.571915208069 Henry Cohn, 2026, needs more optimization.
10 778 0.572424257058 Henry Cohn, 2026, needs more optimization.
10 779 0.572920038441 Numaro AI Autoresearch, 11,000+ New Verified Spherical-Code Records from AI Autoresearch, Numaro Research Report NUMARO-2026-015 (2026), https://numaro.tech/research/spherical-codes-2026/.
10 781 0.573151362309 Henry Cohn, 2026, needs more optimization.
10 782 0.573320768790 Henry Cohn, 2026, needs more optimization.
10 783 0.573459589612 Henry Cohn, 2026, needs more optimization.
10 784 0.573670379535 Henry Cohn, 2026, needs more optimization.
10 785 0.573704082749 Henry Cohn, 2026, needs more optimization.
10 786 0.576354277756 Henry Cohn, 2026, needs more optimization.
10 787 0.576679992169 Henry Cohn, 2026, needs more optimization.
10 788 0.577086614520 Henry Cohn, 2026, needs more optimization.
10 789 0.577165058597 Henry Cohn, 2026, needs more optimization.
10 790 0.577888391799 Henry Cohn, 2026, needs more optimization.
10 791 0.578162153643 Henry Cohn, 2026, needs more optimization.
10 792 0.578622331331 Henry Cohn, 2026, needs more optimization.
10 793 0.578942432523 Henry Cohn, 2026, needs more optimization.
10 794 0.579618425332 Henry Cohn, 2026, needs more optimization.
10 795 0.579866111775 Henry Cohn, 2026, needs more optimization.
10 796 0.580139707375 Henry Cohn, 2026, needs more optimization.
10 797 0.580537272969 Henry Cohn, 2026, needs more optimization.
10 798 0.580620170518 Henry Cohn, 2026, needs more optimization.
10 799 0.581819310924 Henry Cohn, 2026, needs more optimization.
10 800 0.581951158851 Henry Cohn, 2026, needs more optimization.
10 801 0.582158595295 Henry Cohn, 2026, needs more optimization.
10 802 0.583082046591 Henry Cohn, 2026, needs more optimization.
10 803 0.583367438111 Henry Cohn, 2026, needs more optimization.
10 804 0.583560609954 Henry Cohn, 2026, needs more optimization.
10 805 0.584225045269 Henry Cohn, 2026, needs more optimization.
10 806 0.584338625807 Henry Cohn, 2026, needs more optimization.
10 807 0.584417065681 Henry Cohn, 2026, needs more optimization.
10 808 0.584468827235 Henry Cohn, 2026, needs more optimization.
10 809 0.584763205700 Henry Cohn, 2026, needs more optimization.
10 810 0.585258286359 Henry Cohn, 2026, needs more optimization.
10 811 0.585302959276 Henry Cohn, 2026, needs more optimization.
10 812 0.585398994607 Henry Cohn, 2026, needs more optimization.
10 813 0.585459952156 Henry Cohn, 2026, needs more optimization.
10 814 0.585582550383 Henry Cohn, 2026, needs more optimization.
10 815 0.585648794906 Henry Cohn, 2026, needs more optimization.
10 816 0.585766571121 Henry Cohn, 2026, needs more optimization.
10 817 0.585973756344 Henry Cohn, 2026, needs more optimization.
10 818 0.586207341629 Henry Cohn, 2026, needs more optimization.
10 819 0.586432030534 Henry Cohn, 2026, needs more optimization.
10 820 0.586548806322 Henry Cohn, 2026, needs more optimization.
10 821 0.586785576546 Henry Cohn, 2026, needs more optimization.
10 822 0.587077504666 Henry Cohn, 2026, needs more optimization.
10 823 0.587262218781 Henry Cohn, 2026, needs more optimization.
10 824 0.587273346584 Henry Cohn, 2026, needs more optimization.
10 825 0.587330880922 Henry Cohn, 2026, needs more optimization.
10 826 0.587382821709 Henry Cohn, 2026, needs more optimization.
10 827 0.587577920865 Henry Cohn, 2026, needs more optimization.
10 828 0.588494788636 Henry Cohn, 2026, needs more optimization.
10 829 0.588810599252 Henry Cohn, 2026, needs more optimization.
10 830 0.588991024655 Henry Cohn, 2026, needs more optimization.
10 831 0.589282854193 Henry Cohn, 2026, needs more optimization.
10 832 0.589549103826 Henry Cohn, 2026, needs more optimization.
10 834 0.589687506135 Henry Cohn, 2026, needs more optimization.
10 835 0.589917769592 Henry Cohn, 2026, needs more optimization.
10 836 0.589998511728 Henry Cohn, 2026, needs more optimization.
10 837 0.590066892970 Henry Cohn, 2026, needs more optimization.
10 838 0.590292849739 Henry Cohn, 2026, needs more optimization.
10 839 0.590432511540 Henry Cohn, 2026, needs more optimization.
10 840 0.590665594244 Henry Cohn, 2026, needs more optimization.
10 841 0.590856231375 Henry Cohn, 2026, needs more optimization.
10 842 0.590882368348 Henry Cohn, 2026, needs more optimization.
10 843 0.590898928875 Henry Cohn, 2026, needs more optimization.
10 844 0.590901981156 Henry Cohn, 2026, needs more optimization.
10 845 0.591175971163 Henry Cohn, 2026, needs more optimization.
10 846 0.591512240110 Henry Cohn, 2026, needs more optimization.
10 847 0.591524927305 Henry Cohn, 2026, needs more optimization.
10 848 0.591600902892 Henry Cohn, 2026, needs more optimization.
10 851 0.591629734483 Henry Cohn, 2026, needs more optimization.
10 854 0.591779808958 Henry Cohn, 2026, needs more optimization.
10 855 0.591881139570 Henry Cohn, 2026, needs more optimization.
10 856 0.591903017040 Henry Cohn, 2026, needs more optimization.
10 857 0.591916216965 Henry Cohn, 2026, needs more optimization.
10 858 0.592017393455 Henry Cohn, 2026, needs more optimization.
10 859 0.592063098301 Henry Cohn, 2026, needs more optimization.
10 860 0.592306041777 Henry Cohn, 2026, needs more optimization.
10 861 0.592409853590 Henry Cohn, 2026, needs more optimization.
10 862 0.592436759006 Henry Cohn, 2026, needs more optimization.
10 863 0.592556023189 Henry Cohn, 2026, needs more optimization.
10 864 0.592569984948 Henry Cohn, 2026, needs more optimization.
10 865 0.592590115264 Henry Cohn, 2026, needs more optimization.
10 866 0.592599485767 Henry Cohn, 2026, needs more optimization.
10 867 0.592603839047 Henry Cohn, 2026, needs more optimization.
10 868 0.592608641478 Henry Cohn, 2026, needs more optimization.
10 869 0.592690026032 Henry Cohn, 2026, needs more optimization.
10 870 0.592694764243 Henry Cohn, 2026, needs more optimization.
10 871 0.592700399546 Henry Cohn, 2026, needs more optimization.
10 872 0.592708281341 Henry Cohn, 2026, needs more optimization.
10 873 0.592710175415 Henry Cohn, 2026, needs more optimization.
10 874 0.592956113898 Henry Cohn, 2026, needs more optimization.
10 879 0.592967021596 Henry Cohn, 2026, needs more optimization.
10 881 0.592984077399 Henry Cohn, 2026, needs more optimization.
10 882 0.593094416397 Henry Cohn, 2026, needs more optimization.
10 883 0.593099505992 Henry Cohn, 2026, needs more optimization.
10 884 0.593126942270 Henry Cohn, 2026, needs more optimization.
10 885 0.593251903062 Henry Cohn, 2026, needs more optimization.
10 886 0.593488328223 Henry Cohn, 2026, needs more optimization.
10 887 0.593561099620 Henry Cohn, 2026, needs more optimization.
10 888 0.593722921731 Henry Cohn, 2026, needs more optimization.
10 890 0.593732845150 Henry Cohn, 2026, needs more optimization.
10 891 0.593809562182 Henry Cohn, 2026, needs more optimization.
10 892 0.593859180612 Henry Cohn, 2026, needs more optimization.
10 893 0.593863739852 Henry Cohn, 2026, needs more optimization.
10 894 0.593889007441 Henry Cohn, 2026, needs more optimization.
10 895 0.593970148556 Henry Cohn, 2026, needs more optimization.
10 896 0.593997115170 Henry Cohn, 2026, needs more optimization.
10 897 0.594068535792 Henry Cohn, 2026, needs more optimization.
10 898 0.594069578019 Henry Cohn, 2026, needs more optimization.
10 903 0.594070264845 Henry Cohn, 2026, needs more optimization.
10 904 0.594071923041 Henry Cohn, 2026, needs more optimization.
10 905 0.594073775633 Henry Cohn, 2026, needs more optimization.
10 907 0.594075151945 Henry Cohn, 2026, needs more optimization.
10 908 0.594076126942 Henry Cohn, 2026, needs more optimization.
10 909 0.594093696528 Henry Cohn, 2026, needs more optimization.
10 910 0.594104471564 Henry Cohn, 2026, needs more optimization.
10 911 0.594165909008 Henry Cohn, 2026, needs more optimization.
10 912 0.594170149852 Henry Cohn, 2026, needs more optimization.
10 913 0.594181959362 Henry Cohn, 2026, needs more optimization.
10 914 0.594195178620 Henry Cohn, 2026, needs more optimization.
10 915 0.594255502205 Henry Cohn, 2026, needs more optimization.
10 916 0.594258398223 Henry Cohn, 2026, needs more optimization.
10 917 0.594272131635 Henry Cohn, 2026, needs more optimization.
10 919 0.594358010689 Henry Cohn, 2026, needs more optimization.
10 920 0.594382286169 Henry Cohn, 2026, needs more optimization.
10 921 0.594390552615 Henry Cohn, 2026, needs more optimization.
10 922 0.594407907049 Henry Cohn, 2026, needs more optimization.
10 923 0.594480298891 Henry Cohn, 2026, needs more optimization.
10 925 0.594542848902 Henry Cohn, 2026, needs more optimization.
10 927 0.594639435816 Henry Cohn, 2026, needs more optimization.
10 928 0.594664157842 Henry Cohn, 2026, needs more optimization.
10 929 0.594787237659 Henry Cohn, 2026, needs more optimization.
10 1024 0.6 Subcode of a code of size 1190 from T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
5⁢x−3
11 23 0.066201272532 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
891⁢x3−121⁢x2−11⁢x+1
11 24 0.077294525867 H. Cohn, Small spherical and projective codes, data set, updated 2025, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
Minimal polynomial listed in plain text data
11 25 0.083618757829 H. Cohn, Small spherical and projective codes, data set, updated 2023, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
11 26 0.090957106782 H. Cohn, Small spherical and projective codes, data set, 2022, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
11 27 0.096579767338 H. Cohn, Small spherical and projective codes, data set, 2022, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
11 28 0.102062072616 H. Cohn, Small spherical and projective codes, data set, 2022, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
96⁢x2−1
11 29 0.108541175054 H. Cohn, Small spherical and projective codes, data set, updated 2025, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
Minimal polynomial listed in plain text data
11 30 0.111111111112 H. Cohn, Small spherical and projective codes, data set, 2022, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
9⁢x−1
11 31 0.116882716629 H. Cohn, Small spherical and projective codes, data set, 2022, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
1880159⁢x4+662980⁢x3+23850⁢x2−9500⁢x−625
11 32 0.127120178791 H. Cohn, Small spherical and projective codes, data set, 2022, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
11 33 0.130869404972 Henry Cohn, 2023.
4276703⁢x4+1417464⁢x3−4824⁢x2−23328⁢x−1296
11 35 0.134804262191 Henry Cohn, 2023.
379⁢x2−14⁢x−5
11 36 0.135617659465 Henry Cohn, 2023.
34679⁢x4+11944⁢x3+264⁢x2−224⁢x−16
11 37 0.141119306055 Henry Cohn, 2023.
11 40 0.142857142858 H. Cohn, D. de Laat, and N. Leijenhorst, Optimality of spherical codes via exact semidefinite programming bounds, preprint, 2024, arXiv:2403.16874.
7⁢x−1
11 41 0.151608920662 Henry Cohn, 2023.
215⁢x2−26⁢x−1
11 42 0.152689377129 Henry Cohn, 2023.
441⁢x4+84⁢x3−66⁢x2+1
11 43 0.154540745580 Henry Cohn, 2024.
11 44 0.164387348702 Henry Cohn, 2023.
11 45 0.167764862361 Henry Cohn, 2023.
11 46 0.173024920814 Henry Cohn, 2023.
11 47 0.193275935700 Henry Cohn, 2025.
11 48 0.198565163418 Henry Cohn, 2025.
11 49 0.201215495510 Henry Cohn, 2025.
11 50 0.204597123448 Henry Cohn, 2026.
11 51 0.204957387535 Henry Cohn, 2023.
Minimal polynomial listed in plain text data
11 52 0.208005237402 Henry Cohn, 2024.
11 53 0.209746584158 Henry Cohn, 2026.
11 54 0.210461540583 Henry Cohn, 2026, needs more optimization.
11 55 0.211949051009 Henry Cohn, 2026.
11 56 0.214650086321 Henry Cohn, 2026.
11 61 0.214737233855 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
31⁢x2−2⁢x−1
11 68 0.232764852407 Henry Cohn, 2024.
295⁢x2−30⁢x−9
11 69 0.241565014044 Henry Cohn, 2025.
Minimal polynomial listed in plain text data
11 70 0.244726315701 Henry Cohn, 2026.
263⁢x8−408⁢x7+27724⁢x6−10136⁢x5−11182⁢x4+5880⁢x3−932⁢x2+56⁢x−1
11 71 0.251063071270 Henry Cohn, 2026.
11 72 0.253208781807 Henry Cohn, 2026, needs more optimization.
11 73 0.253336088026 Henry Cohn, 2026, needs more optimization.
11 74 0.253830472877 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
11 75 0.255729129431 Henry Cohn, 2026, needs more optimization.
11 76 0.255742967679 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
11 77 0.259849546155 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
11 78 0.260087123998 A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
11 79 0.260685334645 A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
11 80 0.261163095118 A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
11 81 0.261593527993 A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
11 82 0.263122012609 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
11 83 0.263833259782 A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
11 84 0.265027768340 Henry Cohn, 2026, needs more optimization.
11 85 0.266212319585 Henry Cohn, 2026, needs more optimization.
11 90 0.267191024627 Henry Cohn, 2026.
71⁢x2−4⁢x−4
11 91 0.273036354862 Henry Cohn, 2026, needs more optimization.
11 92 0.280393211256 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
11 93 0.281446853846 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
11 94 0.282407583866 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
11 95 0.283407734005 Henry Cohn, 2026, needs more optimization.
11 96 0.284687651687 Henry Cohn, 2026, needs more optimization.
11 97 0.285749106769 Henry Cohn, 2026, needs more optimization.
11 98 0.287338503170 A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
11 99 0.288695061214 Henry Cohn, 2026, needs more optimization.
11 100 0.299860274487 Henry Cohn, 2026, needs more optimization.
11 101 0.302856217462 Henry Cohn, 2026, needs more optimization.
11 102 0.304440333187 Henry Cohn, 2026, needs more optimization.
11 103 0.305231205253 Henry Cohn, 2026, needs more optimization.
11 104 0.305233810012 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
11 105 0.305250484673 A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
11 106 0.306431391981 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
11 107 0.309834633216 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
11 108 0.313206839612 A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
11 109 0.319003371306 A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
11 110 0.321697571595 Henry Cohn, 2026, needs more optimization.
11 111 0.322266842253 A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
11 112 0.322372471980 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
11 113 0.322494933863 Henry Cohn, 2026, needs more optimization.
11 114 0.322758411874 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
11 115 0.322930921448 A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
11 116 0.323595455196 A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
11 117 0.324275804961 A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
11 118 0.324838464869 A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
11 119 0.324907761719 A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
11 120 0.325028609540 A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
11 121 0.325463885933 A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
11 122 0.325937891107 Henry Cohn, 2026, needs more optimization.
11 123 0.328143225937 Henry Cohn, 2026, needs more optimization.
11 124 0.328653380506 Henry Cohn, 2026, needs more optimization.
11 125 0.330504742078 Henry Cohn, 2026, needs more optimization.
11 126 0.331457050269 Henry Cohn, 2026, needs more optimization.
11 127 0.332257232390 Henry Cohn, 2026, needs more optimization.
11 128 0.332276380864 Henry Cohn, 2026, needs more optimization.
11 129 0.332381318550 Henry Cohn, 2026, needs more optimization.
11 130 0.332405306810 Henry Cohn, 2026, needs more optimization.
11 131 0.332653846548 Henry Cohn, 2026, needs more optimization.
11 132 0.333235729975 Henry Cohn, 2026, needs more optimization.
11 136 0.333333333334 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
3⁢x−1
11 156 0.333333333334 M. Ganzhinov, Highly symmetric lines, Linear Algebra Appl. 722 (2025), 12–37, doi:10.1016/j.laa.2025.05.002.
3⁢x−1
11 157 0.360498839595 Henry Cohn, 2026, needs more optimization.
11 158 0.363706056288 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
11 159 0.366633560605 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
11 160 0.369951940027 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
11 161 0.372394242184 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
11 162 0.374654217310 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
11 166 0.375 M. Ganzhinov and P. R. J. Östergård, Spherical codes with prescribed signed permutation automorphisms inside shells of low-dimensional integer lattices, IEEE Trans. Inform. Theory 70 (2024), 8669–8674, doi:10.1109/tit.2024.3462593, arXiv:2403.04330.
8⁢x−3
11 167 0.384617324400 Henry Cohn, 2026, needs more optimization.
11 168 0.385169105802 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
11 169 0.386585972528 Henry Cohn, 2026, needs more optimization.
11 170 0.387214821580 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
11 171 0.388164239274 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
11 172 0.388779269103 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
11 173 0.389289609469 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
11 174 0.390733987502 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
11 175 0.391624895980 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
11 176 0.392543227616 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
11 177 0.393783898539 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
11 178 0.394049483938 Henry Cohn, 2026, needs more optimization.
11 179 0.394871095040 Henry Cohn, 2026, needs more optimization.
11 180 0.395420314910 Henry Cohn, 2026, needs more optimization.
11 181 0.395965255461 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
11 182 0.396243041299 Henry Cohn, 2026, needs more optimization.
11 183 0.396243060809 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
11 184 0.396269867531 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
11 185 0.396770241824 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
11 186 0.397048933969 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
11 187 0.397332416122 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
11 188 0.398636638187 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
11 189 0.399730744898 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
11 190 0.399838012420 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
11 191 0.400000041773 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
11 192 0.400766876925 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
11 193 0.401394878180 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
11 194 0.401696814414 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
11 195 0.402900251707 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
11 196 0.403578338814 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
11 197 0.405074614093 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
11 198 0.405509965705 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
11 199 0.405617344627 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
11 200 0.405726954163 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
11 201 0.406171026591 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
11 202 0.406279174779 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
11 203 0.406542526457 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
11 204 0.406926703900 Henry Cohn, 2026, needs more optimization.
11 205 0.406927169481 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
11 206 0.408530044426 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
11 207 0.409185768646 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
11 208 0.410219895544 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
11 209 0.410675234551 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
11 210 0.413903800408 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
11 211 0.415200887894 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
11 212 0.415838209099 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
11 213 0.416466213280 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
11 214 0.416823078786 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
11 215 0.417249269623 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
11 216 0.417742413254 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
11 217 0.418210367143 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
11 218 0.418787459278 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
11 219 0.419297784217 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
11 220 0.419669067156 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
11 221 0.420310566767 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
11 222 0.420771332989 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
11 223 0.421373063340 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
11 224 0.421876334157 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
11 225 0.422465198776 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
11 226 0.423259475157 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
11 227 0.423755509676 Henry Cohn, 2026, needs more optimization.
11 228 0.424182257026 Henry Cohn, 2026, needs more optimization.
11 229 0.424444814454 Henry Cohn, 2026, needs more optimization.
11 230 0.425093293056 Henry Cohn, 2026, needs more optimization.
11 231 0.425405076221 Henry Cohn, 2026, needs more optimization.
11 232 0.425729359404 Henry Cohn, 2026, needs more optimization.
11 233 0.425933764502 Henry Cohn, 2026, needs more optimization.
11 234 0.426257706714 Henry Cohn, 2026, needs more optimization.
11 235 0.426723492779 Henry Cohn, 2026, needs more optimization.
11 236 0.426950029038 Henry Cohn, 2026, needs more optimization.
11 237 0.427230542446 Henry Cohn, 2026, needs more optimization.
11 238 0.427618173398 Henry Cohn, 2026, needs more optimization.
11 239 0.427787186534 Henry Cohn, 2026, needs more optimization.
11 240 0.427985898828 Henry Cohn, 2026, needs more optimization.
11 241 0.428354657767 Henry Cohn, 2026, needs more optimization.
11 242 0.428508464469 Henry Cohn, 2026, needs more optimization.
11 243 0.429023372681 Henry Cohn, 2026, needs more optimization.
11 244 0.429658115918 Henry Cohn, 2026, needs more optimization.
11 245 0.430429645614 Henry Cohn, 2026, needs more optimization.
11 246 0.430675188374 Henry Cohn, 2026, needs more optimization.
11 247 0.430832323608 Henry Cohn, 2026, needs more optimization.
11 248 0.431478153966 Henry Cohn, 2026, needs more optimization.
11 249 0.432389960862 Henry Cohn, 2026, needs more optimization.
11 250 0.433204836729 Henry Cohn, 2026, needs more optimization.
11 251 0.433535644775 Henry Cohn, 2026, needs more optimization.
11 252 0.433970580878 Henry Cohn, 2026, needs more optimization.
11 253 0.435457666442 Henry Cohn, 2026, needs more optimization.
11 254 0.435930198867 Henry Cohn, 2026, needs more optimization.
11 255 0.436494258828 Henry Cohn, 2026, needs more optimization.
11 256 0.437919490803 Henry Cohn, 2026, needs more optimization.
11 257 0.438151551520 Henry Cohn, 2026, needs more optimization.
11 258 0.438173056215 Henry Cohn, 2026, needs more optimization.
11 259 0.438187337614 Henry Cohn, 2026, needs more optimization.
11 260 0.438187339157 Henry Cohn, 2026, needs more optimization.
11 261 0.438223420930 Henry Cohn, 2026, needs more optimization.
11 262 0.438264923463 Henry Cohn, 2026, needs more optimization.
11 263 0.438264925530 Henry Cohn, 2026, needs more optimization.
11 264 0.438276711059 Henry Cohn, 2026, needs more optimization.
11 265 0.438370668750 Henry Cohn, 2026, needs more optimization.
11 266 0.438422382120 Henry Cohn, 2026, needs more optimization.
11 267 0.438484771379 Henry Cohn, 2026, needs more optimization.
11 268 0.438506652378 A. Kravatsky, V. Khrulkov, and I. Oseledets, ImprovEvolve: basin-hopping meets LLM-guided evolutionary search, ICML 2026 AI4Math Workshop Poster, https://openreview.net/forum?id=nE1q0gRDNr, arXiv:2602.10233, after some further optimization.
11 269 0.438602932604 Henry Cohn, 2026, needs more optimization.
11 270 0.439115025470 Henry Cohn, 2026, needs more optimization.
11 271 0.439350437010 Henry Cohn, 2026, needs more optimization.
11 272 0.439852922662 Henry Cohn, 2026, needs more optimization.
11 273 0.440062843983 Henry Cohn, 2026, needs more optimization.
11 274 0.440154454774 Henry Cohn, 2026, needs more optimization.
11 275 0.440514833148 Henry Cohn, 2026, needs more optimization.
11 276 0.440743686941 Henry Cohn, 2026, needs more optimization.
11 277 0.441102538556 Henry Cohn, 2026, needs more optimization.
11 278 0.441352282773 Henry Cohn, 2026, needs more optimization.
11 279 0.441566676819 Henry Cohn, 2026, needs more optimization.
11 280 0.441918079574 Henry Cohn, 2026, needs more optimization.
11 281 0.442403956591 Henry Cohn, 2026, needs more optimization.
11 282 0.442668488446 Henry Cohn, 2026, needs more optimization.
11 283 0.442750422518 Henry Cohn, 2026, needs more optimization.
11 284 0.443022311601 Henry Cohn, 2026, needs more optimization.
11 285 0.443552754500 Henry Cohn, 2026, needs more optimization.
11 286 0.444107669051 Henry Cohn, 2026, needs more optimization.
11 287 0.444177210545 Henry Cohn, 2026, needs more optimization.
11 288 0.444763052470 Henry Cohn, 2026, needs more optimization.
11 289 0.444869175082 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
11 290 0.445397834674 Henry Cohn, 2026, needs more optimization.
11 291 0.445602444574 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
11 292 0.445955190608 Henry Cohn, 2026, needs more optimization.
11 293 0.446820522033 Henry Cohn, 2026, needs more optimization.
11 294 0.447624436072 Henry Cohn, 2026, needs more optimization.
11 295 0.449273725245 Henry Cohn, 2026, needs more optimization.
11 296 0.450073652054 Henry Cohn, 2026, needs more optimization.
11 297 0.451008917329 Henry Cohn, 2026, needs more optimization.
11 298 0.453312373583 Henry Cohn, 2026, needs more optimization.
11 299 0.454249703563 Henry Cohn, 2026, needs more optimization.
11 300 0.455140159310 Henry Cohn, 2026, needs more optimization.
11 301 0.455677387701 Henry Cohn, 2026, needs more optimization.
11 302 0.456169784216 Henry Cohn, 2026, needs more optimization.
11 303 0.457617522036 Henry Cohn, 2026, needs more optimization.
11 304 0.458902650656 Henry Cohn, 2026, needs more optimization.
11 305 0.459742670442 Henry Cohn, 2026, needs more optimization.
11 306 0.460525123129 Henry Cohn, 2026, needs more optimization.
11 307 0.461214061773 Henry Cohn, 2026, needs more optimization.
11 308 0.462078242397 Henry Cohn, 2026, needs more optimization.
11 309 0.462661679627 Henry Cohn, 2026, needs more optimization.
11 310 0.463354826215 Henry Cohn, 2026, needs more optimization.
11 311 0.463571722709 Henry Cohn, 2026, needs more optimization.
11 312 0.464070090154 Henry Cohn, 2026, needs more optimization.
11 313 0.464235486257 Henry Cohn, 2026, needs more optimization.
11 314 0.464721021375 Henry Cohn, 2026, needs more optimization.
11 315 0.464908846245 Henry Cohn, 2026, needs more optimization.
11 316 0.465130645598 Henry Cohn, 2026, needs more optimization.
11 317 0.465593832556 Henry Cohn, 2026, needs more optimization.
11 318 0.465932854299 Henry Cohn, 2026, needs more optimization.
11 319 0.466187906799 Henry Cohn, 2026, needs more optimization.
11 320 0.466344800145 Henry Cohn, 2026, needs more optimization.
11 321 0.466865203979 Henry Cohn, 2026, needs more optimization.
11 322 0.466979933669 Henry Cohn, 2026, needs more optimization.
11 323 0.467734163640 Henry Cohn, 2026, needs more optimization.
11 324 0.468123615315 Henry Cohn, 2026, needs more optimization.
11 325 0.468668772711 Henry Cohn, 2026, needs more optimization.
11 326 0.468899947245 Henry Cohn, 2026, needs more optimization.
11 327 0.469196735150 Henry Cohn, 2026, needs more optimization.
11 328 0.469735476208 Henry Cohn, 2026, needs more optimization.
11 329 0.470020051052 Henry Cohn, 2026, needs more optimization.
11 342 0.470588235295 Henry Cohn, 2026.
17⁢x−8
11 343 0.472339723600 Henry Cohn, 2026, needs more optimization.
11 344 0.473621574774 Henry Cohn, 2026, needs more optimization.
11 345 0.474461114066 Henry Cohn, 2026, needs more optimization.
11 346 0.474889752173 Henry Cohn, 2026, needs more optimization.
11 347 0.475248140219 Henry Cohn, 2026, needs more optimization.
11 348 0.475927666990 Henry Cohn, 2026, needs more optimization.
11 349 0.476438839637 Henry Cohn, 2026, needs more optimization.
11 350 0.476739838502 Henry Cohn, 2026, needs more optimization.
11 351 0.477069630196 Henry Cohn, 2026, needs more optimization.
11 352 0.477382706441 Henry Cohn, 2026, needs more optimization.
11 353 0.477681459767 Henry Cohn, 2026, needs more optimization.
11 354 0.478289674205 Henry Cohn, 2026, needs more optimization.
11 355 0.478646417992 Henry Cohn, 2026, needs more optimization.
11 356 0.478966074576 Henry Cohn, 2026, needs more optimization.
11 357 0.479084561022 Henry Cohn, 2026, needs more optimization.
11 358 0.479214096907 Henry Cohn, 2026, needs more optimization.
11 359 0.479314906378 Henry Cohn, 2026, needs more optimization.
11 360 0.479396593369 Henry Cohn, 2026, needs more optimization.
11 361 0.479466700368 Henry Cohn, 2026, needs more optimization.
11 362 0.479502947340 Henry Cohn, 2026, needs more optimization.
11 363 0.479728916103 Henry Cohn, 2026, needs more optimization.
11 364 0.479760009599 Henry Cohn, 2026, needs more optimization.
11 365 0.479889451064 Henry Cohn, 2026, needs more optimization.
11 366 0.480002506612 Henry Cohn, 2026, needs more optimization.
11 367 0.480017665109 Henry Cohn, 2026, needs more optimization.
11 368 0.480104575510 Henry Cohn, 2026, needs more optimization.
11 369 0.480173010036 Henry Cohn, 2026, needs more optimization.
11 370 0.480212528064 Henry Cohn, 2026, needs more optimization.
11 371 0.480344407320 Henry Cohn, 2026, needs more optimization.
11 372 0.480453605949 Henry Cohn, 2026, needs more optimization.
11 373 0.480471299131 Henry Cohn, 2026, needs more optimization.
11 374 0.480682039278 Henry Cohn, 2026, needs more optimization.
11 375 0.480991178967 Henry Cohn, 2026, needs more optimization.
11 376 0.481602953724 Henry Cohn, 2026, needs more optimization.
11 377 0.481675556161 Henry Cohn, 2026, needs more optimization.
11 378 0.481773140374 Henry Cohn, 2026, needs more optimization.
11 379 0.482256141410 Henry Cohn, 2026, needs more optimization.
11 380 0.482734751497 Henry Cohn, 2026, needs more optimization.
11 381 0.482924317335 Henry Cohn, 2026, needs more optimization.
11 382 0.483170871234 Henry Cohn, 2026, needs more optimization.
11 383 0.483499274500 Henry Cohn, 2026, needs more optimization.
11 384 0.483874382861 Henry Cohn, 2026, needs more optimization.
11 385 0.483968031222 Henry Cohn, 2026, needs more optimization.
11 386 0.484125868862 Henry Cohn, 2026, needs more optimization.
11 387 0.484234004684 Henry Cohn, 2026, needs more optimization.
11 388 0.484853522481 Henry Cohn, 2026, needs more optimization.
11 389 0.485093946068 Henry Cohn, 2026, needs more optimization.
11 390 0.485113696378 Henry Cohn, 2026, needs more optimization.
11 391 0.485150542505 Henry Cohn, 2026, needs more optimization.
11 392 0.485155365019 Henry Cohn, 2026, needs more optimization.
11 393 0.485164156630 Henry Cohn, 2026, needs more optimization.
11 394 0.485193976927 Henry Cohn, 2026, needs more optimization.
11 395 0.485220831282 Henry Cohn, 2026, needs more optimization.
11 396 0.485241754556 Henry Cohn, 2026, needs more optimization.
11 397 0.485679429339 Henry Cohn, 2026, needs more optimization.
11 398 0.485685027673 Henry Cohn, 2026, needs more optimization.
11 399 0.485731040517 Henry Cohn, 2026, needs more optimization.
11 400 0.486000062121 Henry Cohn, 2026, needs more optimization.
11 402 0.486163146789 Henry Cohn, 2026, needs more optimization.
11 403 0.486168804296 Henry Cohn, 2026, needs more optimization.
11 404 0.486171492421 Henry Cohn, 2026, needs more optimization.
11 406 0.486242683878 Henry Cohn, 2026, needs more optimization.
11 407 0.486252630685 Henry Cohn, 2026, needs more optimization.
11 408 0.486443788132 Henry Cohn, 2026, needs more optimization.
11 409 0.486577300085 Henry Cohn, 2026, needs more optimization.
11 410 0.486713124819 Henry Cohn, 2026, needs more optimization.
11 411 0.487340513034 Henry Cohn, 2026, needs more optimization.
11 412 0.488064045584 Henry Cohn, 2026, needs more optimization.
11 413 0.488446898300 Henry Cohn, 2026, needs more optimization.
11 414 0.488884429023 Henry Cohn, 2026, needs more optimization.
11 415 0.488928658758 Henry Cohn, 2026, needs more optimization.
11 416 0.489055020963 Henry Cohn, 2026, needs more optimization.
11 417 0.489129797029 Henry Cohn, 2026, needs more optimization.
11 418 0.489294759994 Henry Cohn, 2026, needs more optimization.
11 419 0.489364102298 Henry Cohn, 2026, needs more optimization.
11 420 0.489550356237 Henry Cohn, 2026, needs more optimization.
11 421 0.489622839175 Henry Cohn, 2026, needs more optimization.
11 422 0.489823273852 Henry Cohn, 2026, needs more optimization.
11 423 0.489852565710 Henry Cohn, 2026, needs more optimization.
11 424 0.489999775387 Henry Cohn, 2026, needs more optimization.
11 425 0.490472223232 Henry Cohn, 2026, needs more optimization.
11 426 0.490680318201 Henry Cohn, 2026, needs more optimization.
11 427 0.490903274851 Henry Cohn, 2026, needs more optimization.
11 428 0.491079817838 Henry Cohn, 2026, needs more optimization.
11 429 0.491310248440 Henry Cohn, 2026, needs more optimization.
11 430 0.491584748822 Henry Cohn, 2026, needs more optimization.
11 431 0.491815871554 Henry Cohn, 2026, needs more optimization.
11 432 0.491935419166 Henry Cohn, 2026, needs more optimization.
11 433 0.492098014031 Henry Cohn, 2026, needs more optimization.
11 434 0.492275289861 Henry Cohn, 2026, needs more optimization.
11 435 0.492573519111 Henry Cohn, 2026, needs more optimization.
11 436 0.492638245490 Henry Cohn, 2026, needs more optimization.
11 437 0.492776045213 Henry Cohn, 2026, needs more optimization.
11 438 0.492801745659 Henry Cohn, 2026, needs more optimization.
11 439 0.492843547870 Henry Cohn, 2026, needs more optimization.
11 440 0.493000314333 Henry Cohn, 2026, needs more optimization.
11 441 0.493006785931 Henry Cohn, 2026, needs more optimization.
11 442 0.493039780268 Henry Cohn, 2026, needs more optimization.
11 443 0.493050395666 Henry Cohn, 2026, needs more optimization.
11 444 0.493229032726 Henry Cohn, 2026, needs more optimization.
11 445 0.493280755899 Henry Cohn, 2026, needs more optimization.
11 446 0.493337197693 Henry Cohn, 2026, needs more optimization.
11 447 0.493349761184 Henry Cohn, 2026, needs more optimization.
11 448 0.493368224288 Henry Cohn, 2026, needs more optimization.
11 449 0.495054450388 Henry Cohn, 2026, needs more optimization.
11 450 0.495212966880 Henry Cohn, 2026, needs more optimization.
11 451 0.495413781993 Henry Cohn, 2026, needs more optimization.
11 452 0.495517893371 Henry Cohn, 2026, needs more optimization.
11 453 0.495604901355 Henry Cohn, 2026, needs more optimization.
11 454 0.495826135841 Henry Cohn, 2026, needs more optimization.
11 456 0.495912981914 Henry Cohn, 2026, needs more optimization.
11 457 0.495993139966 Henry Cohn, 2026, needs more optimization.
11 458 0.496134792821 Henry Cohn, 2026, needs more optimization.
11 459 0.496346674062 Henry Cohn, 2026, needs more optimization.
11 460 0.496626444852 Henry Cohn, 2026, needs more optimization.
11 461 0.496826082492 Henry Cohn, 2026, needs more optimization.
11 462 0.496875499605 Henry Cohn, 2026, needs more optimization.
11 463 0.496955535325 Henry Cohn, 2026, needs more optimization.
11 464 0.497222843063 Henry Cohn, 2026, needs more optimization.
11 465 0.497335134468 Henry Cohn, 2026, needs more optimization.
11 466 0.497349849445 Henry Cohn, 2026, needs more optimization.
11 467 0.497484968069 Henry Cohn, 2026, needs more optimization.
11 468 0.497559924652 Henry Cohn, 2026, needs more optimization.
11 469 0.497715309435 Henry Cohn, 2026, needs more optimization.
11 470 0.497776465796 Henry Cohn, 2026, needs more optimization.
11 471 0.497902678085 Henry Cohn, 2026, needs more optimization.
11 472 0.497975919384 Henry Cohn, 2026, needs more optimization.
11 473 0.498391093749 Henry Cohn, 2026, needs more optimization.
11 474 0.498438058399 Henry Cohn, 2026, needs more optimization.
11 475 0.498722492865 Henry Cohn, 2026, needs more optimization.
11 476 0.498801765805 Henry Cohn, 2026, needs more optimization.
11 477 0.498893899428 Henry Cohn, 2026, needs more optimization.
11 482 0.499630490823 Henry Cohn, 2026, needs more optimization.
11 484 0.499630962725 Henry Cohn, 2026, needs more optimization.
11 486 0.499632897397 Henry Cohn, 2026, needs more optimization.
11 487 0.499633597765 Henry Cohn, 2026, needs more optimization.
11 489 0.499634897959 Henry Cohn, 2026, needs more optimization.
11 490 0.499635396156 Henry Cohn, 2026, needs more optimization.
11 492 0.499635857743 Henry Cohn, 2026, needs more optimization.
11 493 0.499635857786 Henry Cohn, 2026, needs more optimization.
11 494 0.499635979692 Henry Cohn, 2026, needs more optimization.
11 495 0.499637906761 Henry Cohn, 2026, needs more optimization.
11 496 0.499638052832 Henry Cohn, 2026, needs more optimization.
11 497 0.499638409429 Henry Cohn, 2026, needs more optimization.
11 498 0.499640759842 Henry Cohn, 2026, needs more optimization.
11 503 0.499642636202 Henry Cohn, 2026, needs more optimization.
11 505 0.499644577954 Henry Cohn, 2026, needs more optimization.
11 507 0.499645238658 Henry Cohn, 2026, needs more optimization.
11 512 0.499645882033 Henry Cohn, 2026, needs more optimization.
11 514 0.499646973686 Henry Cohn, 2026, needs more optimization.
11 516 0.499648375785 Henry Cohn, 2026, needs more optimization.
11 517 0.499649549252 Henry Cohn, 2026, needs more optimization.
11 518 0.499649581048 Henry Cohn, 2026, needs more optimization.
11 522 0.499650778627 Henry Cohn, 2026, needs more optimization.
11 523 0.499651522172 Henry Cohn, 2026, needs more optimization.
11 524 0.499651978873 Henry Cohn, 2026, needs more optimization.
11 525 0.499651979801 Henry Cohn, 2026, needs more optimization.
11 526 0.499652347581 Henry Cohn, 2026, needs more optimization.
11 527 0.499652633231 Henry Cohn, 2026, needs more optimization.
11 529 0.499652907864 Henry Cohn, 2026, needs more optimization.
11 530 0.499653655997 Henry Cohn, 2026, needs more optimization.
11 532 0.499654106241 Henry Cohn, 2026, needs more optimization.
11 535 0.499655103199 Henry Cohn, 2026, needs more optimization.
11 536 0.499655206527 Henry Cohn, 2026, needs more optimization.
11 537 0.499657430739 Henry Cohn, 2026, needs more optimization.
11 539 0.499658154259 Henry Cohn, 2026, needs more optimization.
11 540 0.499658652314 Henry Cohn, 2026, needs more optimization.
11 541 0.499658695596 Henry Cohn, 2026, needs more optimization.
11 543 0.499659025244 Henry Cohn, 2026, needs more optimization.
11 545 0.499660031290 Henry Cohn, 2026, needs more optimization.
11 549 0.499660740131 Henry Cohn, 2026, needs more optimization.
11 550 0.499660876129 Henry Cohn, 2026, needs more optimization.
11 554 0.499660995711 Henry Cohn, 2026, needs more optimization.
11 555 0.499661194303 Henry Cohn, 2026, needs more optimization.
11 556 0.499661267405 Henry Cohn, 2026, needs more optimization.
11 558 0.499661607406 Henry Cohn, 2026, needs more optimization.
11 559 0.499661688897 Henry Cohn, 2026, needs more optimization.
11 564 0.499662184841 Henry Cohn, 2026, needs more optimization.
11 569 0.499662536249 Henry Cohn, 2026, needs more optimization.
11 571 0.499662568274 Henry Cohn, 2026, needs more optimization.
11 573 0.499662636177 Henry Cohn, 2026, needs more optimization.
11 574 0.499662700402 Henry Cohn, 2026, needs more optimization.
11 576 0.499662830518 Henry Cohn, 2026, needs more optimization.
11 578 0.499662888363 Henry Cohn, 2026, needs more optimization.
11 581 0.499663590024 Henry Cohn, 2026, needs more optimization.
11 582 0.499663808280 Henry Cohn, 2026, needs more optimization.
11 584 0.499663825564 Henry Cohn, 2026, needs more optimization.
11 585 0.499664042002 Henry Cohn, 2026, needs more optimization.
11 586 0.499665774267 Henry Cohn, 2026, needs more optimization.
11 588 0.499666200407 Henry Cohn, 2026, needs more optimization.
11 591 0.499666326568 Henry Cohn, 2026, needs more optimization.
11 592 0.499669023519 Henry Cohn, 2026, needs more optimization.
11 593 0.499999985865 Henry Cohn, 2026, needs more optimization.
11 604 0.5 F. Bianchi, Y. Kwon, A. Pappu, and J. Zou, Harnessing the collective intelligence of AI agents in the wild for new discoveries, preprint, 2026, arXiv:2606.10402.
2⁢x−1
11 605 0.507413365513 Henry Cohn, 2026, needs more optimization.
11 606 0.511334746644 Henry Cohn, 2026, needs more optimization.
11 607 0.511427497694 Henry Cohn, 2026, needs more optimization.
11 608 0.511756777241 Henry Cohn, 2026, needs more optimization.
11 609 0.512058530680 Henry Cohn, 2026, needs more optimization.
11 610 0.512092001466 Henry Cohn, 2026, needs more optimization.
11 611 0.512191490972 Henry Cohn, 2026, needs more optimization.
11 612 0.512248156131 Henry Cohn, 2026, needs more optimization.
11 614 0.512273853966 Henry Cohn, 2026, needs more optimization.
11 615 0.512584253709 Henry Cohn, 2026, needs more optimization.
11 616 0.512831437259 Henry Cohn, 2026, needs more optimization.
11 617 0.513085855772 Henry Cohn, 2026, needs more optimization.
11 618 0.513409156996 Henry Cohn, 2026, needs more optimization.
11 619 0.513919042539 Henry Cohn, 2026, needs more optimization.
11 620 0.514034401463 Henry Cohn, 2026, needs more optimization.
11 621 0.514680254281 Henry Cohn, 2026, needs more optimization.
11 622 0.515098607752 Henry Cohn, 2026, needs more optimization.
11 623 0.515450465382 Henry Cohn, 2026, needs more optimization.
11 624 0.515632666949 Henry Cohn, 2026, needs more optimization.
11 625 0.516067402605 Henry Cohn, 2026, needs more optimization.
11 626 0.516368221845 Henry Cohn, 2026, needs more optimization.
11 627 0.516458350727 Henry Cohn, 2026, needs more optimization.
11 628 0.516912957078 Henry Cohn, 2026, needs more optimization.
11 629 0.517526791539 Henry Cohn, 2026, needs more optimization.
11 630 0.518189100803 Henry Cohn, 2026, needs more optimization.
11 631 0.518835992466 Henry Cohn, 2026, needs more optimization.
11 632 0.519498422707 Henry Cohn, 2026, needs more optimization.
11 633 0.520251365247 Henry Cohn, 2026, needs more optimization.
11 634 0.520673060809 Henry Cohn, 2026, needs more optimization.
11 636 0.521921341194 Henry Cohn, 2026, needs more optimization.
11 637 0.523121578674 Henry Cohn, 2026, needs more optimization.
11 638 0.525024844396 Henry Cohn, 2026, needs more optimization.
11 639 0.525602365561 Henry Cohn, 2026, needs more optimization.
11 640 0.527322376725 Henry Cohn, 2026, needs more optimization.
11 642 0.528403377167 Henry Cohn, 2026, needs more optimization.
11 643 0.528436180241 Henry Cohn, 2026, needs more optimization.
11 644 0.528441728791 Henry Cohn, 2026, needs more optimization.
11 645 0.528462884677 Henry Cohn, 2026, needs more optimization.
11 646 0.528485425763 Henry Cohn, 2026, needs more optimization.
11 647 0.528487371521 Henry Cohn, 2026, needs more optimization.
11 648 0.528504653480 Henry Cohn, 2026, needs more optimization.
11 649 0.528507786460 Henry Cohn, 2026, needs more optimization.
11 650 0.528520167631 Henry Cohn, 2026, needs more optimization.
11 651 0.528528870116 Henry Cohn, 2026, needs more optimization.
11 652 0.528587241940 Henry Cohn, 2026, needs more optimization.
11 653 0.528600191818 Henry Cohn, 2026, needs more optimization.
11 654 0.528953642351 Henry Cohn, 2026, needs more optimization.
11 655 0.529242298714 Henry Cohn, 2026, needs more optimization.
11 656 0.529764712216 Henry Cohn, 2026, needs more optimization.
11 657 0.530449275578 Henry Cohn, 2026, needs more optimization.
11 658 0.531022195145 Henry Cohn, 2026, needs more optimization.
11 659 0.531484096578 Henry Cohn, 2026, needs more optimization.
11 660 0.531983336819 Henry Cohn, 2026, needs more optimization.
11 661 0.533046675707 Henry Cohn, 2026, needs more optimization.
11 662 0.533551270383 Henry Cohn, 2026, needs more optimization.
11 663 0.533924490994 Henry Cohn, 2026, needs more optimization.
11 664 0.534256208601 Henry Cohn, 2026, needs more optimization.
11 665 0.534795157400 Henry Cohn, 2026, needs more optimization.
11 666 0.535077735487 Henry Cohn, 2026, needs more optimization.
11 667 0.535548561370 Henry Cohn, 2026, needs more optimization.
11 668 0.535862285697 Henry Cohn, 2026, needs more optimization.
11 669 0.536128841844 Henry Cohn, 2026, needs more optimization.
11 670 0.536273377041 Henry Cohn, 2026, needs more optimization.
11 671 0.536536508497 Henry Cohn, 2026, needs more optimization.
11 672 0.536578351389 Henry Cohn, 2026, needs more optimization.
11 673 0.536598197308 Henry Cohn, 2026, needs more optimization.
11 674 0.536631242194 Henry Cohn, 2026, needs more optimization.
11 675 0.536802074766 Henry Cohn, 2026, needs more optimization.
11 676 0.537173293846 Henry Cohn, 2026, needs more optimization.
11 677 0.537532374560 Henry Cohn, 2026, needs more optimization.
11 678 0.537625015033 Henry Cohn, 2026, needs more optimization.
11 679 0.538273994653 Henry Cohn, 2026, needs more optimization.
11 680 0.538611420985 Henry Cohn, 2026, needs more optimization.
11 681 0.538845533994 Henry Cohn, 2026, needs more optimization.
11 682 0.539212606007 Henry Cohn, 2026, needs more optimization.
11 683 0.539543194606 Henry Cohn, 2026, needs more optimization.
11 684 0.539701682354 Henry Cohn, 2026, needs more optimization.
11 685 0.540117213430 Henry Cohn, 2026, needs more optimization.
11 686 0.540468815021 Henry Cohn, 2026, needs more optimization.
11 687 0.540802946281 Henry Cohn, 2026, needs more optimization.
11 688 0.541251285971 Henry Cohn, 2026, needs more optimization.
11 689 0.541715406016 Henry Cohn, 2026, needs more optimization.
11 690 0.541756893924 Henry Cohn, 2026, needs more optimization.
11 691 0.541790746126 Henry Cohn, 2026, needs more optimization.
11 692 0.541801622779 Henry Cohn, 2026, needs more optimization.
11 693 0.543043386122 Henry Cohn, 2026, needs more optimization.
11 694 0.543157505955 Henry Cohn, 2026, needs more optimization.
11 695 0.543555741173 Henry Cohn, 2026, needs more optimization.
11 696 0.543954537125 Henry Cohn, 2026, needs more optimization.
11 697 0.544270829866 Henry Cohn, 2026, needs more optimization.
11 698 0.544565621736 Henry Cohn, 2026, needs more optimization.
11 699 0.544776040649 Henry Cohn, 2026, needs more optimization.
11 700 0.545121280489 Henry Cohn, 2026, needs more optimization.
11 701 0.545369225548 Henry Cohn, 2026, needs more optimization.
11 702 0.545656554581 Henry Cohn, 2026, needs more optimization.
11 703 0.545930158095 Henry Cohn, 2026, needs more optimization.
11 704 0.546179821540 Henry Cohn, 2026, needs more optimization.
11 705 0.546481515092 Henry Cohn, 2026, needs more optimization.
11 706 0.546635272268 Henry Cohn, 2026, needs more optimization.
11 707 0.546883111300 Henry Cohn, 2026, needs more optimization.
11 708 0.547091159272 Henry Cohn, 2026, needs more optimization.
11 709 0.547354598451 Henry Cohn, 2026, needs more optimization.
11 710 0.547628853119 Henry Cohn, 2026, needs more optimization.
11 711 0.547919164568 Henry Cohn, 2026, needs more optimization.
11 712 0.548092550096 Henry Cohn, 2026, needs more optimization.
11 713 0.548313710074 Henry Cohn, 2026, needs more optimization.
11 714 0.548353663472 Henry Cohn, 2026, needs more optimization.
11 715 0.548575697466 Henry Cohn, 2026, needs more optimization.
11 716 0.549027641432 Henry Cohn, 2026, needs more optimization.
11 717 0.549069803421 Henry Cohn, 2026, needs more optimization.
11 718 0.549403862308 Henry Cohn, 2026, needs more optimization.
11 719 0.549951696610 Henry Cohn, 2026, needs more optimization.
11 720 0.549976791786 Henry Cohn, 2026, needs more optimization.
11 721 0.550349093093 Henry Cohn, 2026, needs more optimization.
11 722 0.550409959158 Henry Cohn, 2026, needs more optimization.
11 723 0.550581562312 Henry Cohn, 2026, needs more optimization.
11 724 0.550745572616 Henry Cohn, 2026, needs more optimization.
11 725 0.550804834965 Henry Cohn, 2026, needs more optimization.
11 726 0.551350422869 Henry Cohn, 2026, needs more optimization.
11 729 0.551396591488 Henry Cohn, 2026, needs more optimization.
11 730 0.551430657492 Henry Cohn, 2026, needs more optimization.
11 731 0.551595240563 Henry Cohn, 2026, needs more optimization.
11 732 0.551632243069 Henry Cohn, 2026, needs more optimization.
11 733 0.551654008648 Henry Cohn, 2026, needs more optimization.
11 734 0.551716506874 Henry Cohn, 2026, needs more optimization.
11 735 0.551829503102 Henry Cohn, 2026, needs more optimization.
11 736 0.551875632711 Henry Cohn, 2026, needs more optimization.
11 737 0.551926846524 Henry Cohn, 2026, needs more optimization.
11 738 0.551956429080 Henry Cohn, 2026, needs more optimization.
11 739 0.551980445893 Henry Cohn, 2026, needs more optimization.
11 740 0.552000935289 Henry Cohn, 2026, needs more optimization.
11 741 0.554261324289 Henry Cohn, 2026, needs more optimization.
11 742 0.554462010679 Henry Cohn, 2026, needs more optimization.
11 743 0.555079260333 Henry Cohn, 2026, needs more optimization.
11 745 0.555164367093 Henry Cohn, 2026, needs more optimization.
11 746 0.555377568571 Henry Cohn, 2026, needs more optimization.
11 982 0.555555555556 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
9⁢x−5
11 983 0.560837721037 Numaro AI Autoresearch, 11,000+ New Verified Spherical-Code Records from AI Autoresearch, Numaro Research Report NUMARO-2026-015 (2026), https://numaro.tech/research/spherical-codes-2026/.
11 984 0.562683590870 Numaro AI Autoresearch, 11,000+ New Verified Spherical-Code Records from AI Autoresearch, Numaro Research Report NUMARO-2026-015 (2026), https://numaro.tech/research/spherical-codes-2026/.
11 985 0.563555049705 Numaro AI Autoresearch, 11,000+ New Verified Spherical-Code Records from AI Autoresearch, Numaro Research Report NUMARO-2026-015 (2026), https://numaro.tech/research/spherical-codes-2026/.
11 986 0.564050312045 Numaro AI Autoresearch, 11,000+ New Verified Spherical-Code Records from AI Autoresearch, Numaro Research Report NUMARO-2026-015 (2026), https://numaro.tech/research/spherical-codes-2026/.
11 987 0.564337505574 Numaro AI Autoresearch, 11,000+ New Verified Spherical-Code Records from AI Autoresearch, Numaro Research Report NUMARO-2026-015 (2026), https://numaro.tech/research/spherical-codes-2026/.
11 988 0.564553501127 Numaro AI Autoresearch, 11,000+ New Verified Spherical-Code Records from AI Autoresearch, Numaro Research Report NUMARO-2026-015 (2026), https://numaro.tech/research/spherical-codes-2026/.
11 989 0.564687704652 Numaro AI Autoresearch, 11,000+ New Verified Spherical-Code Records from AI Autoresearch, Numaro Research Report NUMARO-2026-015 (2026), https://numaro.tech/research/spherical-codes-2026/.
11 990 0.564792472799 Numaro AI Autoresearch, 11,000+ New Verified Spherical-Code Records from AI Autoresearch, Numaro Research Report NUMARO-2026-015 (2026), https://numaro.tech/research/spherical-codes-2026/.
11 991 0.564854696069 Numaro AI Autoresearch, 11,000+ New Verified Spherical-Code Records from AI Autoresearch, Numaro Research Report NUMARO-2026-015 (2026), https://numaro.tech/research/spherical-codes-2026/.
11 992 0.564877127788 Numaro AI Autoresearch, 11,000+ New Verified Spherical-Code Records from AI Autoresearch, Numaro Research Report NUMARO-2026-015 (2026), https://numaro.tech/research/spherical-codes-2026/.
11 993 0.566242341854 Numaro AI Autoresearch, 11,000+ New Verified Spherical-Code Records from AI Autoresearch, Numaro Research Report NUMARO-2026-015 (2026), https://numaro.tech/research/spherical-codes-2026/.
11 994 0.566797906784 Numaro AI Autoresearch, 11,000+ New Verified Spherical-Code Records from AI Autoresearch, Numaro Research Report NUMARO-2026-015 (2026), https://numaro.tech/research/spherical-codes-2026/.
11 995 0.567169847205 Numaro AI Autoresearch, 11,000+ New Verified Spherical-Code Records from AI Autoresearch, Numaro Research Report NUMARO-2026-015 (2026), https://numaro.tech/research/spherical-codes-2026/.
11 996 0.567445746363 Numaro AI Autoresearch, 11,000+ New Verified Spherical-Code Records from AI Autoresearch, Numaro Research Report NUMARO-2026-015 (2026), https://numaro.tech/research/spherical-codes-2026/.
11 997 0.568088062435 Numaro AI Autoresearch, 11,000+ New Verified Spherical-Code Records from AI Autoresearch, Numaro Research Report NUMARO-2026-015 (2026), https://numaro.tech/research/spherical-codes-2026/.
11 998 0.568464600551 Numaro AI Autoresearch, 11,000+ New Verified Spherical-Code Records from AI Autoresearch, Numaro Research Report NUMARO-2026-015 (2026), https://numaro.tech/research/spherical-codes-2026/.
11 999 0.568867627920 Numaro AI Autoresearch, 11,000+ New Verified Spherical-Code Records from AI Autoresearch, Numaro Research Report NUMARO-2026-015 (2026), https://numaro.tech/research/spherical-codes-2026/.
11 1000 0.569144568167 Numaro AI Autoresearch, 11,000+ New Verified Spherical-Code Records from AI Autoresearch, Numaro Research Report NUMARO-2026-015 (2026), https://numaro.tech/research/spherical-codes-2026/.
11 1001 0.569383214074 Numaro AI Autoresearch, 11,000+ New Verified Spherical-Code Records from AI Autoresearch, Numaro Research Report NUMARO-2026-015 (2026), https://numaro.tech/research/spherical-codes-2026/.
11 1002 0.569639206096 Numaro AI Autoresearch, 11,000+ New Verified Spherical-Code Records from AI Autoresearch, Numaro Research Report NUMARO-2026-015 (2026), https://numaro.tech/research/spherical-codes-2026/.
11 1003 0.569901811628 Numaro AI Autoresearch, 11,000+ New Verified Spherical-Code Records from AI Autoresearch, Numaro Research Report NUMARO-2026-015 (2026), https://numaro.tech/research/spherical-codes-2026/.
11 1004 0.570106342639 Numaro AI Autoresearch, 11,000+ New Verified Spherical-Code Records from AI Autoresearch, Numaro Research Report NUMARO-2026-015 (2026), https://numaro.tech/research/spherical-codes-2026/.
11 1005 0.570296080258 Henry Cohn, 2026, needs more optimization.
11 1006 0.570500165163 Numaro AI Autoresearch, 11,000+ New Verified Spherical-Code Records from AI Autoresearch, Numaro Research Report NUMARO-2026-015 (2026), https://numaro.tech/research/spherical-codes-2026/.
11 1007 0.570636512950 Henry Cohn, 2026, needs more optimization.
11 1008 0.570782470842 Numaro AI Autoresearch, 11,000+ New Verified Spherical-Code Records from AI Autoresearch, Numaro Research Report NUMARO-2026-015 (2026), https://numaro.tech/research/spherical-codes-2026/.
11 1009 0.570923694358 Numaro AI Autoresearch, 11,000+ New Verified Spherical-Code Records from AI Autoresearch, Numaro Research Report NUMARO-2026-015 (2026), https://numaro.tech/research/spherical-codes-2026/.
11 1010 0.571063194829 Numaro AI Autoresearch, 11,000+ New Verified Spherical-Code Records from AI Autoresearch, Numaro Research Report NUMARO-2026-015 (2026), https://numaro.tech/research/spherical-codes-2026/.
11 1011 0.571312741410 Numaro AI Autoresearch, 11,000+ New Verified Spherical-Code Records from AI Autoresearch, Numaro Research Report NUMARO-2026-015 (2026), https://numaro.tech/research/spherical-codes-2026/.
11 1012 0.571445895660 Numaro AI Autoresearch, 11,000+ New Verified Spherical-Code Records from AI Autoresearch, Numaro Research Report NUMARO-2026-015 (2026), https://numaro.tech/research/spherical-codes-2026/.
11 1013 0.571627040037 Numaro AI Autoresearch, 11,000+ New Verified Spherical-Code Records from AI Autoresearch, Numaro Research Report NUMARO-2026-015 (2026), https://numaro.tech/research/spherical-codes-2026/.
11 1014 0.571814986621 Numaro AI Autoresearch, 11,000+ New Verified Spherical-Code Records from AI Autoresearch, Numaro Research Report NUMARO-2026-015 (2026), https://numaro.tech/research/spherical-codes-2026/.
11 1015 0.571936595035 Numaro AI Autoresearch, 11,000+ New Verified Spherical-Code Records from AI Autoresearch, Numaro Research Report NUMARO-2026-015 (2026), https://numaro.tech/research/spherical-codes-2026/.
11 1016 0.572062925763 Numaro AI Autoresearch, 11,000+ New Verified Spherical-Code Records from AI Autoresearch, Numaro Research Report NUMARO-2026-015 (2026), https://numaro.tech/research/spherical-codes-2026/.
11 1017 0.572191694736 Numaro AI Autoresearch, 11,000+ New Verified Spherical-Code Records from AI Autoresearch, Numaro Research Report NUMARO-2026-015 (2026), https://numaro.tech/research/spherical-codes-2026/.
11 1018 0.572359192484 Numaro AI Autoresearch, 11,000+ New Verified Spherical-Code Records from AI Autoresearch, Numaro Research Report NUMARO-2026-015 (2026), https://numaro.tech/research/spherical-codes-2026/.
11 1019 0.572477252388 Numaro AI Autoresearch, 11,000+ New Verified Spherical-Code Records from AI Autoresearch, Numaro Research Report NUMARO-2026-015 (2026), https://numaro.tech/research/spherical-codes-2026/.
11 1020 0.572599530382 Numaro AI Autoresearch, 11,000+ New Verified Spherical-Code Records from AI Autoresearch, Numaro Research Report NUMARO-2026-015 (2026), https://numaro.tech/research/spherical-codes-2026/.
11 1021 0.572658156256 Numaro AI Autoresearch, 11,000+ New Verified Spherical-Code Records from AI Autoresearch, Numaro Research Report NUMARO-2026-015 (2026), https://numaro.tech/research/spherical-codes-2026/.
11 1022 0.572792667922 Numaro AI Autoresearch, 11,000+ New Verified Spherical-Code Records from AI Autoresearch, Numaro Research Report NUMARO-2026-015 (2026), https://numaro.tech/research/spherical-codes-2026/.
11 1023 0.572912620272 Numaro AI Autoresearch, 11,000+ New Verified Spherical-Code Records from AI Autoresearch, Numaro Research Report NUMARO-2026-015 (2026), https://numaro.tech/research/spherical-codes-2026/.
11 1024 0.573029621713 Numaro AI Autoresearch, 11,000+ New Verified Spherical-Code Records from AI Autoresearch, Numaro Research Report NUMARO-2026-015 (2026), https://numaro.tech/research/spherical-codes-2026/.
12 25 0.061281914575 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
1200⁢x3−144⁢x2−12⁢x+1
12 26 0.071428571429 T. Ericson and V. Zinoviev, Spherical codes generated by binary partitions of symmetric pointsets, IEEE Trans. Inform. Theory 41 (1995), 107–129, doi:10.1109/18.370114.
14⁢x−1
12 27 0.074764926182 H. Cohn, Small spherical and projective codes, data set, 2022, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
12 28 0.082592206268 H. Cohn, Small spherical and projective codes, data set, 2022, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
12 29 0.084348009310 H. Cohn, Small spherical and projective codes, data set, 2022, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
496⁢x4+92⁢x3−57⁢x2−8⁢x+1
12 30 0.089146601434 H. Cohn, Small spherical and projective codes, data set, 2022, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
3856⁢x4+1456⁢x3+100⁢x2−12⁢x−1
12 31 0.098704091241 H. Cohn, Small spherical and projective codes, data set, 2022, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
863⁢x2+6⁢x−9
12 32 0.098704091241 H. Cohn, Small spherical and projective codes, data set, 2022, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
863⁢x2+6⁢x−9
12 34 0.112004618870 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
44⁢x2+4⁢x−1
12 35 0.119914058434 Henry Cohn, 2025.
12 36 0.121730661114 Henry Cohn, 2026.
12 37 0.121971459128 Henry Cohn, 2023.
359⁢x2+30⁢x−9
12 38 0.130785955647 Henry Cohn, 2026.
12 39 0.132497435001 Henry Cohn, 2023.
12 40 0.133638243588 Henry Cohn, 2023.
12 41 0.135922539556 Henry Cohn, 2023.
12 42 0.136597789057 Henry Cohn, 2023.
5296⁢x4+1248⁢x3−40⁢x2−24⁢x−1
12 43 0.139595542735 Henry Cohn, 2023.
Minimal polynomial listed in plain text data
12 44 0.141964936980 Henry Cohn, 2023.
736256⁢x8−133120⁢x7−146176⁢x6−13824⁢x5+8368⁢x4+1568⁢x3−72⁢x2−24⁢x−1
12 45 0.149653254074 Henry Cohn, 2024.
12 46 0.150221879934 Henry Cohn, 2025.
12 50 0.150442862439 Henry Cohn, 2023.
956⁢x2−84⁢x−9
12 51 0.159810400056 Henry Cohn, 2023.
3600⁢x5−1080⁢x4−252⁢x3+36⁢x2+9⁢x−1
12 52 0.180095470186 Henry Cohn, 2025.
12 53 0.187397967438 A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
12 54 0.189746662791 Henry Cohn, 2024.
12 55 0.193319611131 Henry Cohn, 2025.
12 60 0.193457871625 Henry Cohn, 2026.
3088⁢x4−1184⁢x3−120⁢x2+40⁢x+1
12 61 0.196565668411 Henry Cohn, 2026.
12 62 0.197162933815 Henry Cohn, 2026.
24⁢x3+92⁢x2−14⁢x−1
12 63 0.207401048725 Henry Cohn, 2026.
12 64 0.210566554872 A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
12 65 0.214409160183 Henry Cohn, 2026.
12 66 0.215046351057 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
12 67 0.215314925312 Henry Cohn, 2026.
12 68 0.220094074998 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
12 69 0.225149391956 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
12 70 0.228644479119 Henry Cohn, 2026, needs more optimization.
12 71 0.230446504601 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
12 72 0.231181160385 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
12 73 0.232372132321 Henry Cohn, 2026, needs more optimization.
12 74 0.233297480885 Henry Cohn, 2026, needs more optimization.
12 75 0.235723787813 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
12 76 0.236708116611 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
12 77 0.237968057446 Henry Cohn, 2025.
12 78 0.239700240785 A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
12 79 0.241071143297 A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
12 80 0.243291248047 A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
12 81 0.243910094468 A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
12 90 0.244488618750 A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
29⁢x2−3⁢x−1
12 91 0.250930942836 A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
12 92 0.260985425422 Henry Cohn, 2026.
12 93 0.263892498486 Henry Cohn, 2026, needs more optimization.
12 94 0.264660922399 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
12 95 0.265090859018 Henry Cohn, 2026, needs more optimization.
12 96 0.265464666410 Henry Cohn, 2026.
12 97 0.266011542070 Henry Cohn, 2026, needs more optimization.
12 98 0.266355304971 Henry Cohn, 2026, needs more optimization.
12 99 0.266726368773 Henry Cohn, 2026, needs more optimization.
12 100 0.266944127341 Henry Cohn, 2026, needs more optimization.
12 101 0.267152385945 Henry Cohn, 2026, needs more optimization.
12 102 0.267190937318 Henry Cohn, 2026, needs more optimization.
12 103 0.268908249429 Henry Cohn, 2026, needs more optimization.
12 104 0.271239758605 Henry Cohn, 2026, needs more optimization.
12 106 0.271795861692 A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
12 107 0.273390148195 Henry Cohn, 2026, needs more optimization.
12 108 0.276780663196 Henry Cohn, 2026, needs more optimization.
12 109 0.277498639787 Henry Cohn, 2026, needs more optimization.
12 110 0.277860219276 Henry Cohn, 2026, needs more optimization.
12 111 0.278763623393 Henry Cohn, 2026, needs more optimization.
12 112 0.279437784712 Henry Cohn, 2026, needs more optimization.
12 113 0.281952061154 Henry Cohn, 2026, needs more optimization.
12 114 0.290549700654 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
12 115 0.291590400846 Henry Cohn, 2026, needs more optimization.
12 116 0.292122916878 Henry Cohn, 2026, needs more optimization.
12 117 0.292984687977 Henry Cohn, 2026, needs more optimization.
12 118 0.293554163132 Henry Cohn, 2026, needs more optimization.
12 119 0.294519594653 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
12 121 0.294708984704 Henry Cohn, 2026, needs more optimization.
12 122 0.303301200891 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
12 123 0.304340404139 Henry Cohn, 2026, needs more optimization.
12 124 0.304347105250 Henry Cohn, 2026, needs more optimization.
12 125 0.304349311006 Henry Cohn, 2026, needs more optimization.
12 126 0.304786532401 Henry Cohn, 2026, needs more optimization.
12 127 0.306791570832 Henry Cohn, 2026, needs more optimization.
12 128 0.307553171033 Henry Cohn, 2026, needs more optimization.
12 129 0.307806672146 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
12 130 0.308010886898 Henry Cohn, 2026, needs more optimization.
12 131 0.308541210130 Henry Cohn, 2026, needs more optimization.
12 132 0.309435848972 Henry Cohn, 2026, needs more optimization.
12 133 0.310040611247 Henry Cohn, 2026, needs more optimization.
12 134 0.311212709651 Henry Cohn, 2026, needs more optimization.
12 135 0.312205898262 Henry Cohn, 2026, needs more optimization.
12 136 0.313692305444 Henry Cohn, 2026, needs more optimization.
12 137 0.315154710150 Henry Cohn, 2026, needs more optimization.
12 138 0.317519073238 Henry Cohn, 2026, needs more optimization.
12 139 0.319376149051 Henry Cohn, 2026, needs more optimization.
12 140 0.320917530535 Henry Cohn, 2026, needs more optimization.
12 141 0.321102799249 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
12 142 0.321565455485 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
12 143 0.322132950651 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
12 144 0.322572320903 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
12 145 0.322873661938 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
12 146 0.323290874972 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
12 147 0.323719197468 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
12 148 0.323994119226 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
12 149 0.324620822065 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
12 150 0.325260098964 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
12 151 0.325809341292 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
12 152 0.326321663813 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
12 153 0.326821520560 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
12 154 0.327965037594 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
12 155 0.328555194466 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
12 156 0.328981906702 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
12 157 0.329306192531 Henry Cohn, 2026, needs more optimization.
12 158 0.329534270887 Henry Cohn, 2026, needs more optimization.
12 159 0.329764587525 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
12 160 0.329883275287 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
12 161 0.329968853538 Henry Cohn, 2026, needs more optimization.
12 162 0.330007408627 Henry Cohn, 2026, needs more optimization.
12 163 0.330804376046 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
12 164 0.331393865082 Henry Cohn, 2026, needs more optimization.
12 165 0.331803782549 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
12 166 0.332096158980 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
12 167 0.332377819386 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
12 168 0.332676111088 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
12 169 0.332921530355 Henry Cohn, 2026, needs more optimization.
12 170 0.332977509174 Henry Cohn, 2026, needs more optimization.
12 171 0.333031418963 Henry Cohn, 2026, needs more optimization.
12 172 0.333034017068 Henry Cohn, 2026, needs more optimization.
12 173 0.333098836451 Henry Cohn, 2026, needs more optimization.
12 174 0.333131478348 Henry Cohn, 2026, needs more optimization.
12 175 0.333161140228 Henry Cohn, 2026, needs more optimization.
12 176 0.333177544405 Henry Cohn, 2026, needs more optimization.
12 177 0.333201852174 Henry Cohn, 2026, needs more optimization.
12 178 0.333235352306 Henry Cohn, 2026, needs more optimization.
12 179 0.333346681047 Henry Cohn, 2026, needs more optimization.
12 180 0.335315982338 Henry Cohn, 2026, needs more optimization.
12 181 0.344148690380 Henry Cohn, 2026, needs more optimization.
12 182 0.345707568076 Henry Cohn, 2026, needs more optimization.
12 183 0.346689859941 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
12 184 0.348740625019 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
12 185 0.349469788690 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
12 186 0.351955580829 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
12 187 0.352415522658 Henry Cohn, 2026, needs more optimization.
12 188 0.354015511131 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
12 189 0.355202107092 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
12 190 0.356415709332 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
12 191 0.356862090570 Henry Cohn, 2026, needs more optimization.
12 192 0.357734068825 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
12 193 0.359194638786 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
12 194 0.360734713675 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
12 195 0.361980775927 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
12 196 0.362338641055 Henry Cohn, 2026, needs more optimization.
12 197 0.363761799260 Henry Cohn, 2026, needs more optimization.
12 198 0.364883884439 Henry Cohn, 2026, needs more optimization.
12 199 0.365934344470 Henry Cohn, 2026, needs more optimization.
12 200 0.366326852552 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
12 201 0.367709397217 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
12 202 0.368651729993 Henry Cohn, 2026, needs more optimization.
12 203 0.369586636440 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
12 204 0.370826756049 Henry Cohn, 2026, needs more optimization.
12 205 0.371790058950 Henry Cohn, 2026, needs more optimization.
12 206 0.372698132962 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
12 207 0.374079377437 Henry Cohn, 2026, needs more optimization.
12 208 0.374452500509 Henry Cohn, 2026, needs more optimization.
12 210 0.375 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001, Appendix D.12.12. The appendix lists the code size as 209, but the construction works just as well for 210.
8⁢x−3
12 211 0.377535931750 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
12 212 0.377586869324 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
12 213 0.378002538414 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
12 214 0.378532872840 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
12 215 0.378724966306 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
12 216 0.379128122299 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
12 217 0.381256067144 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
12 218 0.382073621383 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
12 219 0.382479776216 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
12 220 0.383240932176 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
12 221 0.383703204160 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
12 222 0.384012040467 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
12 223 0.384295798324 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
12 224 0.384543113213 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
12 225 0.384687851420 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
12 226 0.384887573354 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
12 227 0.385947086253 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
12 228 0.386267396620 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
12 229 0.386677922812 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
12 230 0.387246121102 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
12 231 0.387711470854 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
12 232 0.390389578500 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
12 233 0.390887751190 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
12 234 0.391034413069 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
12 235 0.391174179074 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
12 236 0.391313049455 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
12 237 0.391490212524 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
12 238 0.392101368780 Henry Cohn, 2026, needs more optimization.
12 239 0.392516205823 Henry Cohn, 2026, needs more optimization.
12 240 0.392766424465 Henry Cohn, 2026, needs more optimization.
12 241 0.392893846932 Henry Cohn, 2026, needs more optimization.
12 242 0.395034954291 Henry Cohn, 2026, needs more optimization.
12 243 0.396618071011 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
12 244 0.398235409341 Henry Cohn, 2026, needs more optimization.
12 245 0.399043814905 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
12 246 0.399557569660 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
12 247 0.399968167938 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
12 248 0.399996288039 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
12 288 0.4 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
5⁢x−2
12 290 0.4 Henry Cohn, 2026.
5⁢x−2
12 291 0.401561521406 Henry Cohn, 2026, needs more optimization.
12 292 0.405515923765 Henry Cohn, 2026, needs more optimization.
12 293 0.408672914757 Henry Cohn, 2026, needs more optimization.
12 294 0.410762638181 Henry Cohn, 2026, needs more optimization.
12 295 0.412718267509 Henry Cohn, 2026, needs more optimization.
12 296 0.413925463524 Henry Cohn, 2026, needs more optimization.
12 297 0.414793458041 Henry Cohn, 2026, needs more optimization.
12 298 0.416903009880 Henry Cohn, 2026, needs more optimization.
12 299 0.418406557341 Henry Cohn, 2026, needs more optimization.
12 300 0.419714343320 Henry Cohn, 2026, needs more optimization.
12 301 0.420799040424 Henry Cohn, 2026, needs more optimization.
12 302 0.422032349066 Henry Cohn, 2026, needs more optimization.
12 303 0.423112224865 Henry Cohn, 2026, needs more optimization.
12 304 0.424101038022 Henry Cohn, 2026, needs more optimization.
12 305 0.425035079679 Henry Cohn, 2026, needs more optimization.
12 306 0.426437192483 Henry Cohn, 2026, needs more optimization.
12 307 0.427413446826 Henry Cohn, 2026, needs more optimization.
12 308 0.427677217668 Henry Cohn, 2026, needs more optimization.
12 309 0.428197862131 Henry Cohn, 2026, needs more optimization.
12 310 0.429227554548 Henry Cohn, 2026, needs more optimization.
12 311 0.430175105984 Henry Cohn, 2026, needs more optimization.
12 312 0.430420981483 Henry Cohn, 2026, needs more optimization.
12 314 0.430422635344 Henry Cohn, 2026, needs more optimization.
12 315 0.430427268086 Henry Cohn, 2026, needs more optimization.
12 316 0.430432079052 Henry Cohn, 2026, needs more optimization.
12 317 0.430444601898 Henry Cohn, 2026, needs more optimization.
12 318 0.430456421477 Henry Cohn, 2026, needs more optimization.
12 319 0.430459987798 Henry Cohn, 2026, needs more optimization.
12 320 0.430466327247 Henry Cohn, 2026, needs more optimization.
12 321 0.430467717903 Henry Cohn, 2026, needs more optimization.
12 323 0.430468691104 Henry Cohn, 2026, needs more optimization.
12 324 0.430472628413 Henry Cohn, 2026, needs more optimization.
12 325 0.430474693737 Henry Cohn, 2026, needs more optimization.
12 326 0.430502196752 Henry Cohn, 2026, needs more optimization.
12 327 0.430505653574 Henry Cohn, 2026, needs more optimization.
12 328 0.430518947973 Henry Cohn, 2026, needs more optimization.
12 329 0.430520276211 Henry Cohn, 2026, needs more optimization.
12 330 0.430535688261 Henry Cohn, 2026, needs more optimization.
12 331 0.430552864321 Henry Cohn, 2026, needs more optimization.
12 332 0.430560272040 Henry Cohn, 2026, needs more optimization.
12 333 0.430560931480 Henry Cohn, 2026, needs more optimization.
12 334 0.430575850148 Henry Cohn, 2026, needs more optimization.
12 335 0.430587339527 Henry Cohn, 2026, needs more optimization.
12 336 0.430600927134 Henry Cohn, 2026, needs more optimization.
12 337 0.430618437783 Henry Cohn, 2026, needs more optimization.
12 338 0.430620779543 Henry Cohn, 2026, needs more optimization.
12 339 0.430622940540 Henry Cohn, 2026, needs more optimization.
12 341 0.430630101563 Henry Cohn, 2026, needs more optimization.
12 342 0.430630451187 Henry Cohn, 2026, needs more optimization.
12 343 0.430635589169 Henry Cohn, 2026, needs more optimization.
12 344 0.430642531845 Henry Cohn, 2026, needs more optimization.
12 345 0.430651706191 Henry Cohn, 2026, needs more optimization.
12 346 0.430662699062 Henry Cohn, 2026, needs more optimization.
12 347 0.430679114502 Henry Cohn, 2026, needs more optimization.
12 348 0.430698091855 Henry Cohn, 2026, needs more optimization.
12 349 0.430712282884 Henry Cohn, 2026, needs more optimization.
12 350 0.430719503201 Henry Cohn, 2026, needs more optimization.
12 351 0.430730204092 Henry Cohn, 2026, needs more optimization.
12 352 0.430893783911 Henry Cohn, 2026, needs more optimization.
12 353 0.431000601602 Henry Cohn, 2026, needs more optimization.
12 354 0.431034104427 Henry Cohn, 2026, needs more optimization.
12 355 0.434295350745 Henry Cohn, 2026, needs more optimization.
12 356 0.436638326064 Henry Cohn, 2026, needs more optimization.
12 357 0.438056208318 Henry Cohn, 2026, needs more optimization.
12 358 0.438979534791 Henry Cohn, 2026, needs more optimization.
12 359 0.439621720814 Henry Cohn, 2026, needs more optimization.
12 360 0.439769950837 Henry Cohn, 2026, needs more optimization.
12 361 0.440114640129 Henry Cohn, 2026, needs more optimization.
12 362 0.440420208430 Henry Cohn, 2026, needs more optimization.
12 363 0.441097810836 Henry Cohn, 2026, needs more optimization.
12 364 0.441313957892 Henry Cohn, 2026, needs more optimization.
12 366 0.441432473732 Henry Cohn, 2026, needs more optimization.
12 367 0.441668846857 Henry Cohn, 2026, needs more optimization.
12 368 0.441713586254 Henry Cohn, 2026, needs more optimization.
12 369 0.441865731528 Henry Cohn, 2026, needs more optimization.
12 370 0.442064764112 Henry Cohn, 2026, needs more optimization.
12 371 0.442367578851 Henry Cohn, 2026, needs more optimization.
12 372 0.442436643853 Henry Cohn, 2026, needs more optimization.
12 373 0.442749031779 Henry Cohn, 2026, needs more optimization.
12 374 0.443286560125 Henry Cohn, 2026, needs more optimization.
12 408 0.444444444445 M. Ganzhinov and P. R. J. Östergård, Spherical codes with prescribed signed permutation automorphisms inside shells of low-dimensional integer lattices, IEEE Trans. Inform. Theory 70 (2024), 8669–8674, doi:10.1109/tit.2024.3462593, arXiv:2403.04330.
9⁢x−4
12 409 0.447146015856 Henry Cohn, 2026, needs more optimization.
12 410 0.447927222103 Henry Cohn, 2026, needs more optimization.
12 411 0.448614438877 Henry Cohn, 2026, needs more optimization.
12 412 0.449177210531 Henry Cohn, 2026, needs more optimization.
12 414 0.450178469819 Henry Cohn, 2026, needs more optimization.
12 415 0.450346673674 Henry Cohn, 2026, needs more optimization.
12 416 0.450350613072 Henry Cohn, 2026, needs more optimization.
12 417 0.450647728368 Henry Cohn, 2026, needs more optimization.
12 418 0.450927601529 Henry Cohn, 2026, needs more optimization.
12 419 0.451165602385 Henry Cohn, 2026, needs more optimization.
12 420 0.451467882545 Henry Cohn, 2026, needs more optimization.
12 421 0.451743725235 Henry Cohn, 2026, needs more optimization.
12 422 0.452044046012 Henry Cohn, 2026, needs more optimization.
12 423 0.452511732690 Henry Cohn, 2026, needs more optimization.
12 424 0.456866164527 Henry Cohn, 2026, needs more optimization.
12 425 0.457275783082 Henry Cohn, 2026, needs more optimization.
12 426 0.458828564947 Henry Cohn, 2026, needs more optimization.
12 427 0.461035002412 Henry Cohn, 2026, needs more optimization.
12 428 0.461062317640 Henry Cohn, 2026, needs more optimization.
12 429 0.462329224326 Henry Cohn, 2026, needs more optimization.
12 430 0.462789541978 Henry Cohn, 2026, needs more optimization.
12 431 0.462825433409 Henry Cohn, 2026, needs more optimization.
12 432 0.463001909311 Henry Cohn, 2026, needs more optimization.
12 433 0.463787725405 Henry Cohn, 2026, needs more optimization.
12 434 0.463942210788 Henry Cohn, 2026, needs more optimization.
12 435 0.464551251880 Henry Cohn, 2026, needs more optimization.
12 436 0.464656078267 Henry Cohn, 2026, needs more optimization.
12 437 0.465590568417 Henry Cohn, 2026, needs more optimization.
12 438 0.466348829841 Henry Cohn, 2026, needs more optimization.
12 439 0.466413761120 Henry Cohn, 2026, needs more optimization.
12 440 0.466422343909 Henry Cohn, 2026, needs more optimization.
12 441 0.466520804646 Henry Cohn, 2026, needs more optimization.
12 442 0.466669284852 Henry Cohn, 2026, needs more optimization.
12 443 0.466767769785 Henry Cohn, 2026, needs more optimization.
12 444 0.466840408052 Henry Cohn, 2026, needs more optimization.
12 445 0.467482199307 Henry Cohn, 2026, needs more optimization.
12 446 0.467547527909 Henry Cohn, 2026, needs more optimization.
12 447 0.467790501639 Henry Cohn, 2026, needs more optimization.
12 448 0.467959022347 Henry Cohn, 2026, needs more optimization.
12 449 0.468542577450 Henry Cohn, 2026, needs more optimization.
12 450 0.468599885517 Henry Cohn, 2026, needs more optimization.
12 451 0.468746776685 Henry Cohn, 2026, needs more optimization.
12 452 0.468778032059 Henry Cohn, 2026, needs more optimization.
12 453 0.468843638143 Henry Cohn, 2026, needs more optimization.
12 454 0.469163609384 Henry Cohn, 2026, needs more optimization.
12 455 0.469244289886 Henry Cohn, 2026, needs more optimization.
12 456 0.469275545075 Henry Cohn, 2026, needs more optimization.
12 457 0.469575179312 Henry Cohn, 2026, needs more optimization.
12 458 0.469994935942 Henry Cohn, 2026, needs more optimization.
12 459 0.470103387064 Henry Cohn, 2026, needs more optimization.
12 460 0.470285068863 Henry Cohn, 2026, needs more optimization.
12 461 0.470404029799 Henry Cohn, 2026, needs more optimization.
12 462 0.470450032134 Henry Cohn, 2026, needs more optimization.
12 463 0.470760058428 Henry Cohn, 2026, needs more optimization.
12 464 0.471169009244 Henry Cohn, 2026, needs more optimization.
12 465 0.471248170429 Henry Cohn, 2026, needs more optimization.
12 466 0.471615016355 Henry Cohn, 2026, needs more optimization.
12 467 0.472118095816 Henry Cohn, 2026, needs more optimization.
12 468 0.472310296158 Henry Cohn, 2026, needs more optimization.
12 469 0.472485559345 Henry Cohn, 2026, needs more optimization.
12 470 0.472535601841 Henry Cohn, 2026, needs more optimization.
12 471 0.472610840057 Henry Cohn, 2026, needs more optimization.
12 473 0.472812956110 Henry Cohn, 2026, needs more optimization.
12 474 0.472899374000 Henry Cohn, 2026, needs more optimization.
12 475 0.472994794749 Henry Cohn, 2026, needs more optimization.
12 476 0.473070503236 Henry Cohn, 2026, needs more optimization.
12 477 0.473214934062 Henry Cohn, 2026, needs more optimization.
12 478 0.473499787361 Henry Cohn, 2026, needs more optimization.
12 479 0.473617192181 Henry Cohn, 2026, needs more optimization.
12 480 0.473949022308 Henry Cohn, 2026, needs more optimization.
12 481 0.473957161247 Henry Cohn, 2026, needs more optimization.
12 482 0.474322374732 Henry Cohn, 2026, needs more optimization.
12 483 0.474341801162 Henry Cohn, 2026, needs more optimization.
12 484 0.474663969969 Henry Cohn, 2026, needs more optimization.
12 485 0.474719662706 Henry Cohn, 2026, needs more optimization.
12 486 0.474837263661 Henry Cohn, 2026, needs more optimization.
12 487 0.474983246818 Henry Cohn, 2026, needs more optimization.
12 488 0.475229217493 Henry Cohn, 2026, needs more optimization.
12 489 0.475978091998 Henry Cohn, 2026, needs more optimization.
12 490 0.476005407149 Henry Cohn, 2026, needs more optimization.
12 491 0.476106237520 Henry Cohn, 2026, needs more optimization.
12 492 0.476233665532 Henry Cohn, 2026, needs more optimization.
12 493 0.476383117471 Henry Cohn, 2026, needs more optimization.
12 494 0.476541652368 Henry Cohn, 2026, needs more optimization.
12 495 0.476698430711 Henry Cohn, 2026, needs more optimization.
12 496 0.476740534831 Henry Cohn, 2026, needs more optimization.
12 498 0.476932518229 Henry Cohn, 2026, needs more optimization.
12 499 0.477020276495 Henry Cohn, 2026, needs more optimization.
12 500 0.477509639188 Henry Cohn, 2026, needs more optimization.
12 501 0.477557105777 Henry Cohn, 2026, needs more optimization.
12 502 0.477685320833 Henry Cohn, 2026, needs more optimization.
12 503 0.477805256955 Henry Cohn, 2026, needs more optimization.
12 504 0.478167714789 Henry Cohn, 2026, needs more optimization.
12 505 0.478466028275 Henry Cohn, 2026, needs more optimization.
12 506 0.478482196760 Henry Cohn, 2026, needs more optimization.
12 507 0.478770452537 Henry Cohn, 2026, needs more optimization.
12 508 0.478880564588 Henry Cohn, 2026, needs more optimization.
12 509 0.479081090783 Henry Cohn, 2026, needs more optimization.
12 510 0.479099561606 Henry Cohn, 2026, needs more optimization.
12 511 0.479137513757 Henry Cohn, 2026, needs more optimization.
12 512 0.479521386875 Henry Cohn, 2026, needs more optimization.
12 513 0.479702418134 Henry Cohn, 2026, needs more optimization.
12 514 0.479777297907 Henry Cohn, 2026, needs more optimization.
12 515 0.479890315354 Henry Cohn, 2026, needs more optimization.
12 516 0.479928912062 Henry Cohn, 2026, needs more optimization.
12 517 0.480063348327 Henry Cohn, 2026, needs more optimization.
12 518 0.480159242194 Henry Cohn, 2026, needs more optimization.
12 519 0.480426021690 Henry Cohn, 2026, needs more optimization.
12 520 0.480534298398 Henry Cohn, 2026, needs more optimization.
12 521 0.481138392477 Henry Cohn, 2026, needs more optimization.
12 522 0.481212034685 Henry Cohn, 2026, needs more optimization.
12 523 0.481353579234 Henry Cohn, 2026, needs more optimization.
12 524 0.481404907940 Henry Cohn, 2026, needs more optimization.
12 525 0.481599164095 Henry Cohn, 2026, needs more optimization.
12 526 0.481771147521 Henry Cohn, 2026, needs more optimization.
12 527 0.481858188305 Henry Cohn, 2026, needs more optimization.
12 528 0.481996421028 Henry Cohn, 2026, needs more optimization.
12 529 0.482178025639 Henry Cohn, 2026, needs more optimization.
12 530 0.482356610039 Henry Cohn, 2026, needs more optimization.
12 531 0.482422201810 Henry Cohn, 2026, needs more optimization.
12 532 0.482566214002 Henry Cohn, 2026, needs more optimization.
12 533 0.482694142854 Henry Cohn, 2026, needs more optimization.
12 534 0.482747561544 Henry Cohn, 2026, needs more optimization.
12 535 0.482901518040 Henry Cohn, 2026, needs more optimization.
12 536 0.483032034713 Henry Cohn, 2026, needs more optimization.
12 537 0.483093972476 Henry Cohn, 2026, needs more optimization.
12 538 0.483222007315 Henry Cohn, 2026, needs more optimization.
12 539 0.483378793676 Henry Cohn, 2026, needs more optimization.
12 540 0.483444980466 Henry Cohn, 2026, needs more optimization.
12 541 0.483497321150 Henry Cohn, 2026, needs more optimization.
12 542 0.483651708642 Henry Cohn, 2026, needs more optimization.
12 543 0.483800177458 Henry Cohn, 2026, needs more optimization.
12 544 0.483882695594 Henry Cohn, 2026, needs more optimization.
12 545 0.483952027814 Henry Cohn, 2026, needs more optimization.
12 546 0.484045588589 Henry Cohn, 2026, needs more optimization.
12 547 0.484339956802 Henry Cohn, 2026, needs more optimization.
12 548 0.484586301902 Henry Cohn, 2026, needs more optimization.
12 549 0.484841101061 Henry Cohn, 2026, needs more optimization.
12 550 0.484981298477 Henry Cohn, 2026, needs more optimization.
12 551 0.485174669196 Henry Cohn, 2026, needs more optimization.
12 552 0.485306355411 Henry Cohn, 2026, needs more optimization.
12 553 0.485358010696 Henry Cohn, 2026, needs more optimization.
12 554 0.485574768934 Henry Cohn, 2026, needs more optimization.
12 555 0.485663708966 Henry Cohn, 2026, needs more optimization.
12 556 0.485706860756 Henry Cohn, 2026, needs more optimization.
12 557 0.485818699762 Henry Cohn, 2026, needs more optimization.
12 558 0.485925978344 Henry Cohn, 2026, needs more optimization.
12 559 0.486090146951 Henry Cohn, 2026, needs more optimization.
12 560 0.486178495479 Henry Cohn, 2026, needs more optimization.
12 561 0.486273486618 Henry Cohn, 2026, needs more optimization.
12 562 0.486315203282 Henry Cohn, 2026, needs more optimization.
12 563 0.486510886146 Henry Cohn, 2026, needs more optimization.
12 564 0.486580466662 Henry Cohn, 2026, needs more optimization.
12 565 0.486657523098 Henry Cohn, 2026, needs more optimization.
12 566 0.486739371001 Henry Cohn, 2026, needs more optimization.
12 567 0.486788948479 Henry Cohn, 2026, needs more optimization.
12 568 0.486972439379 Henry Cohn, 2026, needs more optimization.
12 569 0.487087978223 Henry Cohn, 2026, needs more optimization.
12 570 0.487246673885 Henry Cohn, 2026, needs more optimization.
12 571 0.487377309902 Henry Cohn, 2026, needs more optimization.
12 572 0.487472216927 Henry Cohn, 2026, needs more optimization.
12 573 0.487552873941 Henry Cohn, 2026, needs more optimization.
12 574 0.487641381301 Henry Cohn, 2026, needs more optimization.
12 575 0.487707514907 Henry Cohn, 2026, needs more optimization.
12 576 0.487733531660 Henry Cohn, 2026, needs more optimization.
12 577 0.487967916851 Henry Cohn, 2026, needs more optimization.
12 578 0.488175587065 Henry Cohn, 2026, needs more optimization.
12 579 0.488253938202 Henry Cohn, 2026, needs more optimization.
12 580 0.488293014812 Henry Cohn, 2026, needs more optimization.
12 581 0.488319653998 Henry Cohn, 2026, needs more optimization.
12 582 0.488343237558 Henry Cohn, 2026, needs more optimization.
12 583 0.488408208587 Henry Cohn, 2026, needs more optimization.
12 584 0.488463730168 Henry Cohn, 2026, needs more optimization.
12 585 0.488589277800 Henry Cohn, 2026, needs more optimization.
12 586 0.488670508719 Henry Cohn, 2026, needs more optimization.
12 587 0.488735707299 Henry Cohn, 2026, needs more optimization.
12 588 0.488884820745 Henry Cohn, 2026, needs more optimization.
12 589 0.488952168547 Henry Cohn, 2026, needs more optimization.
12 590 0.489086433531 Henry Cohn, 2026, needs more optimization.
12 591 0.489143503357 Henry Cohn, 2026, needs more optimization.
12 592 0.489205867114 Henry Cohn, 2026, needs more optimization.
12 593 0.489322973937 Henry Cohn, 2026, needs more optimization.
12 594 0.489369059049 Henry Cohn, 2026, needs more optimization.
12 595 0.489506240281 Henry Cohn, 2026, needs more optimization.
12 596 0.489544985885 Henry Cohn, 2026, needs more optimization.
12 597 0.489560460941 Henry Cohn, 2026, needs more optimization.
12 598 0.489679647885 Henry Cohn, 2026, needs more optimization.
12 599 0.489760489847 Henry Cohn, 2026, needs more optimization.
12 600 0.489768062586 Henry Cohn, 2026, needs more optimization.
12 601 0.489887830183 Henry Cohn, 2026, needs more optimization.
12 602 0.489957711761 Henry Cohn, 2026, needs more optimization.
12 603 0.490096698531 Henry Cohn, 2026, needs more optimization.
12 604 0.490191189034 Henry Cohn, 2026, needs more optimization.
12 605 0.490270465680 Henry Cohn, 2026, needs more optimization.
12 606 0.490337776857 Henry Cohn, 2026, needs more optimization.
12 608 0.490482306500 Henry Cohn, 2026, needs more optimization.
12 609 0.490533460529 Henry Cohn, 2026, needs more optimization.
12 610 0.490598028870 Henry Cohn, 2026, needs more optimization.
12 611 0.490685806064 Henry Cohn, 2026, needs more optimization.
12 612 0.490702556999 Henry Cohn, 2026, needs more optimization.
12 613 0.490900085991 Henry Cohn, 2026, needs more optimization.
12 614 0.490939157268 Henry Cohn, 2026, needs more optimization.
12 615 0.491015855781 Henry Cohn, 2026, needs more optimization.
12 616 0.491192343253 Henry Cohn, 2026, needs more optimization.
12 617 0.491317484050 Henry Cohn, 2026, needs more optimization.
12 618 0.491404557893 Henry Cohn, 2026, needs more optimization.
12 619 0.491421036878 Henry Cohn, 2026, needs more optimization.
12 620 0.491572963096 Henry Cohn, 2026, needs more optimization.
12 621 0.491651153080 Henry Cohn, 2026, needs more optimization.
12 622 0.491714935577 Henry Cohn, 2026, needs more optimization.
12 623 0.491746473845 Henry Cohn, 2026, needs more optimization.
12 624 0.491800810574 Henry Cohn, 2026, needs more optimization.
12 625 0.491851612304 Henry Cohn, 2026, needs more optimization.
12 626 0.491913769590 Henry Cohn, 2026, needs more optimization.
12 627 0.491951428529 Henry Cohn, 2026, needs more optimization.
12 628 0.492034236900 Henry Cohn, 2026, needs more optimization.
12 629 0.492053859726 Henry Cohn, 2026, needs more optimization.
12 630 0.492088714974 Henry Cohn, 2026, needs more optimization.
12 633 0.492161986978 Henry Cohn, 2026, needs more optimization.
12 634 0.492213698212 Henry Cohn, 2026, needs more optimization.
12 635 0.492308696820 Henry Cohn, 2026, needs more optimization.
12 636 0.492350382273 Henry Cohn, 2026, needs more optimization.
12 637 0.492373867029 Henry Cohn, 2026, needs more optimization.
12 638 0.492377678750 Henry Cohn, 2026, needs more optimization.
12 639 0.492429266472 Henry Cohn, 2026, needs more optimization.
12 640 0.492493034038 Henry Cohn, 2026, needs more optimization.
12 642 0.492523636541 A. Kravatsky, V. Khrulkov, and I. Oseledets, ImprovEvolve: basin-hopping meets LLM-guided evolutionary search, ICML 2026 AI4Math Workshop Poster, https://openreview.net/forum?id=nE1q0gRDNr, arXiv:2602.10233, after some further optimization.
12 643 0.492547664619 Henry Cohn, 2026, needs more optimization.
12 644 0.492657639231 Henry Cohn, 2026, needs more optimization.
12 645 0.492708274626 Henry Cohn, 2026, needs more optimization.
12 646 0.492759125048 Henry Cohn, 2026, needs more optimization.
12 647 0.492853674025 Henry Cohn, 2026, needs more optimization.
12 648 0.493227077162 Henry Cohn, 2026, needs more optimization.
12 649 0.493306631464 Henry Cohn, 2026, needs more optimization.
12 650 0.493332618508 Henry Cohn, 2026, needs more optimization.
12 651 0.493392394871 Henry Cohn, 2026, needs more optimization.
12 652 0.493416038462 Henry Cohn, 2026, needs more optimization.
12 653 0.493456913956 Henry Cohn, 2026, needs more optimization.
12 654 0.493464475773 Henry Cohn, 2026, needs more optimization.
12 655 0.493581548215 Henry Cohn, 2026, needs more optimization.
12 656 0.493609539482 Henry Cohn, 2026, needs more optimization.
12 657 0.493627835147 Henry Cohn, 2026, needs more optimization.
12 658 0.493747687682 Henry Cohn, 2026, needs more optimization.
12 659 0.493791417516 Henry Cohn, 2026, needs more optimization.
12 660 0.493821647039 Henry Cohn, 2026, needs more optimization.
12 661 0.493873434645 Henry Cohn, 2026, needs more optimization.
12 662 0.493926929209 Henry Cohn, 2026, needs more optimization.
12 663 0.493968708921 Henry Cohn, 2026, needs more optimization.
12 664 0.494074606511 Henry Cohn, 2026, needs more optimization.
12 665 0.494218332899 Henry Cohn, 2026, needs more optimization.
12 666 0.494267127743 Henry Cohn, 2026, needs more optimization.
12 667 0.494298279589 Henry Cohn, 2026, needs more optimization.
12 668 0.494334035850 Henry Cohn, 2026, needs more optimization.
12 669 0.494382802477 Henry Cohn, 2026, needs more optimization.
12 670 0.494521041659 Henry Cohn, 2026, needs more optimization.
12 671 0.494558414473 Henry Cohn, 2026, needs more optimization.
12 672 0.494615981270 Henry Cohn, 2026, needs more optimization.
12 673 0.494658483127 Henry Cohn, 2026, needs more optimization.
12 674 0.494666010038 Henry Cohn, 2026, needs more optimization.
12 676 0.494682011699 Henry Cohn, 2026, needs more optimization.
12 677 0.494706112639 Henry Cohn, 2026, needs more optimization.
12 678 0.494725664459 Henry Cohn, 2026, needs more optimization.
12 679 0.494814427225 Henry Cohn, 2026, needs more optimization.
12 680 0.494849791580 Henry Cohn, 2026, needs more optimization.
12 681 0.494893078444 Henry Cohn, 2026, needs more optimization.
12 682 0.494993877397 Henry Cohn, 2026, needs more optimization.
12 683 0.495069811726 Henry Cohn, 2026, needs more optimization.
12 684 0.495093328068 Henry Cohn, 2026, needs more optimization.
12 685 0.495105457219 Henry Cohn, 2026, needs more optimization.
12 686 0.495127985311 Henry Cohn, 2026, needs more optimization.
12 687 0.495149353226 Henry Cohn, 2026, needs more optimization.
12 688 0.495231964044 Henry Cohn, 2026, needs more optimization.
12 689 0.495307278621 Henry Cohn, 2026, needs more optimization.
12 690 0.495365279323 Henry Cohn, 2026, needs more optimization.
12 691 0.495423558105 Henry Cohn, 2026, needs more optimization.
12 692 0.495456261425 Henry Cohn, 2026, needs more optimization.
12 693 0.495522319886 Henry Cohn, 2026, needs more optimization.
12 694 0.495537054959 Henry Cohn, 2026, needs more optimization.
12 695 0.495565340491 Henry Cohn, 2026, needs more optimization.
12 696 0.495586531308 Henry Cohn, 2026, needs more optimization.
12 697 0.495633897234 Henry Cohn, 2026, needs more optimization.
12 698 0.495661946278 Henry Cohn, 2026, needs more optimization.
12 699 0.495744224743 Henry Cohn, 2026, needs more optimization.
12 700 0.495760131615 Henry Cohn, 2026, needs more optimization.
12 701 0.495788000897 Henry Cohn, 2026, needs more optimization.
12 702 0.495867444799 Henry Cohn, 2026, needs more optimization.
12 703 0.495876169373 Henry Cohn, 2026, needs more optimization.
12 704 0.495918140398 Henry Cohn, 2026, needs more optimization.
12 705 0.495950637413 Henry Cohn, 2026, needs more optimization.
12 706 0.496023563630 Henry Cohn, 2026, needs more optimization.
12 707 0.496045497513 Henry Cohn, 2026, needs more optimization.
12 708 0.496106015427 Henry Cohn, 2026, needs more optimization.
12 709 0.496148787356 Henry Cohn, 2026, needs more optimization.
12 710 0.496160091303 Henry Cohn, 2026, needs more optimization.
12 711 0.496192804476 Henry Cohn, 2026, needs more optimization.
12 712 0.496206988528 Henry Cohn, 2026, needs more optimization.
12 713 0.496298855687 Henry Cohn, 2026, needs more optimization.
12 714 0.496310416220 Henry Cohn, 2026, needs more optimization.
12 715 0.496312835746 Henry Cohn, 2026, needs more optimization.
12 716 0.496332058519 Henry Cohn, 2026, needs more optimization.
12 717 0.496345554075 Henry Cohn, 2026, needs more optimization.
12 718 0.496378854114 Henry Cohn, 2026, needs more optimization.
12 719 0.496392975885 Henry Cohn, 2026, needs more optimization.
12 721 0.496415704593 Henry Cohn, 2026, needs more optimization.
12 722 0.496425393464 Henry Cohn, 2026, needs more optimization.
12 723 0.496439076927 Henry Cohn, 2026, needs more optimization.
12 724 0.496461016255 Henry Cohn, 2026, needs more optimization.
12 725 0.496467175216 Henry Cohn, 2026, needs more optimization.
12 726 0.496499737873 Henry Cohn, 2026, needs more optimization.
12 727 0.496503053686 Henry Cohn, 2026, needs more optimization.
12 728 0.496520348422 Henry Cohn, 2026, needs more optimization.
12 729 0.496537621221 Henry Cohn, 2026, needs more optimization.
12 730 0.496544355796 Henry Cohn, 2026, needs more optimization.
12 731 0.496553397603 Henry Cohn, 2026, needs more optimization.
12 732 0.496554317197 Henry Cohn, 2026, needs more optimization.
12 733 0.496557749447 Henry Cohn, 2026, needs more optimization.
12 734 0.496562605972 A. Kravatsky, V. Khrulkov, and I. Oseledets, ImprovEvolve: basin-hopping meets LLM-guided evolutionary search, ICML 2026 AI4Math Workshop Poster, https://openreview.net/forum?id=nE1q0gRDNr, arXiv:2602.10233, after some further optimization.
12 735 0.496805952049 Henry Cohn, 2026, needs more optimization.
12 736 0.496814588826 Henry Cohn, 2026, needs more optimization.
12 737 0.496821382460 Henry Cohn, 2026, needs more optimization.
12 738 0.496822866442 Henry Cohn, 2026, needs more optimization.
12 739 0.496836339317 Henry Cohn, 2026, needs more optimization.
12 742 0.496848338390 Henry Cohn, 2026, needs more optimization.
12 743 0.496857600508 Henry Cohn, 2026, needs more optimization.
12 744 0.496868595878 Henry Cohn, 2026, needs more optimization.
12 745 0.496904373102 Henry Cohn, 2026, needs more optimization.
12 746 0.496933073833 Henry Cohn, 2026, needs more optimization.
12 748 0.496982954636 Henry Cohn, 2026, needs more optimization.
12 749 0.496996307436 Henry Cohn, 2026, needs more optimization.
12 750 0.496999970835 Henry Cohn, 2026, needs more optimization.
12 751 0.497004087656 Henry Cohn, 2026, needs more optimization.
12 752 0.497014094646 Henry Cohn, 2026, needs more optimization.
12 753 0.497025356714 Henry Cohn, 2026, needs more optimization.
12 754 0.497032684414 Henry Cohn, 2026, needs more optimization.
12 755 0.497036505283 Henry Cohn, 2026, needs more optimization.
12 756 0.497124146769 Henry Cohn, 2026, needs more optimization.
12 757 0.498329567069 Henry Cohn, 2026, needs more optimization.
12 758 0.499463904263 Henry Cohn, 2026, needs more optimization.
12 759 0.499795263871 Henry Cohn, 2026, needs more optimization.
12 760 0.499817133784 Henry Cohn, 2026, needs more optimization.
12 763 0.499892342494 Henry Cohn, 2026, needs more optimization.
12 766 0.499928504904 Henry Cohn, 2026, needs more optimization.
12 770 0.499969105065 Henry Cohn, 2026, needs more optimization.
12 773 0.499972926874 Henry Cohn, 2026, needs more optimization.
12 792 0.499991696120 Henry Cohn, 2026, needs more optimization.
12 822 0.499992852818 Henry Cohn, 2026, needs more optimization.
12 829 0.499999013854 Numaro AI Autoresearch, 11,000+ New Verified Spherical-Code Records from AI Autoresearch, Numaro Research Report NUMARO-2026-015 (2026), https://numaro.tech/research/spherical-codes-2026/.
12 841 0.499999937615 R. Takhanov, Z. Assylbekov, and S. Yun, Structure of kissing arrangements in ℝ12 and a place for the 841st sphere, preprint, 2026, arXiv:2606.18984, after some further optimization.
12 842 0.500899993878 R. Takhanov, Z. Assylbekov, and S. Yun, Structure of kissing arrangements in ℝ12 and a place for the 841st sphere, preprint, 2026, arXiv:2606.18984, after some further optimization.
12 843 0.504400747135 Henry Cohn, 2026, needs more optimization.
12 844 0.504401014939 R. Takhanov, Z. Assylbekov, and S. Yun, Structure of kissing arrangements in ℝ12 and a place for the 841st sphere, preprint, 2026, arXiv:2606.18984, after some further optimization.
12 845 0.506045446893 Henry Cohn, 2026, needs more optimization.
12 846 0.507106305571 Henry Cohn, 2026, needs more optimization.
12 847 0.508067393527 Henry Cohn, 2026, needs more optimization.
12 848 0.517686211595 Henry Cohn, 2026, needs more optimization.
12 849 0.518017264586 Henry Cohn, 2026, needs more optimization.
12 850 0.518717279752 Henry Cohn, 2026, needs more optimization.
12 851 0.518970321024 Henry Cohn, 2026, needs more optimization.
12 852 0.519378070812 Henry Cohn, 2026, needs more optimization.
12 853 0.519696764004 Henry Cohn, 2026, needs more optimization.
12 854 0.520097539222 Henry Cohn, 2026, needs more optimization.
12 855 0.520364195627 Henry Cohn, 2026, needs more optimization.
12 856 0.520792927768 Henry Cohn, 2026, needs more optimization.
12 857 0.521078053413 Henry Cohn, 2026, needs more optimization.
12 858 0.521414675859 Henry Cohn, 2026, needs more optimization.
12 859 0.521986464732 Henry Cohn, 2026, needs more optimization.
12 860 0.522315287179 Henry Cohn, 2026, needs more optimization.
12 861 0.522617010444 Henry Cohn, 2026, needs more optimization.
12 862 0.522858990949 Henry Cohn, 2026, needs more optimization.
12 863 0.523058513961 Henry Cohn, 2026, needs more optimization.
12 864 0.523300647665 Henry Cohn, 2026, needs more optimization.
12 865 0.523710492292 Henry Cohn, 2026, needs more optimization.
12 866 0.524007486319 Henry Cohn, 2026, needs more optimization.
12 867 0.524196146476 Henry Cohn, 2026, needs more optimization.
12 868 0.524344863996 Henry Cohn, 2026, needs more optimization.
12 869 0.524650490644 Henry Cohn, 2026, needs more optimization.
12 870 0.524845358115 Henry Cohn, 2026, needs more optimization.
12 871 0.525046247718 Henry Cohn, 2026, needs more optimization.
12 872 0.525522319535 Henry Cohn, 2026, needs more optimization.
12 873 0.525784452957 Henry Cohn, 2026, needs more optimization.
12 874 0.526138895541 Henry Cohn, 2026, needs more optimization.
12 875 0.526343504163 Henry Cohn, 2026, needs more optimization.
12 876 0.526600715563 Henry Cohn, 2026, needs more optimization.
12 877 0.526852224337 Henry Cohn, 2026, needs more optimization.
12 878 0.527157428551 Henry Cohn, 2026, needs more optimization.
12 879 0.527385157108 Henry Cohn, 2026, needs more optimization.
12 880 0.527622603234 Henry Cohn, 2026, needs more optimization.
12 881 0.527861508365 Henry Cohn, 2026, needs more optimization.
12 882 0.528190589236 Henry Cohn, 2026, needs more optimization.
12 883 0.528427855458 Henry Cohn, 2026, needs more optimization.
12 884 0.528781703753 Henry Cohn, 2026, needs more optimization.
12 885 0.528980938947 Henry Cohn, 2026, needs more optimization.
12 886 0.529157233562 Henry Cohn, 2026, needs more optimization.
12 887 0.529452343422 Henry Cohn, 2026, needs more optimization.
12 888 0.529685589850 Henry Cohn, 2026, needs more optimization.
12 889 0.530263810533 Henry Cohn, 2026, needs more optimization.
12 890 0.530460974080 Henry Cohn, 2026, needs more optimization.
12 891 0.530609603974 Henry Cohn, 2026, needs more optimization.
12 892 0.530883064861 Henry Cohn, 2026, needs more optimization.
12 893 0.531077214852 Henry Cohn, 2026, needs more optimization.
12 894 0.531313972250 Henry Cohn, 2026, needs more optimization.
12 895 0.531646823572 Henry Cohn, 2026, needs more optimization.
12 896 0.531865832156 Henry Cohn, 2026, needs more optimization.
12 897 0.532169581199 Henry Cohn, 2026, needs more optimization.
12 898 0.532311283801 Henry Cohn, 2026, needs more optimization.
12 899 0.532500252859 Henry Cohn, 2026, needs more optimization.
12 900 0.532652248960 Henry Cohn, 2026, needs more optimization.
12 901 0.532807582875 Henry Cohn, 2026, needs more optimization.
12 902 0.533033701444 Henry Cohn, 2026, needs more optimization.
12 903 0.533209243302 Henry Cohn, 2026, needs more optimization.
12 904 0.533473881785 Henry Cohn, 2026, needs more optimization.
12 905 0.533685916611 Henry Cohn, 2026, needs more optimization.
12 906 0.533919916442 Henry Cohn, 2026, needs more optimization.
12 907 0.534081365736 Henry Cohn, 2026, needs more optimization.
12 908 0.534327766087 Henry Cohn, 2026, needs more optimization.
12 909 0.534456826540 Henry Cohn, 2026, needs more optimization.
12 910 0.534629812618 Henry Cohn, 2026, needs more optimization.
12 911 0.534842859051 Henry Cohn, 2026, needs more optimization.
12 912 0.535045899711 Henry Cohn, 2026, needs more optimization.
12 913 0.535246969133 Henry Cohn, 2026, needs more optimization.
12 914 0.535524938191 Henry Cohn, 2026, needs more optimization.
12 915 0.535846446836 Henry Cohn, 2026, needs more optimization.
12 916 0.536052523995 Henry Cohn, 2026, needs more optimization.
12 917 0.536204790847 Henry Cohn, 2026, needs more optimization.
12 918 0.536563329369 Henry Cohn, 2026, needs more optimization.
12 919 0.536795896956 Henry Cohn, 2026, needs more optimization.
12 920 0.537016728666 Henry Cohn, 2026, needs more optimization.
12 921 0.537165411505 Henry Cohn, 2026, needs more optimization.
12 922 0.537350965699 Henry Cohn, 2026, needs more optimization.
12 923 0.537540585922 Henry Cohn, 2026, needs more optimization.
12 924 0.537750837951 Henry Cohn, 2026, needs more optimization.
12 925 0.537830884119 Henry Cohn, 2026, needs more optimization.
12 926 0.538086023754 Henry Cohn, 2026, needs more optimization.
12 927 0.538206488543 Henry Cohn, 2026, needs more optimization.
12 928 0.538368860329 Henry Cohn, 2026, needs more optimization.
12 929 0.538551580718 Henry Cohn, 2026, needs more optimization.
12 930 0.538707490450 Henry Cohn, 2026, needs more optimization.
12 931 0.538968698094 Henry Cohn, 2026, needs more optimization.
12 932 0.539136616731 Henry Cohn, 2026, needs more optimization.
12 933 0.539324437401 Henry Cohn, 2026, needs more optimization.
12 934 0.539473250050 Henry Cohn, 2026, needs more optimization.
12 935 0.539689841271 Henry Cohn, 2026, needs more optimization.
12 936 0.539859224176 Henry Cohn, 2026, needs more optimization.
12 937 0.540070244868 Henry Cohn, 2026, needs more optimization.
12 938 0.540266359180 Henry Cohn, 2026, needs more optimization.
12 939 0.540482311575 Henry Cohn, 2026, needs more optimization.
12 940 0.540661514483 Henry Cohn, 2026, needs more optimization.
12 941 0.540895594855 Henry Cohn, 2026, needs more optimization.
12 942 0.540999756447 Henry Cohn, 2026, needs more optimization.
12 943 0.541120806081 Henry Cohn, 2026, needs more optimization.
12 944 0.541292516354 Henry Cohn, 2026, needs more optimization.
12 945 0.541511857671 Henry Cohn, 2026, needs more optimization.
12 946 0.541663293535 Henry Cohn, 2026, needs more optimization.
12 947 0.541978459080 Henry Cohn, 2026, needs more optimization.
12 948 0.542096302840 Henry Cohn, 2026, needs more optimization.
12 949 0.542233555458 Henry Cohn, 2026, needs more optimization.
12 950 0.542378723401 Henry Cohn, 2026, needs more optimization.
12 951 0.542524081037 Henry Cohn, 2026, needs more optimization.
12 952 0.542744363056 Henry Cohn, 2026, needs more optimization.
12 953 0.543027508483 Henry Cohn, 2026, needs more optimization.
12 954 0.543178516653 Henry Cohn, 2026, needs more optimization.
12 955 0.543395550103 Henry Cohn, 2026, needs more optimization.
12 956 0.543465776262 Henry Cohn, 2026, needs more optimization.
12 957 0.543654537325 Henry Cohn, 2026, needs more optimization.
12 958 0.543787151184 Henry Cohn, 2026, needs more optimization.
12 959 0.543953030282 Henry Cohn, 2026, needs more optimization.
12 960 0.544099983342 Henry Cohn, 2026, needs more optimization.
12 961 0.544223407458 Henry Cohn, 2026, needs more optimization.
12 962 0.544426943869 Henry Cohn, 2026, needs more optimization.
12 963 0.544527105927 Henry Cohn, 2026, needs more optimization.
12 964 0.544703214890 Henry Cohn, 2026, needs more optimization.
12 965 0.544829670420 Henry Cohn, 2026, needs more optimization.
12 966 0.544918218657 Henry Cohn, 2026, needs more optimization.
12 967 0.545087726957 Henry Cohn, 2026, needs more optimization.
12 968 0.545246459567 Henry Cohn, 2026, needs more optimization.
12 969 0.545452057702 Henry Cohn, 2026, needs more optimization.
12 970 0.545506442868 Henry Cohn, 2026, needs more optimization.
12 971 0.545619143517 Henry Cohn, 2026, needs more optimization.
12 972 0.545732157733 Henry Cohn, 2026, needs more optimization.
12 973 0.545924313046 Henry Cohn, 2026, needs more optimization.
12 974 0.546122245503 Henry Cohn, 2026, needs more optimization.
12 975 0.546255972073 Henry Cohn, 2026, needs more optimization.
12 976 0.546389584763 Henry Cohn, 2026, needs more optimization.
12 977 0.546545894086 Henry Cohn, 2026, needs more optimization.
12 978 0.546666085743 Henry Cohn, 2026, needs more optimization.
12 979 0.546788506801 Henry Cohn, 2026, needs more optimization.
12 980 0.546873684269 Henry Cohn, 2026, needs more optimization.
12 981 0.547035415364 Henry Cohn, 2026, needs more optimization.
12 982 0.547118860265 Henry Cohn, 2026, needs more optimization.
12 983 0.547260115356 Henry Cohn, 2026, needs more optimization.
12 984 0.547413200629 Henry Cohn, 2026, needs more optimization.
12 985 0.547576695232 Henry Cohn, 2026, needs more optimization.
12 986 0.547709726483 Henry Cohn, 2026, needs more optimization.
12 987 0.547790527293 Henry Cohn, 2026, needs more optimization.
12 988 0.547911070124 Numaro AI Autoresearch, 11,000+ New Verified Spherical-Code Records from AI Autoresearch, Numaro Research Report NUMARO-2026-015 (2026), https://numaro.tech/research/spherical-codes-2026/.
12 989 0.548045406205 Henry Cohn, 2026, needs more optimization.
12 990 0.548081851609 Henry Cohn, 2026, needs more optimization.
12 991 0.548240614710 Henry Cohn, 2026, needs more optimization.
12 992 0.548347132293 Henry Cohn, 2026, needs more optimization.
12 993 0.548478498560 Henry Cohn, 2026, needs more optimization.
12 994 0.548658364544 Henry Cohn, 2026, needs more optimization.
12 995 0.548760578655 Henry Cohn, 2026, needs more optimization.
12 996 0.548971768412 Henry Cohn, 2026, needs more optimization.
12 997 0.549075981360 Henry Cohn, 2026, needs more optimization.
12 998 0.549237821547 Henry Cohn, 2026, needs more optimization.
12 999 0.549401607670 Henry Cohn, 2026, needs more optimization.
12 1000 0.549615607951 Henry Cohn, 2026, needs more optimization.
12 1001 0.549717540301 Henry Cohn, 2026, needs more optimization.
12 1002 0.549943833104 Henry Cohn, 2026, needs more optimization.
12 1003 0.550027038604 Henry Cohn, 2026, needs more optimization.
12 1004 0.550197713900 Henry Cohn, 2026, needs more optimization.
12 1005 0.550279913040 Henry Cohn, 2026, needs more optimization.
12 1006 0.550380332945 Henry Cohn, 2026, needs more optimization.
12 1007 0.550479080557 Henry Cohn, 2026, needs more optimization.
12 1008 0.550633942509 Henry Cohn, 2026, needs more optimization.
12 1009 0.550758896913 Henry Cohn, 2026, needs more optimization.
12 1010 0.550949911173 Henry Cohn, 2026, needs more optimization.
12 1011 0.551068496319 Henry Cohn, 2026, needs more optimization.
12 1012 0.551130035576 Henry Cohn, 2026, needs more optimization.
12 1013 0.551303338960 Henry Cohn, 2026, needs more optimization.
12 1014 0.551385480428 Henry Cohn, 2026, needs more optimization.
12 1015 0.551476335320 Henry Cohn, 2026, needs more optimization.
12 1016 0.551681119682 Henry Cohn, 2026, needs more optimization.
12 1017 0.551770220259 Henry Cohn, 2026, needs more optimization.
12 1018 0.551870218521 Henry Cohn, 2026, needs more optimization.
12 1019 0.552078816398 Henry Cohn, 2026, needs more optimization.
12 1020 0.552196627531 Henry Cohn, 2026, needs more optimization.
12 1021 0.552334415437 Henry Cohn, 2026, needs more optimization.
12 1022 0.552430539593 Henry Cohn, 2026, needs more optimization.
12 1023 0.552557376034 Henry Cohn, 2026, needs more optimization.
12 1024 0.552758222855 Henry Cohn, 2026, needs more optimization.
13 27 0.057072523783 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
1573⁢x3−169⁢x2−13⁢x+1
13 28 0.066666666667 T. Ericson and V. Zinoviev, Spherical codes generated by binary partitions of symmetric pointsets, IEEE Trans. Inform. Theory 41 (1995), 107–129, doi:10.1109/18.370114.
15⁢x−1
13 29 0.068098609479 H. Cohn, Small spherical and projective codes, data set, 2022, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
2576⁢x4−640⁢x3−184⁢x2+1
13 30 0.071714034728 H. Cohn, Small spherical and projective codes, data set, 2022, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
55⁢x2+10⁢x−1
13 31 0.071714034728 H. Cohn, Small spherical and projective codes, data set, 2022, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
55⁢x2+10⁢x−1
13 32 0.071714034728 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
55⁢x2+10⁢x−1
13 33 0.089833578043 Henry Cohn, 2026.
13 34 0.090095382331 Henry Cohn, 2023.
13 36 0.092610094433 H. Cohn, D. de Laat, and N. Leijenhorst, Optimality of spherical codes via exact semidefinite programming bounds, preprint, 2024, arXiv:2403.16874.
95⁢x2+2⁢x−1
13 37 0.111409136725 Henry Cohn, 2023.
13 38 0.112004618870 Henry Cohn, 2023.
44⁢x2+4⁢x−1
13 39 0.116893063508 Henry Cohn, 2024.
13 40 0.121353571480 Henry Cohn, 2026.
13 42 0.125 T. Ericson and V. Zinoviev, Spherical codes generated by binary partitions of symmetric pointsets, IEEE Trans. Inform. Theory 41 (1995), 107–129, doi:10.1109/18.370114.
8⁢x−1
13 44 0.126079252818 Henry Cohn, 2025.
6095⁢x2−126⁢x−81
13 48 0.126131983623 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
47⁢x2+2⁢x−1
13 49 0.141095436175 Henry Cohn, 2025.
13 50 0.142459427551 Henry Cohn, 2023.
Minimal polynomial listed in plain text data
13 51 0.145120831484 Henry Cohn, 2023.
Minimal polynomial listed in plain text data
13 52 0.147159522238 Henry Cohn, 2023.
613567⁢x7+96585⁢x6−98333⁢x5−8219⁢x4+381⁢x3+539⁢x2+33⁢x−9
13 53 0.147908234060 Henry Cohn, 2024.
13 54 0.148576022240 Henry Cohn, 2025.
13 55 0.148805252884 Henry Cohn, 2024.
13 56 0.148975682089 Henry Cohn, 2023.
13 57 0.166162190421 Henry Cohn, 2024.
13 58 0.173474302723 Henry Cohn, 2023.
13 59 0.180540658957 Henry Cohn, 2024.
13 60 0.184387527775 Henry Cohn, 2026.
13 61 0.189130618757 Henry Cohn, 2026.
13 62 0.189939244395 Henry Cohn, 2026.
13 63 0.193274783328 Henry Cohn, 2026.
13 64 0.194849252724 Henry Cohn, 2026.
13 65 0.198937958705 Henry Cohn, 2026.
13 66 0.201499955088 Henry Cohn, 2026.
13 67 0.204059765290 Henry Cohn, 2026.
13 68 0.206389080584 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
13 69 0.207586830581 Henry Cohn, 2026, needs more optimization.
13 70 0.208532405116 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
13 71 0.209194383680 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
13 72 0.210224591730 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
13 73 0.211129497028 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
13 74 0.212071472722 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
13 75 0.213204515290 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
13 84 0.214312873432 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
13 85 0.228140059011 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
13 86 0.232176330315 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
13 87 0.234527731359 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
13 88 0.234805231753 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
13 89 0.238564649203 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
13 90 0.241064086681 Henry Cohn, 2026, needs more optimization.
13 91 0.242822995917 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
13 92 0.243421993521 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
13 93 0.244059194231 Henry Cohn, 2026, needs more optimization.
13 94 0.244139893449 Henry Cohn, 2026, needs more optimization.
13 95 0.244205974702 Henry Cohn, 2026, needs more optimization.
13 96 0.244319676046 Henry Cohn, 2026, needs more optimization.
13 97 0.244402830248 Henry Cohn, 2026, needs more optimization.
13 98 0.244474378485 Henry Cohn, 2026, needs more optimization.
13 99 0.245416179324 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
13 100 0.246831266532 Henry Cohn, 2026, needs more optimization.
13 101 0.249341456787 Henry Cohn, 2026, needs more optimization.
13 104 0.25 J. H. Conway, R. H. Hardin, and N. J. A. Sloane, Packing lines, planes, etc.: packings in Grassmannian spaces, Experiment. Math. 5 (1996), 139–159, https://projecteuclid.org/euclid.em/1047565645; T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
4⁢x−1
13 106 0.251575083557 Henry Cohn, 2026.
1031⁢x2−160⁢x−25
13 107 0.257875986004 Henry Cohn, 2026, needs more optimization.
13 108 0.258192353971 Henry Cohn, 2026, needs more optimization.
13 109 0.258968664225 Henry Cohn, 2026, needs more optimization.
13 110 0.259435848370 Henry Cohn, 2026, needs more optimization.
13 111 0.259779809011 Henry Cohn, 2026, needs more optimization.
13 112 0.260602016216 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
13 113 0.261396935151 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
13 114 0.263218957277 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
13 115 0.264240009149 Henry Cohn, 2026, needs more optimization.
13 116 0.266700427057 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
13 117 0.267736447658 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
13 118 0.269243201501 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
13 119 0.270309810815 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
13 120 0.271257293052 Henry Cohn, 2026, needs more optimization.
13 121 0.271465301243 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
13 122 0.272092998383 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
13 123 0.272115929038 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
13 124 0.275835352799 Henry Cohn, 2026, needs more optimization.
13 125 0.276037827247 Henry Cohn, 2026, needs more optimization.
13 126 0.276204069312 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
13 127 0.278086657442 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
13 128 0.280341949746 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
13 129 0.282450640318 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
13 130 0.284583847124 Henry Cohn, 2026, needs more optimization.
13 131 0.285562844542 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
13 132 0.286045162740 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
13 133 0.286660424404 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
13 134 0.288011932103 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
13 135 0.289066229464 Henry Cohn, 2026, needs more optimization.
13 136 0.290045117963 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
13 137 0.291900285724 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
13 138 0.293341713127 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
13 139 0.295014501928 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
13 140 0.295141221716 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
13 141 0.296567202505 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
13 142 0.296679585223 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
13 143 0.296864843946 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
13 144 0.298709271593 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
13 145 0.300185184566 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
13 146 0.300243032935 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
13 147 0.300305290991 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
13 148 0.300834705383 Henry Cohn, 2026, needs more optimization.
13 149 0.300892999776 Henry Cohn, 2026, needs more optimization.
13 150 0.300977858049 Henry Cohn, 2026, needs more optimization.
13 151 0.301154346245 Henry Cohn, 2026, needs more optimization.
13 152 0.301872105772 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
13 153 0.302734953118 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
13 154 0.304063087295 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
13 155 0.305909571592 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
13 156 0.307224073716 Henry Cohn, 2026, needs more optimization.
13 157 0.308477968511 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
13 158 0.309245501605 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
13 159 0.310246321329 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
13 160 0.311701341330 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
13 161 0.312205180565 Henry Cohn, 2026, needs more optimization.
13 162 0.312465614515 Henry Cohn, 2026, needs more optimization.
13 163 0.313057479924 Henry Cohn, 2026, needs more optimization.
13 164 0.314119304203 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
13 165 0.315127129381 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
13 166 0.316171774271 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
13 167 0.316371515093 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
13 168 0.316421487445 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
13 169 0.316779252170 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
13 170 0.317003903211 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
13 171 0.317273821518 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
13 172 0.317968993956 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
13 173 0.318958983514 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
13 174 0.319269826786 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
13 175 0.319868027210 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
13 176 0.320481149654 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
13 177 0.321115497874 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
13 178 0.321789936936 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
13 179 0.322127443770 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
13 180 0.322633627385 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
13 181 0.323274595027 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
13 182 0.323846147144 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
13 183 0.324363968352 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
13 184 0.324830156412 Henry Cohn, 2026, needs more optimization.
13 185 0.325287036341 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
13 186 0.325702398297 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
13 187 0.326100858685 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
13 188 0.326422982345 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
13 189 0.326742770078 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
13 190 0.326952142822 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
13 191 0.327198179789 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
13 192 0.327505990263 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
13 193 0.327553629890 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
13 194 0.327832938882 Henry Cohn, 2026, needs more optimization.
13 195 0.327841626066 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
13 196 0.328728696610 Henry Cohn, 2026, needs more optimization.
13 197 0.328861069461 Henry Cohn, 2026, needs more optimization.
13 198 0.328986487270 Henry Cohn, 2026, needs more optimization.
13 199 0.329136601054 Henry Cohn, 2026, needs more optimization.
13 200 0.329342398496 Henry Cohn, 2026, needs more optimization.
13 201 0.329522676574 Henry Cohn, 2026, needs more optimization.
13 202 0.329689117534 Henry Cohn, 2026, needs more optimization.
13 203 0.332312470001 Henry Cohn, 2026, needs more optimization.
13 208 0.333333333334 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
3⁢x−1
13 209 0.350062261222 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
13 210 0.350781425628 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
13 211 0.351286707469 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
13 212 0.352173596946 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
13 213 0.353210545440 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
13 214 0.354039930456 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
13 215 0.354840321652 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
13 216 0.355533261209 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
13 217 0.356136093649 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
13 218 0.357592618572 Henry Cohn, 2026, needs more optimization.
13 219 0.358094866744 Henry Cohn, 2026, needs more optimization.
13 220 0.358843879959 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
13 221 0.359655748088 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
13 222 0.360485874829 Henry Cohn, 2026, needs more optimization.
13 223 0.361517880709 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
13 224 0.362377334088 Henry Cohn, 2026, needs more optimization.
13 225 0.363226985696 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
13 226 0.364007853334 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
13 227 0.364771643117 Henry Cohn, 2026, needs more optimization.
13 228 0.365433265659 Henry Cohn, 2026, needs more optimization.
13 229 0.366212179515 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
13 230 0.366886072346 Henry Cohn, 2026, needs more optimization.
13 231 0.367679712194 Henry Cohn, 2026, needs more optimization.
13 240 0.368421052632 C. Ma, T. Tao Z., P. Li, M. Liu, H. Chen, Z. Mao, Y. Cheng, Y. Qi, and Y. Yang, Finding kissing numbers with game-theoretic reinforcement learning, preprint, 2025, arXiv:2511.13391.
19⁢x−7
13 246 0.368421052632 Henry Cohn, 2026.
19⁢x−7
13 247 0.371938177702 Henry Cohn, 2026, needs more optimization.
13 248 0.372967208694 Henry Cohn, 2026, needs more optimization.
13 249 0.373012137282 Henry Cohn, 2026, needs more optimization.
13 250 0.374534102135 Henry Cohn, 2026, needs more optimization.
13 251 0.375306480379 Henry Cohn, 2026, needs more optimization.
13 291 0.376384967370 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
23⁢x2−6⁢x−1
13 292 0.380271340361 Henry Cohn, 2026, needs more optimization.
13 293 0.380292762194 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
13 294 0.382525248832 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
13 295 0.383357848287 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
13 296 0.383950542002 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
13 306 0.384615384616 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
13⁢x−5
13 313 0.384615384616 M. Ganzhinov and P. R. J. Östergård, Spherical codes with prescribed signed permutation automorphisms inside shells of low-dimensional integer lattices, IEEE Trans. Inform. Theory 70 (2024), 8669–8674, doi:10.1109/tit.2024.3462593, arXiv:2403.04330.
13⁢x−5
13 314 0.389008395420 Henry Cohn, 2026, needs more optimization.
13 315 0.391819490904 Henry Cohn, 2026, needs more optimization.
13 316 0.393356320290 Henry Cohn, 2026, needs more optimization.
13 317 0.393953119873 Henry Cohn, 2026, needs more optimization.
13 318 0.395166322614 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
13 319 0.396151717794 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
13 320 0.396820139584 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
13 321 0.397924181775 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
13 322 0.398267614996 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
13 336 0.4 M. Ganzhinov and P. R. J. Östergård, Spherical codes with prescribed signed permutation automorphisms inside shells of low-dimensional integer lattices, IEEE Trans. Inform. Theory 70 (2024), 8669–8674, doi:10.1109/tit.2024.3462593, arXiv:2403.04330.
5⁢x−2
13 337 0.4 Henry Cohn, 2026.
5⁢x−2
13 339 0.4 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
5⁢x−2
13 340 0.405636400249 Henry Cohn, 2026, needs more optimization.
13 341 0.407417917914 Henry Cohn, 2026, needs more optimization.
13 342 0.407610253146 Henry Cohn, 2026, needs more optimization.
13 343 0.407664506590 Henry Cohn, 2026, needs more optimization.
13 344 0.408190728765 Henry Cohn, 2026, needs more optimization.
13 345 0.408396629481 Henry Cohn, 2026, needs more optimization.
13 346 0.408737460629 Henry Cohn, 2026, needs more optimization.
13 347 0.409548877064 Henry Cohn, 2026, needs more optimization.
13 348 0.410344005137 Henry Cohn, 2026, needs more optimization.
13 349 0.410707299942 Henry Cohn, 2026, needs more optimization.
13 350 0.410933626845 Henry Cohn, 2026, needs more optimization.
13 351 0.411013167434 Henry Cohn, 2026, needs more optimization.
13 352 0.411768412640 Henry Cohn, 2026, needs more optimization.
13 353 0.412552092950 Henry Cohn, 2026, needs more optimization.
13 354 0.413356465293 Henry Cohn, 2026, needs more optimization.
13 355 0.413992205093 Henry Cohn, 2026, needs more optimization.
13 356 0.414611053466 Henry Cohn, 2026, needs more optimization.
13 357 0.415090646981 Henry Cohn, 2026, needs more optimization.
13 358 0.415644665671 Henry Cohn, 2026, needs more optimization.
13 359 0.416137975944 Henry Cohn, 2026, needs more optimization.
13 360 0.416431424286 Henry Cohn, 2026, needs more optimization.
13 383 0.416666666667 Henry Cohn, 2026.
12⁢x−5
13 384 0.419641221594 Henry Cohn, 2026, needs more optimization.
13 385 0.420757215535 Henry Cohn, 2026, needs more optimization.
13 386 0.421199764176 Henry Cohn, 2026, needs more optimization.
13 387 0.421589411372 Henry Cohn, 2026, needs more optimization.
13 388 0.422314069764 Henry Cohn, 2026, needs more optimization.
13 389 0.423829072352 Henry Cohn, 2026, needs more optimization.
13 390 0.424217243490 Henry Cohn, 2026, needs more optimization.
13 391 0.424690202491 Henry Cohn, 2026, needs more optimization.
13 392 0.425194639844 Henry Cohn, 2026, needs more optimization.
13 393 0.425963316763 Henry Cohn, 2026, needs more optimization.
13 394 0.426551336375 Henry Cohn, 2026, needs more optimization.
13 395 0.427199871974 Henry Cohn, 2026, needs more optimization.
13 396 0.427815954099 Henry Cohn, 2026, needs more optimization.
13 397 0.427873150934 Henry Cohn, 2026, needs more optimization.
13 416 0.428571428572 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
7⁢x−3
13 492 0.428571428572 M. Ganzhinov and P. R. J. Östergård, Spherical codes with prescribed signed permutation automorphisms inside shells of low-dimensional integer lattices, IEEE Trans. Inform. Theory 70 (2024), 8669–8674, doi:10.1109/tit.2024.3462593, arXiv:2403.04330.
7⁢x−3
13 498 0.428571428572 Henry Cohn, 2026.
7⁢x−3
13 499 0.428679829897 Henry Cohn, 2026, needs more optimization.
13 500 0.429496475416 Henry Cohn, 2026, needs more optimization.
13 501 0.429602642763 Henry Cohn, 2026, needs more optimization.
13 502 0.429673395583 Henry Cohn, 2026, needs more optimization.
13 503 0.429681978125 Henry Cohn, 2026, needs more optimization.
13 504 0.429684869714 Henry Cohn, 2026, needs more optimization.
13 505 0.436906969175 Henry Cohn, 2026, needs more optimization.
13 506 0.439525222627 Henry Cohn, 2026, needs more optimization.
13 507 0.441378005941 Henry Cohn, 2026, needs more optimization.
13 508 0.441559000333 Henry Cohn, 2026, needs more optimization.
13 509 0.441576139707 Henry Cohn, 2026, needs more optimization.
13 510 0.441603924413 Henry Cohn, 2026, needs more optimization.
13 511 0.441612098484 Henry Cohn, 2026, needs more optimization.
13 513 0.441637784364 Henry Cohn, 2026, needs more optimization.
13 516 0.441652296338 Henry Cohn, 2026, needs more optimization.
13 517 0.441805537454 Henry Cohn, 2026, needs more optimization.
13 518 0.441854584351 Henry Cohn, 2026, needs more optimization.
13 519 0.442260233837 Henry Cohn, 2026, needs more optimization.
13 520 0.442276183312 Henry Cohn, 2026, needs more optimization.
13 521 0.446597322384 Henry Cohn, 2026, needs more optimization.
13 522 0.446667925744 Henry Cohn, 2026, needs more optimization.
13 523 0.446692434278 Henry Cohn, 2026, needs more optimization.
13 524 0.446701846557 Henry Cohn, 2026, needs more optimization.
13 525 0.446703332334 Henry Cohn, 2026, needs more optimization.
13 528 0.446718521219 Henry Cohn, 2026, needs more optimization.
13 530 0.446730450940 Henry Cohn, 2026, needs more optimization.
13 536 0.447369863649 Henry Cohn, 2026, needs more optimization.
13 537 0.447381653367 Henry Cohn, 2026, needs more optimization.
13 538 0.447384286134 Henry Cohn, 2026, needs more optimization.
13 539 0.447727721144 Henry Cohn, 2026, needs more optimization.
13 540 0.447745031095 Henry Cohn, 2026, needs more optimization.
13 541 0.448179158534 Henry Cohn, 2026, needs more optimization.
13 542 0.448633886313 Henry Cohn, 2026, needs more optimization.
13 543 0.448653803499 Henry Cohn, 2026, needs more optimization.
13 544 0.448686046393 Henry Cohn, 2026, needs more optimization.
13 546 0.448699082684 Henry Cohn, 2026, needs more optimization.
13 547 0.448724655728 Henry Cohn, 2026, needs more optimization.
13 548 0.449043472401 Henry Cohn, 2026, needs more optimization.
13 549 0.449055306437 Henry Cohn, 2026, needs more optimization.
13 550 0.449063863920 Henry Cohn, 2026, needs more optimization.
13 551 0.449394736841 Henry Cohn, 2026, needs more optimization.
13 552 0.449399829320 Henry Cohn, 2026, needs more optimization.
13 553 0.449407705636 Henry Cohn, 2026, needs more optimization.
13 554 0.449412376690 Henry Cohn, 2026, needs more optimization.
13 555 0.449414344964 Henry Cohn, 2026, needs more optimization.
13 556 0.449420607130 Henry Cohn, 2026, needs more optimization.
13 557 0.449439344520 Henry Cohn, 2026, needs more optimization.
13 561 0.450060096958 Henry Cohn, 2026, needs more optimization.
13 562 0.450065651779 Henry Cohn, 2026, needs more optimization.
13 563 0.450653858964 Henry Cohn, 2026, needs more optimization.
13 578 0.454545454546 M. Ganzhinov and P. R. J. Östergård, Spherical codes with prescribed signed permutation automorphisms inside shells of low-dimensional integer lattices, IEEE Trans. Inform. Theory 70 (2024), 8669–8674, doi:10.1109/tit.2024.3462593, arXiv:2403.04330.
11⁢x−5
13 579 0.458822457876 Henry Cohn, 2026, needs more optimization.
13 580 0.458837254470 Henry Cohn, 2026, needs more optimization.
13 581 0.458840696488 Henry Cohn, 2026, needs more optimization.
13 582 0.458841201980 Henry Cohn, 2026, needs more optimization.
13 583 0.458853108560 Henry Cohn, 2026, needs more optimization.
13 584 0.458859397207 Henry Cohn, 2026, needs more optimization.
13 585 0.458888201777 Henry Cohn, 2026, needs more optimization.
13 586 0.458912910414 Henry Cohn, 2026, needs more optimization.
13 587 0.459811649600 Henry Cohn, 2026, needs more optimization.
13 588 0.459825463586 Henry Cohn, 2026, needs more optimization.
13 589 0.459827994531 Henry Cohn, 2026, needs more optimization.
13 590 0.459847758434 Henry Cohn, 2026, needs more optimization.
13 591 0.459849708623 Henry Cohn, 2026, needs more optimization.
13 592 0.459903540576 Henry Cohn, 2026, needs more optimization.
13 593 0.461563407017 Henry Cohn, 2026, needs more optimization.
13 594 0.461590678404 Henry Cohn, 2026, needs more optimization.
13 595 0.462287720663 Henry Cohn, 2026, needs more optimization.
13 596 0.462992166747 Henry Cohn, 2026, needs more optimization.
13 597 0.463686125604 Henry Cohn, 2026, needs more optimization.
13 598 0.464200579812 Henry Cohn, 2026, needs more optimization.
13 599 0.464692202707 Henry Cohn, 2026, needs more optimization.
13 600 0.465425079641 Henry Cohn, 2026, needs more optimization.
13 601 0.465918438616 Henry Cohn, 2026, needs more optimization.
13 602 0.466218405803 Henry Cohn, 2026, needs more optimization.
13 603 0.466257021611 Henry Cohn, 2026, needs more optimization.
13 604 0.466277380709 Henry Cohn, 2026, needs more optimization.
13 605 0.466367888178 Henry Cohn, 2026, needs more optimization.
13 606 0.466433125523 Henry Cohn, 2026, needs more optimization.
13 607 0.466444271841 Henry Cohn, 2026, needs more optimization.
13 608 0.466515257075 Henry Cohn, 2026, needs more optimization.
13 609 0.466527856816 Henry Cohn, 2026, needs more optimization.
13 610 0.466539256208 Henry Cohn, 2026, needs more optimization.
13 611 0.466546886878 Henry Cohn, 2026, needs more optimization.
13 612 0.466558342333 Henry Cohn, 2026, needs more optimization.
13 613 0.466628227525 Henry Cohn, 2026, needs more optimization.
13 614 0.466635229463 Henry Cohn, 2026, needs more optimization.
13 615 0.466838150517 Henry Cohn, 2026, needs more optimization.
13 616 0.466906383770 Henry Cohn, 2026, needs more optimization.
13 617 0.466909780888 Henry Cohn, 2026, needs more optimization.
13 618 0.467032547128 Henry Cohn, 2026, needs more optimization.
13 619 0.467055940936 Henry Cohn, 2026, needs more optimization.
13 620 0.467127006281 Henry Cohn, 2026, needs more optimization.
13 621 0.467164190767 Henry Cohn, 2026, needs more optimization.
13 622 0.467195705456 Henry Cohn, 2026, needs more optimization.
13 623 0.467259204585 Henry Cohn, 2026, needs more optimization.
13 624 0.467295007000 Henry Cohn, 2026, needs more optimization.
13 625 0.467321966416 Henry Cohn, 2026, needs more optimization.
13 626 0.467363053258 Henry Cohn, 2026, needs more optimization.
13 627 0.467452869004 Henry Cohn, 2026, needs more optimization.
13 628 0.467539321477 Henry Cohn, 2026, needs more optimization.
13 629 0.467675792978 Henry Cohn, 2026, needs more optimization.
13 630 0.467690248355 Henry Cohn, 2026, needs more optimization.
13 631 0.469220965062 Henry Cohn, 2026, needs more optimization.
13 632 0.469478450181 Henry Cohn, 2026, needs more optimization.
13 633 0.470306429627 Henry Cohn, 2026, needs more optimization.
13 634 0.470981143957 Henry Cohn, 2026, needs more optimization.
13 635 0.471590815968 Henry Cohn, 2026, needs more optimization.
13 636 0.472064433524 Henry Cohn, 2026, needs more optimization.
13 637 0.472520736740 Henry Cohn, 2026, needs more optimization.
13 638 0.473147635881 Henry Cohn, 2026, needs more optimization.
13 639 0.473598388271 Henry Cohn, 2026, needs more optimization.
13 640 0.474108821679 Henry Cohn, 2026, needs more optimization.
13 641 0.474359094975 Henry Cohn, 2026, needs more optimization.
13 642 0.474903463689 Henry Cohn, 2026, needs more optimization.
13 644 0.475 Henry Cohn, 2026.
40⁢x−19
13 645 0.476047770169 Henry Cohn, 2026, needs more optimization.
13 646 0.476501061919 Henry Cohn, 2026, needs more optimization.
13 647 0.476809832479 Henry Cohn, 2026, needs more optimization.
13 648 0.477170209376 Henry Cohn, 2026, needs more optimization.
13 649 0.477412851544 Henry Cohn, 2026, needs more optimization.
13 650 0.477678422579 Henry Cohn, 2026, needs more optimization.
13 651 0.477831247188 Henry Cohn, 2026, needs more optimization.
13 652 0.477951435064 Henry Cohn, 2026, needs more optimization.
13 653 0.478129266405 Henry Cohn, 2026, needs more optimization.
13 654 0.478244019567 Henry Cohn, 2026, needs more optimization.
13 655 0.478402456515 Henry Cohn, 2026, needs more optimization.
13 656 0.478530065540 Henry Cohn, 2026, needs more optimization.
13 657 0.478693968712 Henry Cohn, 2026, needs more optimization.
13 658 0.478809761183 Henry Cohn, 2026, needs more optimization.
13 659 0.478974463107 Henry Cohn, 2026, needs more optimization.
13 660 0.479187585250 Henry Cohn, 2026, needs more optimization.
13 661 0.479296382950 Henry Cohn, 2026, needs more optimization.
13 662 0.479438563964 Henry Cohn, 2026, needs more optimization.
13 663 0.479588441397 Henry Cohn, 2026, needs more optimization.
13 664 0.479697112976 Henry Cohn, 2026, needs more optimization.
13 665 0.479829432572 Henry Cohn, 2026, needs more optimization.
13 666 0.479905187480 Henry Cohn, 2026, needs more optimization.
13 667 0.480038415461 Henry Cohn, 2026, needs more optimization.
13 668 0.480163186781 Henry Cohn, 2026, needs more optimization.
13 669 0.480330841741 Henry Cohn, 2026, needs more optimization.
13 670 0.480510214587 Henry Cohn, 2026, needs more optimization.
13 671 0.480658574768 Henry Cohn, 2026, needs more optimization.
13 672 0.480729377411 Henry Cohn, 2026, needs more optimization.
13 673 0.480863562631 Numaro AI Autoresearch, 11,000+ New Verified Spherical-Code Records from AI Autoresearch, Numaro Research Report NUMARO-2026-015 (2026), https://numaro.tech/research/spherical-codes-2026/.
13 674 0.480967465247 Henry Cohn, 2026, needs more optimization.
13 675 0.481089922269 Henry Cohn, 2026, needs more optimization.
13 676 0.481203739694 Henry Cohn, 2026, needs more optimization.
13 677 0.481317696726 Henry Cohn, 2026, needs more optimization.
13 678 0.481378248339 Henry Cohn, 2026, needs more optimization.
13 679 0.482028700717 Henry Cohn, 2026, needs more optimization.
13 680 0.482124124331 Henry Cohn, 2026, needs more optimization.
13 681 0.482148953807 Henry Cohn, 2026, needs more optimization.
13 682 0.482306284731 Henry Cohn, 2026, needs more optimization.
13 683 0.482451029969 Henry Cohn, 2026, needs more optimization.
13 684 0.482452527819 Henry Cohn, 2026, needs more optimization.
13 686 0.482460774945 Henry Cohn, 2026, needs more optimization.
13 687 0.482467864832 Henry Cohn, 2026, needs more optimization.
13 688 0.482472648875 Henry Cohn, 2026, needs more optimization.
13 689 0.482495947387 Henry Cohn, 2026, needs more optimization.
13 690 0.482510681227 Henry Cohn, 2026, needs more optimization.
13 691 0.482512081492 Henry Cohn, 2026, needs more optimization.
13 692 0.482923775479 Henry Cohn, 2026, needs more optimization.
13 693 0.483008293485 Henry Cohn, 2026, needs more optimization.
13 694 0.483119933716 Henry Cohn, 2026, needs more optimization.
13 695 0.483290806219 Henry Cohn, 2026, needs more optimization.
13 696 0.483407579837 Henry Cohn, 2026, needs more optimization.
13 697 0.483513309194 Henry Cohn, 2026, needs more optimization.
13 698 0.483784568439 Henry Cohn, 2026, needs more optimization.
13 699 0.483907258032 Henry Cohn, 2026, needs more optimization.
13 700 0.483971279366 Henry Cohn, 2026, needs more optimization.
13 701 0.484204771223 Henry Cohn, 2026, needs more optimization.
13 702 0.484240040078 Henry Cohn, 2026, needs more optimization.
13 703 0.484273728209 Henry Cohn, 2026, needs more optimization.
13 704 0.484291434118 Henry Cohn, 2026, needs more optimization.
13 705 0.484305141976 Henry Cohn, 2026, needs more optimization.
13 706 0.484356293408 Henry Cohn, 2026, needs more optimization.
13 707 0.484463356157 Henry Cohn, 2026, needs more optimization.
13 708 0.484559367685 Henry Cohn, 2026, needs more optimization.
13 709 0.484663674013 Henry Cohn, 2026, needs more optimization.
13 711 0.484673408783 Henry Cohn, 2026, needs more optimization.
13 712 0.484715420420 Henry Cohn, 2026, needs more optimization.
13 713 0.484721990933 Henry Cohn, 2026, needs more optimization.
13 714 0.484745408377 Henry Cohn, 2026, needs more optimization.
13 715 0.484759809967 Henry Cohn, 2026, needs more optimization.
13 716 0.484822768040 Henry Cohn, 2026, needs more optimization.
13 717 0.484843336433 Henry Cohn, 2026, needs more optimization.
13 718 0.484856634198 Henry Cohn, 2026, needs more optimization.
13 719 0.484882053081 Henry Cohn, 2026, needs more optimization.
13 720 0.484892592460 Henry Cohn, 2026, needs more optimization.
13 721 0.484896224100 Henry Cohn, 2026, needs more optimization.
13 722 0.484915731333 Henry Cohn, 2026, needs more optimization.
13 723 0.484933437011 Henry Cohn, 2026, needs more optimization.
13 724 0.484943905772 Henry Cohn, 2026, needs more optimization.
13 725 0.484956519275 Henry Cohn, 2026, needs more optimization.
13 726 0.485548412463 Henry Cohn, 2026, needs more optimization.
13 727 0.485565775767 Henry Cohn, 2026, needs more optimization.
13 728 0.485635312454 Henry Cohn, 2026, needs more optimization.
13 729 0.485722873041 Henry Cohn, 2026, needs more optimization.
13 730 0.485788036181 Henry Cohn, 2026, needs more optimization.
13 731 0.485804809559 Henry Cohn, 2026, needs more optimization.
13 732 0.485865896389 Henry Cohn, 2026, needs more optimization.
13 733 0.485945298572 Henry Cohn, 2026, needs more optimization.
13 734 0.486002453420 Henry Cohn, 2026, needs more optimization.
13 735 0.486120882247 Henry Cohn, 2026, needs more optimization.
13 736 0.486156955195 Henry Cohn, 2026, needs more optimization.
13 737 0.486218136405 Henry Cohn, 2026, needs more optimization.
13 738 0.486267505857 Henry Cohn, 2026, needs more optimization.
13 739 0.486311404079 Henry Cohn, 2026, needs more optimization.
13 740 0.486360728178 Henry Cohn, 2026, needs more optimization.
13 741 0.486426805176 Henry Cohn, 2026, needs more optimization.
13 742 0.486456618458 Henry Cohn, 2026, needs more optimization.
13 743 0.486502443268 Henry Cohn, 2026, needs more optimization.
13 744 0.486604970761 Henry Cohn, 2026, needs more optimization.
13 745 0.486664159371 Henry Cohn, 2026, needs more optimization.
13 746 0.486708591155 Henry Cohn, 2026, needs more optimization.
13 747 0.486727061008 Henry Cohn, 2026, needs more optimization.
13 748 0.486741836585 Henry Cohn, 2026, needs more optimization.
13 749 0.486780221911 Henry Cohn, 2026, needs more optimization.
13 750 0.486848571832 Henry Cohn, 2026, needs more optimization.
13 751 0.486928638168 Henry Cohn, 2026, needs more optimization.
13 752 0.487021128083 Henry Cohn, 2026, needs more optimization.
13 753 0.487134877002 Henry Cohn, 2026, needs more optimization.
13 754 0.487139534940 Henry Cohn, 2026, needs more optimization.
13 755 0.487165947617 Henry Cohn, 2026, needs more optimization.
13 756 0.487214487312 Henry Cohn, 2026, needs more optimization.
13 757 0.487282411397 Henry Cohn, 2026, needs more optimization.
13 758 0.487395961513 Henry Cohn, 2026, needs more optimization.
13 759 0.487406331519 Henry Cohn, 2026, needs more optimization.
13 760 0.487476107745 Henry Cohn, 2026, needs more optimization.
13 761 0.487588620467 Henry Cohn, 2026, needs more optimization.
13 762 0.487609894270 Henry Cohn, 2026, needs more optimization.
13 763 0.487671608639 Henry Cohn, 2026, needs more optimization.
13 764 0.487708791530 Henry Cohn, 2026, needs more optimization.
13 765 0.487740875345 Henry Cohn, 2026, needs more optimization.
13 766 0.487795748190 Henry Cohn, 2026, needs more optimization.
13 767 0.487881350355 Henry Cohn, 2026, needs more optimization.
13 768 0.487918603888 Henry Cohn, 2026, needs more optimization.
13 769 0.487936653119 Henry Cohn, 2026, needs more optimization.
13 770 0.487957707126 Henry Cohn, 2026, needs more optimization.
13 771 0.487974284689 Henry Cohn, 2026, needs more optimization.
13 772 0.488012994525 Henry Cohn, 2026, needs more optimization.
13 773 0.488071860722 Henry Cohn, 2026, needs more optimization.
13 774 0.488111169369 Henry Cohn, 2026, needs more optimization.
13 775 0.488190405497 Henry Cohn, 2026, needs more optimization.
13 776 0.488200993831 Henry Cohn, 2026, needs more optimization.
13 777 0.488258588727 Henry Cohn, 2026, needs more optimization.
13 778 0.488335476900 Henry Cohn, 2026, needs more optimization.
13 779 0.488363925204 Henry Cohn, 2026, needs more optimization.
13 780 0.488463383900 Henry Cohn, 2026, needs more optimization.
13 782 0.488516837868 Henry Cohn, 2026, needs more optimization.
13 783 0.488561339362 Henry Cohn, 2026, needs more optimization.
13 784 0.488643831191 Henry Cohn, 2026, needs more optimization.
13 785 0.488672749133 Henry Cohn, 2026, needs more optimization.
13 786 0.488726419014 Henry Cohn, 2026, needs more optimization.
13 787 0.488754773482 Henry Cohn, 2026, needs more optimization.
13 788 0.488833924789 Henry Cohn, 2026, needs more optimization.
13 789 0.488905176787 Henry Cohn, 2026, needs more optimization.
13 793 0.488922332553 Henry Cohn, 2026, needs more optimization.
13 794 0.488964513270 Henry Cohn, 2026, needs more optimization.
13 795 0.489003450868 Henry Cohn, 2026, needs more optimization.
13 797 0.489058806569 Henry Cohn, 2026, needs more optimization.
13 798 0.489094861479 Henry Cohn, 2026, needs more optimization.
13 799 0.489099708102 Henry Cohn, 2026, needs more optimization.
13 800 0.489136020095 Henry Cohn, 2026, needs more optimization.
13 801 0.489153937362 Henry Cohn, 2026, needs more optimization.
13 802 0.489157604709 Henry Cohn, 2026, needs more optimization.
13 804 0.489217040142 Henry Cohn, 2026, needs more optimization.
13 805 0.489217127139 Henry Cohn, 2026, needs more optimization.
13 806 0.489233705725 Henry Cohn, 2026, needs more optimization.
13 807 0.489256320330 Henry Cohn, 2026, needs more optimization.
13 808 0.489271257509 Henry Cohn, 2026, needs more optimization.
13 809 0.489282405425 Henry Cohn, 2026, needs more optimization.
13 810 0.489294003832 Henry Cohn, 2026, needs more optimization.
13 811 0.489299518078 Henry Cohn, 2026, needs more optimization.
13 812 0.489304055181 Henry Cohn, 2026, needs more optimization.
13 813 0.489315288597 Henry Cohn, 2026, needs more optimization.
13 814 0.489317911479 Henry Cohn, 2026, needs more optimization.
13 815 0.489333111443 Henry Cohn, 2026, needs more optimization.
13 816 0.489344450482 Henry Cohn, 2026, needs more optimization.
13 817 0.489353438099 Henry Cohn, 2026, needs more optimization.
13 818 0.489357877878 Henry Cohn, 2026, needs more optimization.
13 819 0.490539359532 Henry Cohn, 2026, needs more optimization.
13 820 0.490707721454 Henry Cohn, 2026, needs more optimization.
13 821 0.490745878270 Henry Cohn, 2026, needs more optimization.
13 822 0.490792627279 Henry Cohn, 2026, needs more optimization.
13 823 0.490819634443 Henry Cohn, 2026, needs more optimization.
13 824 0.490850248110 Henry Cohn, 2026, needs more optimization.
13 825 0.490889829586 Henry Cohn, 2026, needs more optimization.
13 826 0.490922899893 Henry Cohn, 2026, needs more optimization.
13 827 0.490926972781 Henry Cohn, 2026, needs more optimization.
13 828 0.491023619375 Henry Cohn, 2026, needs more optimization.
13 829 0.491165779969 Henry Cohn, 2026, needs more optimization.
13 830 0.491213340547 Henry Cohn, 2026, needs more optimization.
13 831 0.491255582777 Henry Cohn, 2026, needs more optimization.
13 832 0.491326669380 Henry Cohn, 2026, needs more optimization.
13 834 0.491407386553 Henry Cohn, 2026, needs more optimization.
13 835 0.491436515294 Henry Cohn, 2026, needs more optimization.
13 836 0.491482651592 Henry Cohn, 2026, needs more optimization.
13 837 0.491509167394 Henry Cohn, 2026, needs more optimization.
13 838 0.491590048237 Henry Cohn, 2026, needs more optimization.
13 839 0.491653891515 Henry Cohn, 2026, needs more optimization.
13 840 0.491669155712 Henry Cohn, 2026, needs more optimization.
13 841 0.491720370465 Henry Cohn, 2026, needs more optimization.
13 842 0.491737137831 Henry Cohn, 2026, needs more optimization.
13 843 0.491924742261 Henry Cohn, 2026, needs more optimization.
13 844 0.492018827819 Henry Cohn, 2026, needs more optimization.
13 845 0.492061959160 Henry Cohn, 2026, needs more optimization.
13 846 0.492086049935 Henry Cohn, 2026, needs more optimization.
13 847 0.492163852510 Henry Cohn, 2026, needs more optimization.
13 848 0.492268251983 Henry Cohn, 2026, needs more optimization.
13 849 0.492416466727 Henry Cohn, 2026, needs more optimization.
13 852 0.492584195032 Henry Cohn, 2026, needs more optimization.
13 856 0.492787872320 Henry Cohn, 2026, needs more optimization.
13 857 0.493162562773 Henry Cohn, 2026, needs more optimization.
13 858 0.493214966629 Henry Cohn, 2026, needs more optimization.
13 859 0.493229754174 Henry Cohn, 2026, needs more optimization.
13 860 0.493297251172 Henry Cohn, 2026, needs more optimization.
13 861 0.493352792496 Henry Cohn, 2026, needs more optimization.
13 862 0.493682026218 Henry Cohn, 2026, needs more optimization.
13 863 0.493757029489 Henry Cohn, 2026, needs more optimization.
13 864 0.493785082040 Henry Cohn, 2026, needs more optimization.
13 865 0.494154724125 Henry Cohn, 2026, needs more optimization.
13 866 0.494194893644 Henry Cohn, 2026, needs more optimization.
13 867 0.494207509118 Henry Cohn, 2026, needs more optimization.
13 868 0.494278497696 Henry Cohn, 2026, needs more optimization.
13 869 0.494647505003 Henry Cohn, 2026, needs more optimization.
13 870 0.494758219450 Henry Cohn, 2026, needs more optimization.
13 871 0.494855492724 Henry Cohn, 2026, needs more optimization.
13 872 0.495128125527 Henry Cohn, 2026, needs more optimization.
13 874 0.495214948273 Henry Cohn, 2026, needs more optimization.
13 875 0.495431922802 Henry Cohn, 2026, needs more optimization.
13 876 0.495439298389 Henry Cohn, 2026, needs more optimization.
13 877 0.495546500792 Henry Cohn, 2026, needs more optimization.
13 878 0.495550584512 Henry Cohn, 2026, needs more optimization.
13 879 0.495568257779 Henry Cohn, 2026, needs more optimization.
13 880 0.495589511622 Henry Cohn, 2026, needs more optimization.
13 881 0.495628542366 Henry Cohn, 2026, needs more optimization.
13 882 0.495634980612 Henry Cohn, 2026, needs more optimization.
13 883 0.497158394701 Henry Cohn, 2026, needs more optimization.
13 884 0.497239321328 Henry Cohn, 2026, needs more optimization.
13 885 0.497290083073 Henry Cohn, 2026, needs more optimization.
13 886 0.497406841220 Henry Cohn, 2026, needs more optimization.
13 887 0.497863241154 Henry Cohn, 2026, needs more optimization.
13 888 0.497910980074 Henry Cohn, 2026, needs more optimization.
13 889 0.497958599776 Henry Cohn, 2026, needs more optimization.
13 890 0.498442600586 Henry Cohn, 2026, needs more optimization.
13 891 0.498618338137 Henry Cohn, 2026, needs more optimization.
13 892 0.498797522270 Henry Cohn, 2026, needs more optimization.
13 893 0.499160380814 Henry Cohn, 2026, needs more optimization.
13 894 0.499395389629 Henry Cohn, 2026, needs more optimization.
13 895 0.499575211341 Henry Cohn, 2026, needs more optimization.
13 896 0.499702824653 Henry Cohn, 2026, needs more optimization.
13 897 0.499811837600 Henry Cohn, 2026, needs more optimization.
13 1024 0.5 Subcode of a kissing configuration from J. Leech and N. J. A. Sloane, Sphere packings and error-correcting codes, Canadian J. Math. 23 (1971), 718–745, doi:10.4153/CJM-1971-081-3.
2⁢x−1
14 29 0.053426987342 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
2016⁢x3−196⁢x2−14⁢x+1
14 30 0.0625 H. Cohn, Small spherical and projective codes, data set, 2022, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
16⁢x−1
14 31 0.067582771839 H. Cohn, Small spherical and projective codes, data set, updated 2025, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
14 32 0.071430901841 H. Cohn, Small spherical and projective codes, data set, 2022, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
14 33 0.071678780313 Henry Cohn, 2025.
14 34 0.071706747799 Henry Cohn, 2025.
14 36 0.080003299193 Henry Cohn, 2023.
2156⁢x2+140⁢x−25
14 37 0.087892856445 Henry Cohn, 2023.
Minimal polynomial listed in plain text data
14 38 0.092604004700 Henry Cohn, 2025.
14 39 0.094407135777 Henry Cohn, 2023.
Minimal polynomial listed in plain text data
14 42 0.1 T. Ericson and V. Zinoviev, Spherical codes generated by binary partitions of symmetric pointsets, IEEE Trans. Inform. Theory 41 (1995), 107–129, doi:10.1109/18.370114.
10⁢x−1
14 43 0.112894921393 Henry Cohn, 2025.
14 45 0.112912613537 Henry Cohn, 2023.
167⁢x2−10⁢x−1
14 46 0.114212424977 Henry Cohn, 2024.
14 47 0.114744370065 Henry Cohn, 2026.
14 48 0.114785923011 Henry Cohn, 2023.
1988352⁢x8+1963008⁢x7−108672⁢x6−513152⁢x5−92592⁢x4+19616⁢x3+5240⁢x2+72⁢x−81
14 49 0.125031168050 Henry Cohn, 2025.
14 50 0.126129943174 Henry Cohn, 2025.
14 52 0.126131983623 Henry Cohn, 2023.
47⁢x2+2⁢x−1
14 53 0.127206627186 Henry Cohn, 2025.
14 54 0.135105967369 Henry Cohn, 2024.
14 55 0.136745922263 Henry Cohn, 2023.
14 56 0.139995758129 Henry Cohn, 2024.
14 57 0.142106619426 Henry Cohn, 2025.
14 64 0.142857142858 T. Ericson and V. Zinoviev, Spherical codes generated by binary partitions of symmetric pointsets, IEEE Trans. Inform. Theory 41 (1995), 107–129, doi:10.1109/18.370114.
7⁢x−1
14 65 0.165287555076 Henry Cohn, 2024.
25600⁢x4−5616⁢x3−2736⁢x2+81
14 70 0.166666666667 T. Ericson and V. Zinoviev, Spherical codes generated by binary partitions of symmetric pointsets, IEEE Trans. Inform. Theory 41 (1995), 107–129, doi:10.1109/18.370114.
6⁢x−1
14 71 0.177427267176 Henry Cohn, 2024.
196⁢x4−56⁢x3−28⁢x2+1
14 72 0.180979034910 Henry Cohn, 2026.
14 73 0.184667025692 Henry Cohn, 2026, needs more optimization.
14 75 0.185110498562 Henry Cohn, 2026.
14 76 0.189883320237 Henry Cohn, 2026, needs more optimization.
14 77 0.190266040190 Henry Cohn, 2026, needs more optimization.
14 78 0.191436403890 Henry Cohn, 2026, needs more optimization.
14 79 0.193295826526 Henry Cohn, 2026, needs more optimization.
14 80 0.195567546353 Henry Cohn, 2026, needs more optimization.
14 81 0.198103716529 Henry Cohn, 2026, needs more optimization.
14 82 0.198235129127 Henry Cohn, 2026, needs more optimization.
14 83 0.198270163042 Henry Cohn, 2026, needs more optimization.
14 84 0.198299573201 Henry Cohn, 2026, needs more optimization.
14 85 0.198385443665 Henry Cohn, 2026, needs more optimization.
14 86 0.198448405525 Henry Cohn, 2026, needs more optimization.
14 87 0.198500455261 Henry Cohn, 2026, needs more optimization.
14 88 0.198573144765 Henry Cohn, 2026, needs more optimization.
14 89 0.198677096722 Henry Cohn, 2026, needs more optimization.
14 90 0.198771632430 Henry Cohn, 2026, needs more optimization.
14 91 0.198843416030 Henry Cohn, 2026, needs more optimization.
14 92 0.208456809641 Henry Cohn, 2026, needs more optimization.
14 93 0.211749206649 Henry Cohn, 2026, needs more optimization.
14 94 0.211903258988 Henry Cohn, 2026, needs more optimization.
14 95 0.212179543064 Henry Cohn, 2026, needs more optimization.
14 96 0.212295215604 Henry Cohn, 2026, needs more optimization.
14 98 0.212297015491 Henry Cohn, 2026, needs more optimization.
14 99 0.219093745555 Henry Cohn, 2026, needs more optimization.
14 100 0.223666705565 Henry Cohn, 2026, needs more optimization.
14 101 0.225613148985 Henry Cohn, 2026, needs more optimization.
14 102 0.227325287426 Henry Cohn, 2026, needs more optimization.
14 103 0.228478286962 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
14 112 0.229910395528 Henry Cohn, 2026.
14 113 0.234902627893 Henry Cohn, 2026, needs more optimization.
14 114 0.237359837687 Henry Cohn, 2026, needs more optimization.
14 115 0.239305162774 Henry Cohn, 2026, needs more optimization.
14 116 0.240624685055 Henry Cohn, 2026, needs more optimization.
14 117 0.242104429558 Henry Cohn, 2026, needs more optimization.
14 118 0.243566013833 Henry Cohn, 2026, needs more optimization.
14 119 0.244891424825 Henry Cohn, 2026, needs more optimization.
14 120 0.245340349030 Henry Cohn, 2026, needs more optimization.
14 121 0.245811136405 Henry Cohn, 2026, needs more optimization.
14 122 0.247977863948 Henry Cohn, 2026, needs more optimization.
14 123 0.249943298076 Henry Cohn, 2026, needs more optimization.
14 124 0.251242938878 Henry Cohn, 2026, needs more optimization.
14 125 0.252284736853 Henry Cohn, 2026, needs more optimization.
14 126 0.253277127544 Henry Cohn, 2026, needs more optimization.
14 127 0.254058650995 Henry Cohn, 2026, needs more optimization.
14 128 0.254656731729 Henry Cohn, 2026, needs more optimization.
14 129 0.255353344722 Henry Cohn, 2026, needs more optimization.
14 130 0.255997660067 Henry Cohn, 2026, needs more optimization.
14 131 0.258087112405 Henry Cohn, 2026, needs more optimization.
14 132 0.259496247597 Henry Cohn, 2026, needs more optimization.
14 133 0.261787179504 Henry Cohn, 2026, needs more optimization.
14 134 0.263496074463 Henry Cohn, 2026, needs more optimization.
14 135 0.265062714546 Henry Cohn, 2026, needs more optimization.
14 136 0.266892083849 Henry Cohn, 2026, needs more optimization.
14 137 0.268271970629 Henry Cohn, 2026, needs more optimization.
14 139 0.269360512850 Henry Cohn, 2026, needs more optimization.
14 140 0.269363487446 Henry Cohn, 2026, needs more optimization.
14 141 0.269364430906 Henry Cohn, 2026, needs more optimization.
14 142 0.269374097032 Henry Cohn, 2026, needs more optimization.
14 143 0.269376035718 Henry Cohn, 2026, needs more optimization.
14 144 0.269378581522 Henry Cohn, 2026, needs more optimization.
14 145 0.269385016398 Henry Cohn, 2026, needs more optimization.
14 146 0.269391352219 Henry Cohn, 2026, needs more optimization.
14 147 0.269406350518 Henry Cohn, 2026, needs more optimization.
14 148 0.269435946677 Henry Cohn, 2026, needs more optimization.
14 149 0.269470068873 Henry Cohn, 2026, needs more optimization.
14 150 0.269507460863 Henry Cohn, 2026, needs more optimization.
14 151 0.269752143836 Henry Cohn, 2026, needs more optimization.
14 152 0.269752143884 Henry Cohn, 2026, needs more optimization.
14 153 0.273185531222 Henry Cohn, 2026, needs more optimization.
14 154 0.273722355435 Valentin Khrulkov, 2026, using the program of A. Kravatsky, V. Khrulkov, and I. Oseledets, ImprovEvolve: basin-hopping meets LLM-guided evolutionary search, ICML 2026 AI4Math Workshop Poster, https://openreview.net/forum?id=nE1q0gRDNr, arXiv:2602.10233.
14 156 0.276322194174 Henry Cohn, 2026, needs more optimization.
14 157 0.276370185002 Henry Cohn, 2026, needs more optimization.
14 158 0.276416052658 Henry Cohn, 2026, needs more optimization.
14 159 0.276642407194 Henry Cohn, 2026, needs more optimization.
14 160 0.276958562167 Henry Cohn, 2026, needs more optimization.
14 161 0.277317972773 Henry Cohn, 2026, needs more optimization.
14 162 0.277834331200 Henry Cohn, 2026, needs more optimization.
14 163 0.278238575836 Henry Cohn, 2026, needs more optimization.
14 164 0.278743460292 Henry Cohn, 2026, needs more optimization.
14 165 0.279341017343 Henry Cohn, 2026, needs more optimization.
14 166 0.280058776528 Henry Cohn, 2026, needs more optimization.
14 167 0.281202893108 Henry Cohn, 2026, needs more optimization.
14 168 0.285631980536 Henry Cohn, 2026, needs more optimization.
14 169 0.287704299374 Henry Cohn, 2026, needs more optimization.
14 170 0.288129946888 Henry Cohn, 2026, needs more optimization.
14 171 0.289699476895 Henry Cohn, 2026, needs more optimization.
14 172 0.290661090360 Henry Cohn, 2026, needs more optimization.
14 173 0.290943143907 Henry Cohn, 2026, needs more optimization.
14 174 0.291997254955 Henry Cohn, 2026, needs more optimization.
14 175 0.293044074640 Henry Cohn, 2026, needs more optimization.
14 176 0.293636136257 Henry Cohn, 2026, needs more optimization.
14 177 0.294400737138 Henry Cohn, 2026, needs more optimization.
14 178 0.295382387766 Henry Cohn, 2026, needs more optimization.
14 179 0.295912434658 Henry Cohn, 2026, needs more optimization.
14 180 0.296632646298 Henry Cohn, 2026, needs more optimization.
14 181 0.297692423446 Henry Cohn, 2026, needs more optimization.
14 182 0.297707212125 Henry Cohn, 2026, needs more optimization.
14 183 0.297827648977 Henry Cohn, 2026, needs more optimization.
14 184 0.298055557064 Henry Cohn, 2026, needs more optimization.
14 185 0.298562026509 Henry Cohn, 2026, needs more optimization.
14 186 0.299217900052 Henry Cohn, 2026, needs more optimization.
14 187 0.299608321336 Henry Cohn, 2026, needs more optimization.
14 188 0.300673453293 Henry Cohn, 2026, needs more optimization.
14 189 0.301652342459 Henry Cohn, 2026, needs more optimization.
14 190 0.301796962335 Henry Cohn, 2026, needs more optimization.
14 191 0.302341333297 Henry Cohn, 2026, needs more optimization.
14 192 0.303606917114 Henry Cohn, 2026, needs more optimization.
14 193 0.304407454337 Henry Cohn, 2026, needs more optimization.
14 194 0.305382980797 Henry Cohn, 2026, needs more optimization.
14 195 0.306358075774 Henry Cohn, 2026, needs more optimization.
14 196 0.307724210524 Henry Cohn, 2026, needs more optimization.
14 197 0.308786264417 Henry Cohn, 2026, needs more optimization.
14 198 0.309612855467 Henry Cohn, 2026, needs more optimization.
14 199 0.310675176432 Henry Cohn, 2026, needs more optimization.
14 200 0.311235878990 Henry Cohn, 2026, needs more optimization.
14 201 0.312451765957 Henry Cohn, 2026, needs more optimization.
14 202 0.313150420115 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
14 203 0.313773165210 Henry Cohn, 2026, needs more optimization.
14 204 0.313834945706 Henry Cohn, 2026, needs more optimization.
14 205 0.314016868165 Henry Cohn, 2026, needs more optimization.
14 206 0.314247257358 Henry Cohn, 2026, needs more optimization.
14 207 0.314602219360 Henry Cohn, 2026, needs more optimization.
14 208 0.315008640502 Henry Cohn, 2026, needs more optimization.
14 209 0.315336330184 Henry Cohn, 2026, needs more optimization.
14 210 0.315601513940 Henry Cohn, 2026, needs more optimization.
14 211 0.315962562040 Henry Cohn, 2026, needs more optimization.
14 212 0.316357184068 Henry Cohn, 2026, needs more optimization.
14 213 0.317114763231 Henry Cohn, 2026, needs more optimization.
14 214 0.317568377424 Henry Cohn, 2026, needs more optimization.
14 215 0.318075813082 Henry Cohn, 2026, needs more optimization.
14 216 0.318679102797 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
14 217 0.319194127476 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
14 218 0.319918856837 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
14 219 0.320684355566 Henry Cohn, 2026, needs more optimization.
14 220 0.321037854581 Henry Cohn, 2026, needs more optimization.
14 221 0.321532134060 Henry Cohn, 2026, needs more optimization.
14 222 0.321921128981 Henry Cohn, 2026, needs more optimization.
14 223 0.322282342892 Henry Cohn, 2026, needs more optimization.
14 224 0.322794902738 Henry Cohn, 2026, needs more optimization.
14 225 0.323217541574 Henry Cohn, 2026, needs more optimization.
14 226 0.324023119940 Henry Cohn, 2026, needs more optimization.
14 227 0.324621196335 Henry Cohn, 2026, needs more optimization.
14 228 0.325269661540 Henry Cohn, 2026, needs more optimization.
14 229 0.325847063936 Henry Cohn, 2026, needs more optimization.
14 230 0.326362965726 Henry Cohn, 2026, needs more optimization.
14 231 0.326882168113 Henry Cohn, 2026, needs more optimization.
14 232 0.327532348812 Henry Cohn, 2026, needs more optimization.
14 233 0.328692921832 Henry Cohn, 2026, needs more optimization.
14 234 0.329427067223 Henry Cohn, 2026, needs more optimization.
14 235 0.330538787445 Henry Cohn, 2026, needs more optimization.
14 236 0.331740100168 Henry Cohn, 2026, needs more optimization.
14 237 0.333113714509 Henry Cohn, 2026, needs more optimization.
14 240 0.333333333334 M. Ganzhinov and P. R. J. Östergård, Spherical codes with prescribed signed permutation automorphisms inside shells of low-dimensional integer lattices, IEEE Trans. Inform. Theory 70 (2024), 8669–8674, doi:10.1109/tit.2024.3462593, arXiv:2403.04330.
3⁢x−1
14 252 0.333333333334 C. Ma, T. Tao Z., P. Li, M. Liu, H. Chen, Z. Mao, Y. Cheng, Y. Qi, and Y. Yang, Finding kissing numbers with game-theoretic reinforcement learning, preprint, 2025, arXiv:2511.13391.
3⁢x−1
14 253 0.335257972468 Henry Cohn, 2026, needs more optimization.
14 254 0.335300270177 Henry Cohn, 2026, needs more optimization.
14 255 0.335300597545 Henry Cohn, 2026, needs more optimization.
14 256 0.335544275838 Henry Cohn, 2026, needs more optimization.
14 260 0.335722108295 Henry Cohn, 2026, needs more optimization.
14 261 0.335735458873 Henry Cohn, 2026, needs more optimization.
14 262 0.335900347934 Henry Cohn, 2026, needs more optimization.
14 263 0.335900976756 Henry Cohn, 2026, needs more optimization.
14 264 0.336210536785 Henry Cohn, 2026, needs more optimization.
14 265 0.336264168779 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
14 266 0.337157122508 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
14 281 0.339465385360 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
14 282 0.339465386509 Henry Cohn, 2026, needs more optimization.
14 283 0.339923716325 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
14 284 0.340074483514 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
14 285 0.340590650252 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
14 286 0.341181622341 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
14 287 0.342565745507 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
14 288 0.344237239870 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
14 289 0.345304057625 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
14 290 0.346053105177 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
14 294 0.347198310291 Henry Cohn, 2026, needs more optimization.
14 296 0.347770941783 Henry Cohn, 2026, needs more optimization.
14 297 0.347770941811 Henry Cohn, 2026, needs more optimization.
14 298 0.348275219469 Henry Cohn, 2026, needs more optimization.
14 299 0.348275220220 Henry Cohn, 2026, needs more optimization.
14 300 0.348340475288 Henry Cohn, 2026, needs more optimization.
14 301 0.348673532059 Henry Cohn, 2026, needs more optimization.
14 302 0.349590187951 Henry Cohn, 2026, needs more optimization.
14 303 0.352667012589 Henry Cohn, 2026, needs more optimization.
14 304 0.353975404146 Henry Cohn, 2026, needs more optimization.
14 330 0.355015572415 Henry Cohn, 2026, needs more optimization.
14 335 0.355045564946 Henry Cohn, 2026, needs more optimization.
14 336 0.355078330108 Henry Cohn, 2026, needs more optimization.
14 338 0.355125671090 Henry Cohn, 2026, needs more optimization.
14 339 0.355578825476 Henry Cohn, 2026, needs more optimization.
14 340 0.357142669567 Henry Cohn, 2026, needs more optimization.
14 341 0.358054740256 Henry Cohn, 2026, needs more optimization.
14 342 0.358519266808 Henry Cohn, 2026, needs more optimization.
14 343 0.358546741458 Henry Cohn, 2026, needs more optimization.
14 344 0.359877349878 Henry Cohn, 2026, needs more optimization.
14 345 0.360769864293 Henry Cohn, 2026, needs more optimization.
14 346 0.362854178838 Henry Cohn, 2026, needs more optimization.
14 347 0.364120180273 Henry Cohn, 2026, needs more optimization.
14 348 0.365652407337 Henry Cohn, 2026, needs more optimization.
14 349 0.366605326823 Henry Cohn, 2026, needs more optimization.
14 351 0.366857294830 Henry Cohn, 2026, needs more optimization.
14 352 0.367344197828 Henry Cohn, 2026, needs more optimization.
14 353 0.368112627388 Henry Cohn, 2026, needs more optimization.
14 354 0.369258883088 Henry Cohn, 2026, needs more optimization.
14 355 0.370391928645 Henry Cohn, 2026, needs more optimization.
14 356 0.371138045717 Henry Cohn, 2026, needs more optimization.
14 357 0.371999609029 Henry Cohn, 2026, needs more optimization.
14 358 0.373029409189 Henry Cohn, 2026, needs more optimization.
14 359 0.374138339300 Henry Cohn, 2026, needs more optimization.
14 360 0.374986459037 Henry Cohn, 2026, needs more optimization.
14 361 0.375773879507 Henry Cohn, 2026, needs more optimization.
14 362 0.376466786088 Henry Cohn, 2026, needs more optimization.
14 380 0.377442542892 Henry Cohn, 2026, needs more optimization.
14 381 0.377456239542 Henry Cohn, 2026, needs more optimization.
14 382 0.377632934057 Henry Cohn, 2026, needs more optimization.
14 383 0.377759801302 Henry Cohn, 2026, needs more optimization.
14 384 0.377830162024 Henry Cohn, 2026, needs more optimization.
14 385 0.377913400306 Henry Cohn, 2026, needs more optimization.
14 386 0.378444520871 Henry Cohn, 2026, needs more optimization.
14 387 0.380850202037 Henry Cohn, 2026, needs more optimization.
14 388 0.381594736575 Henry Cohn, 2026, needs more optimization.
14 389 0.381960106701 Henry Cohn, 2026, needs more optimization.
14 390 0.383154197192 Henry Cohn, 2026, needs more optimization.
14 391 0.383158267295 Henry Cohn, 2026, needs more optimization.
14 392 0.384922069754 Henry Cohn, 2026, needs more optimization.
14 393 0.385302984360 Henry Cohn, 2026, needs more optimization.
14 394 0.385377650657 Henry Cohn, 2026, needs more optimization.
14 395 0.385393603470 Henry Cohn, 2026, needs more optimization.
14 396 0.385415381998 Henry Cohn, 2026, needs more optimization.
14 397 0.385484319024 Henry Cohn, 2026, needs more optimization.
14 398 0.385497607343 Henry Cohn, 2026, needs more optimization.
14 399 0.386603323756 Henry Cohn, 2026, needs more optimization.
14 404 0.386745717940 Henry Cohn, 2026, needs more optimization.
14 405 0.386786126168 Henry Cohn, 2026, needs more optimization.
14 406 0.387142581468 Henry Cohn, 2026, needs more optimization.
14 410 0.387221791341 Henry Cohn, 2026, needs more optimization.
14 417 0.387398876783 Henry Cohn, 2026, needs more optimization.
14 418 0.387501344057 Henry Cohn, 2026, needs more optimization.
14 419 0.387554367345 Henry Cohn, 2026, needs more optimization.
14 420 0.388282822630 Henry Cohn, 2026, needs more optimization.
14 421 0.390111917456 Henry Cohn, 2026, needs more optimization.
14 422 0.391129706485 Henry Cohn, 2026, needs more optimization.
14 423 0.391547846054 Henry Cohn, 2026, needs more optimization.
14 435 0.391891891892 Henry Cohn, 2026.
74⁢x−29
14 436 0.394834515682 Henry Cohn, 2026, needs more optimization.
14 437 0.395905398651 Henry Cohn, 2026, needs more optimization.
14 438 0.396519314534 Henry Cohn, 2026, needs more optimization.
14 439 0.396988101982 Henry Cohn, 2026, needs more optimization.
14 440 0.397345835808 Henry Cohn, 2026, needs more optimization.
14 441 0.397630040289 Henry Cohn, 2026, needs more optimization.
14 442 0.398091174693 Henry Cohn, 2026, needs more optimization.
14 443 0.398789626161 Henry Cohn, 2026, needs more optimization.
14 444 0.399265345571 Henry Cohn, 2026, needs more optimization.
14 445 0.399600978200 Henry Cohn, 2026, needs more optimization.
14 466 0.4 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
5⁢x−2
14 496 0.4 Henry Cohn, 2026.
5⁢x−2
14 497 0.402761649589 Henry Cohn, 2026, needs more optimization.
14 498 0.402852311822 Henry Cohn, 2026, needs more optimization.
14 500 0.403337141701 Henry Cohn, 2026, needs more optimization.
14 501 0.406001190221 Henry Cohn, 2026, needs more optimization.
14 502 0.407333850816 Henry Cohn, 2026, needs more optimization.
14 503 0.407824490830 Henry Cohn, 2026, needs more optimization.
14 504 0.409461291585 Henry Cohn, 2026, needs more optimization.
14 505 0.410156338966 Henry Cohn, 2026, needs more optimization.
14 506 0.411338597264 Henry Cohn, 2026, needs more optimization.
14 507 0.411596564001 Henry Cohn, 2026, needs more optimization.
14 508 0.411618556572 Henry Cohn, 2026, needs more optimization.
14 510 0.411762370817 Henry Cohn, 2026, needs more optimization.
14 511 0.411764640791 Henry Cohn, 2026, needs more optimization.
14 512 0.411778213069 Henry Cohn, 2026, needs more optimization.
14 513 0.411923951564 Henry Cohn, 2026, needs more optimization.
14 514 0.411930583356 Henry Cohn, 2026, needs more optimization.
14 515 0.415477071892 Henry Cohn, 2026, needs more optimization.
14 516 0.415533462839 Henry Cohn, 2026, needs more optimization.
14 517 0.416173793462 Henry Cohn, 2026, needs more optimization.
14 555 0.423076923077 Henry Cohn, 2026.
26⁢x−11
14 557 0.423119543564 Henry Cohn, 2026, needs more optimization.
14 558 0.423210157909 Henry Cohn, 2026, needs more optimization.
14 559 0.427438420763 Henry Cohn, 2026, needs more optimization.
14 560 0.427989895905 Henry Cohn, 2026, needs more optimization.
14 600 0.428571428572 M. Ganzhinov and P. R. J. Östergård, Spherical codes with prescribed signed permutation automorphisms inside shells of low-dimensional integer lattices, IEEE Trans. Inform. Theory 70 (2024), 8669–8674, doi:10.1109/tit.2024.3462593, arXiv:2403.04330.
7⁢x−3
14 601 0.429745298318 Henry Cohn, 2026, needs more optimization.
14 602 0.430053764432 Henry Cohn, 2026, needs more optimization.
14 603 0.430222247126 Henry Cohn, 2026, needs more optimization.
14 604 0.430588037803 Henry Cohn, 2026, needs more optimization.
14 605 0.430985253197 Henry Cohn, 2026, needs more optimization.
14 606 0.431126007685 Henry Cohn, 2026, needs more optimization.
14 607 0.431171763469 Henry Cohn, 2026, needs more optimization.
14 608 0.431346650647 Henry Cohn, 2026, needs more optimization.
14 609 0.431487453905 Henry Cohn, 2026, needs more optimization.
14 610 0.431596531607 Henry Cohn, 2026, needs more optimization.
14 611 0.431618164267 Henry Cohn, 2026, needs more optimization.
14 612 0.432117982611 Henry Cohn, 2026, needs more optimization.
14 613 0.432207297890 Henry Cohn, 2026, needs more optimization.
14 614 0.432252109839 Henry Cohn, 2026, needs more optimization.
14 615 0.432780407197 Henry Cohn, 2026, needs more optimization.
14 616 0.432816771682 Henry Cohn, 2026, needs more optimization.
14 617 0.432835936653 Henry Cohn, 2026, needs more optimization.
14 618 0.432858127632 Henry Cohn, 2026, needs more optimization.
14 619 0.432902581274 Henry Cohn, 2026, needs more optimization.
14 620 0.432930994818 Henry Cohn, 2026, needs more optimization.
14 621 0.432954490462 Henry Cohn, 2026, needs more optimization.
14 622 0.432987687154 Henry Cohn, 2026, needs more optimization.
14 623 0.433026658052 Henry Cohn, 2026, needs more optimization.
14 624 0.433072314389 Henry Cohn, 2026, needs more optimization.
14 625 0.433115354332 Henry Cohn, 2026, needs more optimization.
14 626 0.433166868448 Henry Cohn, 2026, needs more optimization.
14 627 0.433208887628 Henry Cohn, 2026, needs more optimization.
14 628 0.433473075747 Henry Cohn, 2026, needs more optimization.
14 629 0.433493937814 Henry Cohn, 2026, needs more optimization.
14 630 0.433537417389 Henry Cohn, 2026, needs more optimization.
14 631 0.433593068228 Henry Cohn, 2026, needs more optimization.
14 632 0.433638979000 Henry Cohn, 2026, needs more optimization.
14 633 0.433680738766 Henry Cohn, 2026, needs more optimization.
14 634 0.433704567187 Henry Cohn, 2026, needs more optimization.
14 635 0.433771236373 Henry Cohn, 2026, needs more optimization.
14 636 0.433799659087 Henry Cohn, 2026, needs more optimization.
14 637 0.433851946524 Henry Cohn, 2026, needs more optimization.
14 638 0.433905131293 Henry Cohn, 2026, needs more optimization.
14 639 0.433911701529 Henry Cohn, 2026, needs more optimization.
14 640 0.434133573446 Henry Cohn, 2026, needs more optimization.
14 641 0.434170079776 Henry Cohn, 2026, needs more optimization.
14 642 0.434171530352 Henry Cohn, 2026, needs more optimization.
14 643 0.434174623195 Henry Cohn, 2026, needs more optimization.
14 644 0.434211428142 Henry Cohn, 2026, needs more optimization.
14 645 0.434400099537 Henry Cohn, 2026, needs more optimization.
14 646 0.434956971318 Henry Cohn, 2026, needs more optimization.
14 647 0.435567861350 Henry Cohn, 2026, needs more optimization.
14 648 0.436671424644 Henry Cohn, 2026, needs more optimization.
14 649 0.437226702171 Henry Cohn, 2026, needs more optimization.
14 650 0.437719547625 Henry Cohn, 2026, needs more optimization.
14 651 0.437994539884 Henry Cohn, 2026, needs more optimization.
14 652 0.438069875655 Henry Cohn, 2026, needs more optimization.
14 653 0.438800358824 Henry Cohn, 2026, needs more optimization.
14 654 0.439315975672 Henry Cohn, 2026, needs more optimization.
14 655 0.439485982488 Henry Cohn, 2026, needs more optimization.
14 656 0.440441303827 Henry Cohn, 2026, needs more optimization.
14 657 0.440811539535 Henry Cohn, 2026, needs more optimization.
14 658 0.440996116621 Henry Cohn, 2026, needs more optimization.
14 659 0.441381729354 Henry Cohn, 2026, needs more optimization.
14 660 0.442014633557 Henry Cohn, 2026, needs more optimization.
14 661 0.442055309705 Henry Cohn, 2026, needs more optimization.
14 662 0.442182388700 Henry Cohn, 2026, needs more optimization.
14 663 0.442317731277 Henry Cohn, 2026, needs more optimization.
14 664 0.442782413832 Henry Cohn, 2026, needs more optimization.
14 665 0.443554084639 Henry Cohn, 2026, needs more optimization.
14 666 0.444032106190 Henry Cohn, 2026, needs more optimization.
14 667 0.444478786513 Henry Cohn, 2026, needs more optimization.
14 668 0.444533013069 Henry Cohn, 2026, needs more optimization.
14 669 0.444866882593 Henry Cohn, 2026, needs more optimization.
14 670 0.445466314357 Henry Cohn, 2026, needs more optimization.
14 671 0.445792542605 Henry Cohn, 2026, needs more optimization.
14 672 0.446304407354 Henry Cohn, 2026, needs more optimization.
14 673 0.446396345477 Henry Cohn, 2026, needs more optimization.
14 674 0.446492711387 Henry Cohn, 2026, needs more optimization.
14 675 0.446774602567 Henry Cohn, 2026, needs more optimization.
14 676 0.446906481692 Henry Cohn, 2026, needs more optimization.
14 677 0.447030014544 Henry Cohn, 2026, needs more optimization.
14 678 0.447152636698 Henry Cohn, 2026, needs more optimization.
14 679 0.447431277874 Henry Cohn, 2026, needs more optimization.
14 680 0.447698760896 Henry Cohn, 2026, needs more optimization.
14 681 0.447768960585 Henry Cohn, 2026, needs more optimization.
14 682 0.448145025094 Henry Cohn, 2026, needs more optimization.
14 683 0.448486084797 Henry Cohn, 2026, needs more optimization.
14 684 0.448743014108 Henry Cohn, 2026, needs more optimization.
14 685 0.448763454966 Henry Cohn, 2026, needs more optimization.
14 686 0.448878163797 Henry Cohn, 2026, needs more optimization.
14 687 0.448981299389 Henry Cohn, 2026, needs more optimization.
14 688 0.449138964388 Henry Cohn, 2026, needs more optimization.
14 689 0.449411130102 Henry Cohn, 2026, needs more optimization.
14 690 0.449617620679 Henry Cohn, 2026, needs more optimization.
14 691 0.449751657819 Henry Cohn, 2026, needs more optimization.
14 692 0.449841004473 Henry Cohn, 2026, needs more optimization.
14 693 0.450073712654 Henry Cohn, 2026, needs more optimization.
14 694 0.450300804922 Henry Cohn, 2026, needs more optimization.
14 696 0.450624285328 Henry Cohn, 2026, needs more optimization.
14 697 0.450767193727 Henry Cohn, 2026, needs more optimization.
14 698 0.450913698339 Henry Cohn, 2026, needs more optimization.
14 699 0.453775179496 Henry Cohn, 2026, needs more optimization.
14 700 0.453780468284 Henry Cohn, 2026, needs more optimization.
14 703 0.453807433546 Henry Cohn, 2026, needs more optimization.
14 704 0.453821018147 Henry Cohn, 2026, needs more optimization.
14 705 0.453867430809 Henry Cohn, 2026, needs more optimization.
14 706 0.453930324712 Henry Cohn, 2026, needs more optimization.
14 707 0.453944047622 Henry Cohn, 2026, needs more optimization.
14 708 0.453956553538 Henry Cohn, 2026, needs more optimization.
14 719 0.454132437118 Henry Cohn, 2026, needs more optimization.
14 896 0.454545454546 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
11⁢x−5
14 897 0.454719198234 Henry Cohn, 2026, needs more optimization.
14 898 0.454817707458 Henry Cohn, 2026, needs more optimization.
14 899 0.454840724962 Henry Cohn, 2026, needs more optimization.
14 900 0.454885871897 Henry Cohn, 2026, needs more optimization.
14 901 0.454907173238 Henry Cohn, 2026, needs more optimization.
14 902 0.454950116357 Henry Cohn, 2026, needs more optimization.
14 903 0.454976116300 Henry Cohn, 2026, needs more optimization.
14 904 0.455052949584 Henry Cohn, 2026, needs more optimization.
14 905 0.455088331951 Henry Cohn, 2026, needs more optimization.
14 906 0.455095640190 Henry Cohn, 2026, needs more optimization.
14 907 0.455107633265 Henry Cohn, 2026, needs more optimization.
14 908 0.455119023736 Henry Cohn, 2026, needs more optimization.
14 909 0.455139329462 Henry Cohn, 2026, needs more optimization.
14 910 0.455157160639 Henry Cohn, 2026, needs more optimization.
14 911 0.455173524036 Henry Cohn, 2026, needs more optimization.
14 912 0.455184631994 Henry Cohn, 2026, needs more optimization.
14 913 0.455195894634 Henry Cohn, 2026, needs more optimization.
14 914 0.455207946351 Henry Cohn, 2026, needs more optimization.
14 915 0.455222098326 Henry Cohn, 2026, needs more optimization.
14 916 0.455247174489 Henry Cohn, 2026, needs more optimization.
14 917 0.455257912262 Henry Cohn, 2026, needs more optimization.
14 918 0.455283172844 Henry Cohn, 2026, needs more optimization.
14 919 0.455313511269 Henry Cohn, 2026, needs more optimization.
14 920 0.455324165934 Henry Cohn, 2026, needs more optimization.
14 921 0.455337179523 Henry Cohn, 2026, needs more optimization.
14 922 0.455343293379 Henry Cohn, 2026, needs more optimization.
14 924 0.455348894148 Henry Cohn, 2026, needs more optimization.
14 925 0.455351203128 Henry Cohn, 2026, needs more optimization.
14 926 0.455358547473 Henry Cohn, 2026, needs more optimization.
14 927 0.455366123620 Henry Cohn, 2026, needs more optimization.
14 928 0.455369060002 Henry Cohn, 2026, needs more optimization.
14 929 0.455374081578 Henry Cohn, 2026, needs more optimization.
14 930 0.455378559501 Henry Cohn, 2026, needs more optimization.
14 931 0.455380566031 Henry Cohn, 2026, needs more optimization.
14 932 0.455388143438 Henry Cohn, 2026, needs more optimization.
14 933 0.455393494380 Henry Cohn, 2026, needs more optimization.
14 934 0.455394915004 Henry Cohn, 2026, needs more optimization.
14 935 0.455397036749 Henry Cohn, 2026, needs more optimization.
14 936 0.455402841336 Henry Cohn, 2026, needs more optimization.
14 937 0.455408325875 Henry Cohn, 2026, needs more optimization.
14 938 0.455412881719 Henry Cohn, 2026, needs more optimization.
14 939 0.455418972906 Henry Cohn, 2026, needs more optimization.
14 940 0.455424794770 Henry Cohn, 2026, needs more optimization.
14 941 0.455428868039 Henry Cohn, 2026, needs more optimization.
14 942 0.455435023372 Henry Cohn, 2026, needs more optimization.
14 943 0.455440173113 Henry Cohn, 2026, needs more optimization.
14 944 0.455446818148 Henry Cohn, 2026, needs more optimization.
14 945 0.455450491925 Henry Cohn, 2026, needs more optimization.
14 946 0.455456617761 Henry Cohn, 2026, needs more optimization.
14 947 0.455459488289 Henry Cohn, 2026, needs more optimization.
14 948 0.455469386987 Henry Cohn, 2026, needs more optimization.
14 949 0.455472905757 Henry Cohn, 2026, needs more optimization.
14 950 0.455477231948 Henry Cohn, 2026, needs more optimization.
14 951 0.455486008927 Henry Cohn, 2026, needs more optimization.
14 952 0.455492851441 Henry Cohn, 2026, needs more optimization.
14 953 0.455498363764 Henry Cohn, 2026, needs more optimization.
14 954 0.455509117681 Henry Cohn, 2026, needs more optimization.
14 955 0.455512297149 Henry Cohn, 2026, needs more optimization.
14 956 0.455534335290 Henry Cohn, 2026, needs more optimization.
14 957 0.455539856909 Henry Cohn, 2026, needs more optimization.
14 958 0.455546202926 Henry Cohn, 2026, needs more optimization.
14 959 0.455553496740 Henry Cohn, 2026, needs more optimization.
14 960 0.455556786875 Henry Cohn, 2026, needs more optimization.
14 961 0.455562812224 Henry Cohn, 2026, needs more optimization.
14 962 0.455567615102 Henry Cohn, 2026, needs more optimization.
14 963 0.455576959829 Henry Cohn, 2026, needs more optimization.
14 964 0.455585396323 Henry Cohn, 2026, needs more optimization.
14 965 0.455592448863 Henry Cohn, 2026, needs more optimization.
14 966 0.455598544130 Henry Cohn, 2026, needs more optimization.
14 967 0.455603819071 Henry Cohn, 2026, needs more optimization.
14 968 0.455609714686 Henry Cohn, 2026, needs more optimization.
14 969 0.455612698212 Henry Cohn, 2026, needs more optimization.
14 970 0.455615965222 Numaro AI Autoresearch, 11,000+ New Verified Spherical-Code Records from AI Autoresearch, Numaro Research Report NUMARO-2026-015 (2026), https://numaro.tech/research/spherical-codes-2026/.
14 971 0.455625986021 Henry Cohn, 2026, needs more optimization.
14 972 0.455631652153 Henry Cohn, 2026, needs more optimization.
14 973 0.455635614930 Henry Cohn, 2026, needs more optimization.
14 974 0.455639935748 Henry Cohn, 2026, needs more optimization.
14 975 0.455647040535 Henry Cohn, 2026, needs more optimization.
14 976 0.455654185310 Henry Cohn, 2026, needs more optimization.
14 978 0.456270230206 Henry Cohn, 2026, needs more optimization.
14 979 0.456270569651 Henry Cohn, 2026, needs more optimization.
14 980 0.456270930923 Henry Cohn, 2026, needs more optimization.
14 982 0.456273066617 Henry Cohn, 2026, needs more optimization.
14 983 0.456274508650 Henry Cohn, 2026, needs more optimization.
14 984 0.456277085636 Henry Cohn, 2026, needs more optimization.
14 985 0.456278009810 Henry Cohn, 2026, needs more optimization.
14 987 0.456280194417 Henry Cohn, 2026, needs more optimization.
14 988 0.456282226412 Henry Cohn, 2026, needs more optimization.
14 989 0.456282974570 Henry Cohn, 2026, needs more optimization.
14 990 0.456284663933 Henry Cohn, 2026, needs more optimization.
14 992 0.456286926875 Henry Cohn, 2026, needs more optimization.
14 993 0.456287405313 Henry Cohn, 2026, needs more optimization.
14 994 0.456288196917 Henry Cohn, 2026, needs more optimization.
14 995 0.456291833889 Henry Cohn, 2026, needs more optimization.
14 996 0.456293301056 Henry Cohn, 2026, needs more optimization.
14 997 0.456295234564 Henry Cohn, 2026, needs more optimization.
14 999 0.456296682794 Henry Cohn, 2026, needs more optimization.
14 1002 0.456301214971 Henry Cohn, 2026, needs more optimization.
14 1003 0.456302021247 Henry Cohn, 2026, needs more optimization.
14 1006 0.456303374549 Henry Cohn, 2026, needs more optimization.
14 1007 0.456303663437 Henry Cohn, 2026, needs more optimization.
14 1008 0.456304792458 Henry Cohn, 2026, needs more optimization.
14 1009 0.456305531850 Henry Cohn, 2026, needs more optimization.
14 1010 0.456308639747 Henry Cohn, 2026, needs more optimization.
14 1012 0.456313716099 Henry Cohn, 2026, needs more optimization.
14 1014 0.456314685518 Henry Cohn, 2026, needs more optimization.
14 1015 0.456314884854 Henry Cohn, 2026, needs more optimization.
14 1016 0.457548189823 Numaro AI Autoresearch, 11,000+ New Verified Spherical-Code Records from AI Autoresearch, Numaro Research Report NUMARO-2026-015 (2026), https://numaro.tech/research/spherical-codes-2026/.
14 1017 0.457550752802 Numaro AI Autoresearch, 11,000+ New Verified Spherical-Code Records from AI Autoresearch, Numaro Research Report NUMARO-2026-015 (2026), https://numaro.tech/research/spherical-codes-2026/.
14 1018 0.457552900659 Numaro AI Autoresearch, 11,000+ New Verified Spherical-Code Records from AI Autoresearch, Numaro Research Report NUMARO-2026-015 (2026), https://numaro.tech/research/spherical-codes-2026/.
14 1019 0.457558070390 Numaro AI Autoresearch, 11,000+ New Verified Spherical-Code Records from AI Autoresearch, Numaro Research Report NUMARO-2026-015 (2026), https://numaro.tech/research/spherical-codes-2026/.
14 1020 0.457564741926 Numaro AI Autoresearch, 11,000+ New Verified Spherical-Code Records from AI Autoresearch, Numaro Research Report NUMARO-2026-015 (2026), https://numaro.tech/research/spherical-codes-2026/.
14 1021 0.457573609024 Numaro AI Autoresearch, 11,000+ New Verified Spherical-Code Records from AI Autoresearch, Numaro Research Report NUMARO-2026-015 (2026), https://numaro.tech/research/spherical-codes-2026/.
14 1022 0.457580644657 Numaro AI Autoresearch, 11,000+ New Verified Spherical-Code Records from AI Autoresearch, Numaro Research Report NUMARO-2026-015 (2026), https://numaro.tech/research/spherical-codes-2026/.
14 1023 0.457585148686 Numaro AI Autoresearch, 11,000+ New Verified Spherical-Code Records from AI Autoresearch, Numaro Research Report NUMARO-2026-015 (2026), https://numaro.tech/research/spherical-codes-2026/.
14 1024 0.457589696189 Numaro AI Autoresearch, 11,000+ New Verified Spherical-Code Records from AI Autoresearch, Numaro Research Report NUMARO-2026-015 (2026), https://numaro.tech/research/spherical-codes-2026/.
15 31 0.050237120373 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
2535⁢x3−225⁢x2−15⁢x+1
15 32 0.058900808489 H. Cohn, Small spherical and projective codes, data set, 2022, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
15 33 0.062706770083 Henry Cohn, 2023.
Minimal polynomial listed in plain text data
15 34 0.066570393658 Henry Cohn, 2025.
15 35 0.070509992992 Henry Cohn, 2023.
15 36 0.070779968044 Henry Cohn, 2023.
5937⁢x4+412⁢x3−202⁢x2−4⁢x+1
15 37 0.078785666352 Henry Cohn, 2025.
15 38 0.079970260232 Henry Cohn, 2026.
15 39 0.082681671944 Henry Cohn, 2023.
347087⁢x8+1080416⁢x7+305012⁢x6+3648⁢x5−20054⁢x4−160⁢x3+276⁢x2−1
15 40 0.086159367074 Henry Cohn, 2023.
15 41 0.093058708471 Henry Cohn, 2026.
15 42 0.096809796022 Henry Cohn, 2023.
15 43 0.099863843733 Henry Cohn, 2025.
15 44 0.099976426707 Henry Cohn, 2025.
15 45 0.102626460761 Henry Cohn, 2026.
15 46 0.110795000982 Henry Cohn, 2025.
15 47 0.111165028345 Henry Cohn, 2026.
15 48 0.112519700675 Henry Cohn, 2026.
15 52 0.112912613537 Henry Cohn, 2025.
167⁢x2−10⁢x−1
15 57 0.115470053838 Henry Cohn, 2024.
75⁢x2−1
15 58 0.119568772343 Henry Cohn, 2025.
15 61 0.128458591981 Henry Cohn, 2025.
263⁢x2−26⁢x−1
15 62 0.129608604388 Henry Cohn, 2026.
15 63 0.129675303921 Henry Cohn, 2026, needs more optimization.
15 64 0.129676245976 Henry Cohn, 2025, needs more optimization.
15 65 0.129676247045 Henry Cohn, 2026, needs more optimization.
15 66 0.142849849465 Henry Cohn, 2025.
15 67 0.144353409494 Henry Cohn, 2023.
15 68 0.146740451793 Henry Cohn, 2026.
15 69 0.160033734974 Henry Cohn, 2024.
15 70 0.160964563056 Henry Cohn, 2024.
15 73 0.161462093425 Henry Cohn, 2026.
15 76 0.168269539561 Henry Cohn, 2026, needs more optimization.
15 77 0.168276608035 Henry Cohn, 2026, needs more optimization.
15 78 0.168276608054 Henry Cohn, 2026, needs more optimization.
15 92 0.168685175113 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
47⁢x2−2⁢x−1
15 93 0.169916676995 Henry Cohn, 2025.
169⁢x4−56⁢x3−30⁢x2+1
15 94 0.186858652290 Henry Cohn, 2026.
15 95 0.187077042680 Henry Cohn, 2026, needs more optimization.
15 96 0.187887288776 Henry Cohn, 2026, needs more optimization.
15 99 0.188666328568 Henry Cohn, 2026, needs more optimization.
15 100 0.189726990692 Henry Cohn, 2026, needs more optimization.
15 101 0.197671411404 Henry Cohn, 2026, needs more optimization.
15 102 0.197758492075 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
15 108 0.199301661815 Henry Cohn, 2026.
347⁢x2−24⁢x−9
15 128 0.2 T. Ericson and V. Zinoviev, Spherical codes generated by binary partitions of symmetric pointsets, IEEE Trans. Inform. Theory 41 (1995), 107–129, doi:10.1109/18.370114.
5⁢x−1
15 129 0.209693852047 Henry Cohn, 2026.
15 130 0.216435024466 Henry Cohn, 2026, needs more optimization.
15 131 0.219738366868 Henry Cohn, 2026, needs more optimization.
15 132 0.221692066410 Henry Cohn, 2026, needs more optimization.
15 135 0.223068626266 Henry Cohn, 2026, needs more optimization.
15 136 0.225990151252 Henry Cohn, 2026.
15 137 0.226886067313 Henry Cohn, 2026, needs more optimization.
15 142 0.227160244714 Henry Cohn, 2026.
15 143 0.232245360831 Numaro AI Autoresearch, 11,000+ New Verified Spherical-Code Records from AI Autoresearch, Numaro Research Report NUMARO-2026-015 (2026), https://numaro.tech/research/spherical-codes-2026/.
15 144 0.235179709766 Henry Cohn, 2026, needs more optimization.
15 145 0.237559195353 Henry Cohn, 2026, needs more optimization.
15 146 0.238420970519 Henry Cohn, 2026, needs more optimization.
15 147 0.238761561006 Henry Cohn, 2026, needs more optimization.
15 149 0.239294215248 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
15 150 0.239558257200 Henry Cohn, 2026, needs more optimization.
15 151 0.239558257213 Henry Cohn, 2026, needs more optimization.
15 152 0.244616813220 Henry Cohn, 2026, needs more optimization.
15 153 0.245232909425 Henry Cohn, 2026, needs more optimization.
15 156 0.248124762896 Henry Cohn, 2026, needs more optimization.
15 157 0.249069470433 Henry Cohn, 2026.
15 158 0.253983486551 Henry Cohn, 2026, needs more optimization.
15 159 0.254468242039 Henry Cohn, 2026, needs more optimization.
15 160 0.254872968711 Henry Cohn, 2026, needs more optimization.
15 161 0.255430934328 Henry Cohn, 2026, needs more optimization.
15 162 0.255981620395 Henry Cohn, 2026, needs more optimization.
15 163 0.257075007896 Henry Cohn, 2026, needs more optimization.
15 164 0.257358935255 Henry Cohn, 2026, needs more optimization.
15 165 0.257391616061 Henry Cohn, 2026, needs more optimization.
15 166 0.257475870539 Henry Cohn, 2026, needs more optimization.
15 167 0.257675998992 Henry Cohn, 2026, needs more optimization.
15 168 0.257852946391 Henry Cohn, 2026, needs more optimization.
15 169 0.258053740983 Henry Cohn, 2026, needs more optimization.
15 170 0.258178686633 Henry Cohn, 2026, needs more optimization.
15 171 0.258365885462 Henry Cohn, 2026, needs more optimization.
15 172 0.258496411309 Henry Cohn, 2026, needs more optimization.
15 173 0.258642110145 Henry Cohn, 2026, needs more optimization.
15 174 0.258727924192 Henry Cohn, 2026, needs more optimization.
15 175 0.258887567112 Henry Cohn, 2026, needs more optimization.
15 176 0.259187685500 Henry Cohn, 2026, needs more optimization.
15 177 0.259562229888 Henry Cohn, 2026, needs more optimization.
15 178 0.259842955350 Henry Cohn, 2026, needs more optimization.
15 179 0.259991881829 Henry Cohn, 2026, needs more optimization.
15 180 0.259992096747 Henry Cohn, 2026, needs more optimization.
15 181 0.260002729182 Henry Cohn, 2026, needs more optimization.
15 182 0.260020124135 Henry Cohn, 2026, needs more optimization.
15 183 0.260128334592 Henry Cohn, 2026, needs more optimization.
15 184 0.260236480218 Henry Cohn, 2026, needs more optimization.
15 185 0.260319703104 Henry Cohn, 2026, needs more optimization.
15 186 0.260377899685 Henry Cohn, 2026, needs more optimization.
15 187 0.260799388302 Henry Cohn, 2026, needs more optimization.
15 188 0.261261056002 Henry Cohn, 2026, needs more optimization.
15 189 0.261738787597 Henry Cohn, 2026, needs more optimization.
15 190 0.262062300382 Henry Cohn, 2026, needs more optimization.
15 191 0.262528165779 Henry Cohn, 2026, needs more optimization.
15 192 0.262840127992 Henry Cohn, 2026, needs more optimization.
15 193 0.263166332849 Henry Cohn, 2026, needs more optimization.
15 194 0.263449664817 Henry Cohn, 2026, needs more optimization.
15 195 0.263683054382 Henry Cohn, 2026, needs more optimization.
15 196 0.263857027540 Henry Cohn, 2026, needs more optimization.
15 197 0.264006784181 Henry Cohn, 2026, needs more optimization.
15 198 0.264187682546 Henry Cohn, 2026, needs more optimization.
15 199 0.264359466476 Henry Cohn, 2026, needs more optimization.
15 200 0.264511777357 Henry Cohn, 2026, needs more optimization.
15 201 0.264666625284 Henry Cohn, 2026, needs more optimization.
15 202 0.264800152607 Henry Cohn, 2026, needs more optimization.
15 203 0.264941288551 Henry Cohn, 2026, needs more optimization.
15 204 0.265062532376 Henry Cohn, 2026, needs more optimization.
15 205 0.265175146062 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
15 206 0.265280235491 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
15 207 0.265424038574 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
15 208 0.265531313478 Henry Cohn, 2026, needs more optimization.
15 209 0.265668672289 Henry Cohn, 2026, needs more optimization.
15 210 0.265783974255 Henry Cohn, 2026, needs more optimization.
15 211 0.265951552753 Henry Cohn, 2026, needs more optimization.
15 212 0.265981663211 Henry Cohn, 2026, needs more optimization.
15 213 0.266095931907 Henry Cohn, 2026, needs more optimization.
15 214 0.266230466933 Henry Cohn, 2026, needs more optimization.
15 215 0.266322309599 Henry Cohn, 2026, needs more optimization.
15 218 0.266362814739 Henry Cohn, 2026, needs more optimization.
15 219 0.266440308323 Henry Cohn, 2026, needs more optimization.
15 220 0.266583431141 Henry Cohn, 2026, needs more optimization.
15 221 0.273150769639 Henry Cohn, 2026, needs more optimization.
15 222 0.284143682917 Henry Cohn, 2026, needs more optimization.
15 223 0.284248874641 Henry Cohn, 2026, needs more optimization.
15 224 0.284358484333 Henry Cohn, 2026, needs more optimization.
15 225 0.285445080925 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
15 229 0.285514881221 Henry Cohn, 2026, needs more optimization.
15 230 0.285521870177 Henry Cohn, 2026, needs more optimization.
15 231 0.285524873559 Henry Cohn, 2026, needs more optimization.
15 232 0.285526420332 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
15 233 0.285536057954 Henry Cohn, 2026, needs more optimization.
15 234 0.285542658647 Henry Cohn, 2026, needs more optimization.
15 235 0.285554981596 Henry Cohn, 2026, needs more optimization.
15 236 0.285562819368 Henry Cohn, 2026, needs more optimization.
15 237 0.285572812768 Henry Cohn, 2026, needs more optimization.
15 238 0.285588158792 Henry Cohn, 2026, needs more optimization.
15 239 0.285607662545 Henry Cohn, 2026, needs more optimization.
15 240 0.285631201311 Henry Cohn, 2026, needs more optimization.
15 241 0.285655301683 Henry Cohn, 2026, needs more optimization.
15 242 0.285672695618 Henry Cohn, 2026, needs more optimization.
15 243 0.286368647226 Henry Cohn, 2026, needs more optimization.
15 244 0.286856261632 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
15 245 0.287245508174 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
15 246 0.287611448663 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
15 247 0.288090813571 Henry Cohn, 2026, needs more optimization.
15 248 0.288361312607 Henry Cohn, 2026, needs more optimization.
15 249 0.291752355455 Henry Cohn, 2026, needs more optimization.
15 250 0.294425453136 Henry Cohn, 2026, needs more optimization.
15 251 0.296602591600 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
15 252 0.297772003102 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
15 253 0.297826535610 Henry Cohn, 2026, needs more optimization.
15 254 0.297925421026 Henry Cohn, 2026, needs more optimization.
15 256 0.297926304913 Henry Cohn, 2026.
15 257 0.302589972218 Henry Cohn, 2026, needs more optimization.
15 258 0.304496844238 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
15 259 0.305956224632 Henry Cohn, 2026, needs more optimization.
15 260 0.307183763306 Henry Cohn, 2026, needs more optimization.
15 261 0.308188885306 Henry Cohn, 2026, needs more optimization.
15 262 0.309418185500 Henry Cohn, 2026, needs more optimization.
15 263 0.309487827396 Henry Cohn, 2026, needs more optimization.
15 264 0.309629622676 Henry Cohn, 2026, needs more optimization.
15 265 0.312019011213 Henry Cohn, 2026, needs more optimization.
15 266 0.313588007464 Henry Cohn, 2026, needs more optimization.
15 267 0.314997636963 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
15 268 0.315497408031 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
15 269 0.316298128740 Henry Cohn, 2026, needs more optimization.
15 270 0.316564747477 Henry Cohn, 2026, needs more optimization.
15 271 0.319100482850 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
15 272 0.321140962165 Henry Cohn, 2026, needs more optimization.
15 273 0.323424042988 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
15 274 0.324905714853 Henry Cohn, 2026, needs more optimization.
15 275 0.326534216016 Henry Cohn, 2026, needs more optimization.
15 276 0.328190852917 Henry Cohn, 2026, needs more optimization.
15 277 0.329935101350 Henry Cohn, 2026, needs more optimization.
15 278 0.331056026153 Henry Cohn, 2026, needs more optimization.
15 279 0.332709973686 Henry Cohn, 2026, needs more optimization.
15 320 0.333333333334 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
3⁢x−1
15 321 0.339294291647 Henry Cohn, 2026, needs more optimization.
15 322 0.340372593682 Henry Cohn, 2026, needs more optimization.
15 323 0.341167529363 Henry Cohn, 2026, needs more optimization.
15 324 0.341829497223 Henry Cohn, 2026, needs more optimization.
15 325 0.342381374003 Henry Cohn, 2026, needs more optimization.
15 326 0.342761028495 Henry Cohn, 2026, needs more optimization.
15 327 0.343116641126 Henry Cohn, 2026, needs more optimization.
15 328 0.343550710210 Henry Cohn, 2026, needs more optimization.
15 329 0.343818999479 Henry Cohn, 2026, needs more optimization.
15 330 0.344477595746 Henry Cohn, 2026, needs more optimization.
15 331 0.345410642400 Henry Cohn, 2026, needs more optimization.
15 332 0.345738285773 Henry Cohn, 2026, needs more optimization.
15 333 0.346488969209 Henry Cohn, 2026, needs more optimization.
15 334 0.347005482769 Henry Cohn, 2026, needs more optimization.
15 335 0.347208952821 Henry Cohn, 2026, needs more optimization.
15 336 0.347471523838 Henry Cohn, 2026, needs more optimization.
15 337 0.347843277456 Henry Cohn, 2026, needs more optimization.
15 338 0.347997449467 Henry Cohn, 2026, needs more optimization.
15 339 0.348165976160 Henry Cohn, 2026, needs more optimization.
15 340 0.348371420269 Henry Cohn, 2026, needs more optimization.
15 341 0.348550143761 Henry Cohn, 2026, needs more optimization.
15 342 0.348831040924 Henry Cohn, 2026, needs more optimization.
15 343 0.349068817683 Henry Cohn, 2026, needs more optimization.
15 344 0.349235140520 Henry Cohn, 2026, needs more optimization.
15 345 0.349398986403 Henry Cohn, 2026, needs more optimization.
15 346 0.349616451122 Henry Cohn, 2026, needs more optimization.
15 347 0.350144714574 Henry Cohn, 2026, needs more optimization.
15 348 0.350468623509 Henry Cohn, 2026, needs more optimization.
15 349 0.350824928373 Henry Cohn, 2026, needs more optimization.
15 350 0.351097195930 Henry Cohn, 2026, needs more optimization.
15 351 0.351295761303 Henry Cohn, 2026, needs more optimization.
15 352 0.351647176973 Henry Cohn, 2026, needs more optimization.
15 353 0.352022838447 Henry Cohn, 2026, needs more optimization.
15 354 0.352269568195 Henry Cohn, 2026, needs more optimization.
15 355 0.352542875815 Henry Cohn, 2026, needs more optimization.
15 356 0.352743610903 Henry Cohn, 2026, needs more optimization.
15 357 0.352948147731 Henry Cohn, 2026, needs more optimization.
15 358 0.353274967188 Henry Cohn, 2026, needs more optimization.
15 359 0.353524426473 Henry Cohn, 2026, needs more optimization.
15 360 0.353747557081 Henry Cohn, 2026, needs more optimization.
15 362 0.355511428880 Henry Cohn, 2026, needs more optimization.
15 363 0.355524296626 Henry Cohn, 2026, needs more optimization.
15 364 0.355533728276 Henry Cohn, 2026, needs more optimization.
15 365 0.355572293386 Henry Cohn, 2026, needs more optimization.
15 366 0.355576839993 Henry Cohn, 2026, needs more optimization.
15 367 0.355613220331 Henry Cohn, 2026, needs more optimization.
15 368 0.355626877757 Henry Cohn, 2026, needs more optimization.
15 369 0.355652248375 Henry Cohn, 2026, needs more optimization.
15 370 0.355682689945 Henry Cohn, 2026, needs more optimization.
15 371 0.355741629825 Henry Cohn, 2026, needs more optimization.
15 372 0.355760698116 Henry Cohn, 2026, needs more optimization.
15 373 0.356497085974 Henry Cohn, 2026, needs more optimization.
15 374 0.356836770389 Henry Cohn, 2026, needs more optimization.
15 375 0.356847132881 Henry Cohn, 2026, needs more optimization.
15 376 0.358253660425 Henry Cohn, 2026, needs more optimization.
15 377 0.358275553798 Henry Cohn, 2026, needs more optimization.
15 378 0.358282791964 Henry Cohn, 2026, needs more optimization.
15 379 0.358283349013 Henry Cohn, 2026, needs more optimization.
15 380 0.358286657805 Henry Cohn, 2026, needs more optimization.
15 381 0.360085867462 Henry Cohn, 2026, needs more optimization.
15 382 0.360735575469 Henry Cohn, 2026, needs more optimization.
15 383 0.361398999321 Henry Cohn, 2026, needs more optimization.
15 384 0.362686502900 Henry Cohn, 2026, needs more optimization.
15 385 0.363039002574 Henry Cohn, 2026, needs more optimization.
15 386 0.363873811230 Henry Cohn, 2026, needs more optimization.
15 387 0.364543981306 Henry Cohn, 2026, needs more optimization.
15 388 0.365651331254 Henry Cohn, 2026, needs more optimization.
15 389 0.366149129447 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
15 390 0.366783064617 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
15 391 0.367234215010 Henry Cohn, 2026, needs more optimization.
15 392 0.367945346703 Henry Cohn, 2026, needs more optimization.
15 393 0.368560034725 Henry Cohn, 2026, needs more optimization.
15 394 0.368923180772 Henry Cohn, 2026, needs more optimization.
15 395 0.369455747927 Henry Cohn, 2026, needs more optimization.
15 396 0.370024820660 Henry Cohn, 2026, needs more optimization.
15 397 0.370266340422 Henry Cohn, 2026, needs more optimization.
15 424 0.370431040067 Henry Cohn, 2026.
287⁢x2−190⁢x+31
15 425 0.370431040067 A. Kravatsky, V. Khrulkov, and I. Oseledets, ImprovEvolve: basin-hopping meets LLM-guided evolutionary search, ICML 2026 AI4Math Workshop Poster, https://openreview.net/forum?id=nE1q0gRDNr, arXiv:2602.10233, after some further optimization.
287⁢x2−190⁢x+31
15 426 0.372209293489 Henry Cohn, 2026, needs more optimization.
15 427 0.373360008117 Henry Cohn, 2026, needs more optimization.
15 428 0.374921306726 Henry Cohn, 2026, needs more optimization.
15 430 0.374922602359 Henry Cohn, 2026, needs more optimization.
15 431 0.374922944117 Henry Cohn, 2026, needs more optimization.
15 432 0.374922997977 Henry Cohn, 2026, needs more optimization.
15 433 0.374963897659 Henry Cohn, 2026, needs more optimization.
15 434 0.374964026594 Henry Cohn, 2026, needs more optimization.
15 435 0.375013080432 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
15 461 0.376462890262 Henry Cohn, 2026, needs more optimization.
15 462 0.376564758957 Henry Cohn, 2026, needs more optimization.
15 466 0.376621612570 Henry Cohn, 2026, needs more optimization.
15 467 0.381192425811 Henry Cohn, 2026, needs more optimization.
15 468 0.382726692026 Henry Cohn, 2026, needs more optimization.
15 469 0.383963705951 Henry Cohn, 2026, needs more optimization.
15 470 0.385340985961 Henry Cohn, 2026, needs more optimization.
15 471 0.386197400456 Henry Cohn, 2026, needs more optimization.
15 472 0.386905286449 Henry Cohn, 2026, needs more optimization.
15 480 0.387503296749 Henry Cohn, 2026, needs more optimization.
15 481 0.390135295314 Henry Cohn, 2026, needs more optimization.
15 482 0.392363245767 Henry Cohn, 2026, needs more optimization.
15 483 0.392370003925 Henry Cohn, 2026, needs more optimization.
15 485 0.392370004218 Henry Cohn, 2026, needs more optimization.
15 486 0.392420077155 Henry Cohn, 2026, needs more optimization.
15 487 0.392427801597 Henry Cohn, 2026, needs more optimization.
15 489 0.392497530212 Henry Cohn, 2026, needs more optimization.
15 490 0.392498693543 Henry Cohn, 2026, needs more optimization.
15 491 0.392521308795 Henry Cohn, 2026, needs more optimization.
15 492 0.392523115553 Henry Cohn, 2026, needs more optimization.
15 494 0.392680159723 Henry Cohn, 2026, needs more optimization.
15 495 0.392695924429 Henry Cohn, 2026, needs more optimization.
15 496 0.392787420722 Henry Cohn, 2026, needs more optimization.
15 498 0.392831410484 Henry Cohn, 2026, needs more optimization.
15 499 0.392897446006 Henry Cohn, 2026, needs more optimization.
15 500 0.392908790451 Henry Cohn, 2026, needs more optimization.
15 501 0.392917835953 Henry Cohn, 2026, needs more optimization.
15 502 0.392988724966 Henry Cohn, 2026, needs more optimization.
15 504 0.393001971678 Henry Cohn, 2026, needs more optimization.
15 505 0.393078814625 Henry Cohn, 2026, needs more optimization.
15 506 0.393129805521 Henry Cohn, 2026, needs more optimization.
15 507 0.393141534758 Henry Cohn, 2026, needs more optimization.
15 508 0.393142500437 Henry Cohn, 2026, needs more optimization.
15 509 0.393312435437 Henry Cohn, 2026, needs more optimization.
15 510 0.393830776886 Henry Cohn, 2026, needs more optimization.
15 511 0.393876064928 Henry Cohn, 2026, needs more optimization.
15 513 0.393897605210 Henry Cohn, 2026, needs more optimization.
15 514 0.394023011920 Henry Cohn, 2026, needs more optimization.
15 515 0.394054735730 Henry Cohn, 2026, needs more optimization.
15 516 0.394256286682 Henry Cohn, 2026, needs more optimization.
15 517 0.394319680216 Henry Cohn, 2026, needs more optimization.
15 518 0.394665710177 Henry Cohn, 2026, needs more optimization.
15 519 0.394880818814 Henry Cohn, 2026, needs more optimization.
15 520 0.395130834167 Henry Cohn, 2026, needs more optimization.
15 521 0.395280035337 Henry Cohn, 2026, needs more optimization.
15 522 0.395565882482 Henry Cohn, 2026, needs more optimization.
15 523 0.395958736763 Henry Cohn, 2026, needs more optimization.
15 524 0.396031386804 Henry Cohn, 2026, needs more optimization.
15 525 0.396074266504 Henry Cohn, 2026, needs more optimization.
15 526 0.396112038086 Henry Cohn, 2026, needs more optimization.
15 527 0.396559557370 Henry Cohn, 2026, needs more optimization.
15 528 0.396569801880 Henry Cohn, 2026, needs more optimization.
15 529 0.396812529039 Henry Cohn, 2026, needs more optimization.
15 530 0.396961977256 Henry Cohn, 2026, needs more optimization.
15 531 0.397062319294 Henry Cohn, 2026, needs more optimization.
15 532 0.397153878317 Henry Cohn, 2026, needs more optimization.
15 533 0.397555373410 Henry Cohn, 2026, needs more optimization.
15 534 0.397569692805 Henry Cohn, 2026, needs more optimization.
15 535 0.397747435113 Henry Cohn, 2026, needs more optimization.
15 536 0.397786399450 Henry Cohn, 2026, needs more optimization.
15 537 0.398147022100 Henry Cohn, 2026, needs more optimization.
15 538 0.398189358755 Henry Cohn, 2026, needs more optimization.
15 539 0.398414580623 Henry Cohn, 2026, needs more optimization.
15 540 0.398518645544 Henry Cohn, 2026, needs more optimization.
15 541 0.398593382063 Henry Cohn, 2026, needs more optimization.
15 542 0.398707135231 Henry Cohn, 2026, needs more optimization.
15 543 0.398776176918 Henry Cohn, 2026, needs more optimization.
15 545 0.399113952468 Henry Cohn, 2026, needs more optimization.
15 546 0.399334960367 Henry Cohn, 2026, needs more optimization.
15 547 0.399632692962 Henry Cohn, 2026, needs more optimization.
15 672 0.4 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
5⁢x−2
15 688 0.4 Henry Cohn, 2025, by enlarging a code from T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
5⁢x−2
15 689 0.404117037740 Henry Cohn, 2026.
15 690 0.407439006131 Henry Cohn, 2026, needs more optimization.
15 691 0.410953465183 Henry Cohn, 2026, needs more optimization.
15 692 0.413563860942 Henry Cohn, 2026, needs more optimization.
15 693 0.414188610693 Henry Cohn, 2026, needs more optimization.
15 694 0.414195271360 Henry Cohn, 2026, needs more optimization.
15 695 0.415967461018 Henry Cohn, 2026, needs more optimization.
15 696 0.416264015530 Henry Cohn, 2026, needs more optimization.
15 697 0.417431374089 Henry Cohn, 2026, needs more optimization.
15 698 0.417432265333 Henry Cohn, 2026, needs more optimization.
15 699 0.417743448088 Henry Cohn, 2026, needs more optimization.
15 700 0.417752361568 Henry Cohn, 2026, needs more optimization.
15 701 0.418064025372 Henry Cohn, 2026, needs more optimization.
15 702 0.418401292368 Henry Cohn, 2026, needs more optimization.
15 703 0.418583500545 Henry Cohn, 2026, needs more optimization.
15 704 0.419086363463 Henry Cohn, 2026, needs more optimization.
15 705 0.419255279826 Henry Cohn, 2026, needs more optimization.
15 706 0.419667581738 Henry Cohn, 2026, needs more optimization.
15 707 0.420428828502 Henry Cohn, 2026, needs more optimization.
15 709 0.420934560252 Henry Cohn, 2026, needs more optimization.
15 710 0.420978793153 Henry Cohn, 2026, needs more optimization.
15 711 0.421051966723 Henry Cohn, 2026, needs more optimization.
15 712 0.421219019384 Henry Cohn, 2026, needs more optimization.
15 713 0.421326439559 Henry Cohn, 2026, needs more optimization.
15 714 0.421440783386 Henry Cohn, 2026, needs more optimization.
15 715 0.421602595732 Henry Cohn, 2026, needs more optimization.
15 716 0.421817630920 Henry Cohn, 2026, needs more optimization.
15 717 0.422130794288 Henry Cohn, 2026, needs more optimization.
15 718 0.422327831361 Henry Cohn, 2026, needs more optimization.
15 719 0.422630932582 Henry Cohn, 2026, needs more optimization.
15 720 0.422830914467 Henry Cohn, 2026, needs more optimization.
15 721 0.423000765254 Henry Cohn, 2026, needs more optimization.
15 722 0.423247517685 Henry Cohn, 2026, needs more optimization.
15 723 0.423564851997 Henry Cohn, 2026, needs more optimization.
15 724 0.423840237570 Henry Cohn, 2026, needs more optimization.
15 725 0.424178028687 Henry Cohn, 2026, needs more optimization.
15 726 0.424346180809 Henry Cohn, 2026, needs more optimization.
15 727 0.424521130919 Henry Cohn, 2026, needs more optimization.
15 728 0.424714825569 Henry Cohn, 2026, needs more optimization.
15 729 0.425034860864 Henry Cohn, 2026, needs more optimization.
15 730 0.425114843789 Henry Cohn, 2026, needs more optimization.
15 731 0.425312683393 Henry Cohn, 2026, needs more optimization.
15 732 0.425480562623 Henry Cohn, 2026, needs more optimization.
15 733 0.425629501153 Henry Cohn, 2026, needs more optimization.
15 734 0.425816174768 Henry Cohn, 2026, needs more optimization.
15 735 0.426015232796 Henry Cohn, 2026, needs more optimization.
15 736 0.426104584288 Henry Cohn, 2026, needs more optimization.
15 737 0.426443802713 Henry Cohn, 2026, needs more optimization.
15 738 0.426650111839 Henry Cohn, 2026, needs more optimization.
15 739 0.426758090076 Henry Cohn, 2026, needs more optimization.
15 740 0.427037506398 Henry Cohn, 2026, needs more optimization.
15 741 0.427282350603 Henry Cohn, 2026, needs more optimization.
15 742 0.427392519126 Henry Cohn, 2026, needs more optimization.
15 743 0.427621171315 Henry Cohn, 2026, needs more optimization.
15 744 0.427677899963 Henry Cohn, 2026, needs more optimization.
15 745 0.427857933311 Henry Cohn, 2026, needs more optimization.
15 746 0.427953736795 Henry Cohn, 2026, needs more optimization.
15 747 0.428130397858 Henry Cohn, 2026, needs more optimization.
15 748 0.428318741397 Henry Cohn, 2026, needs more optimization.
15 749 0.428527548047 Henry Cohn, 2026, needs more optimization.
15 990 0.428571428572 T. Ericson and V. Zinoviev, Spherical codes generated by binary partitions of symmetric pointsets, IEEE Trans. Inform. Theory 41 (1995), 107–129, doi:10.1109/18.370114.
7⁢x−3
15 991 0.439534515834 Numaro AI Autoresearch, 11,000+ New Verified Spherical-Code Records from AI Autoresearch, Numaro Research Report NUMARO-2026-015 (2026), https://numaro.tech/research/spherical-codes-2026/.
15 1024 0.454545454546 C. Ma, T. Tao Z., P. Li, M. Liu, H. Chen, Z. Mao, Y. Cheng, Y. Qi, and Y. Yang, Finding kissing numbers with game-theoretic reinforcement learning, preprint, 2025, arXiv:2511.13391.
11⁢x−5
16 33 0.047421028894 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
3136⁢x3−256⁢x2−16⁢x+1
16 34 0.055555555556 T. Ericson and V. Zinoviev, Spherical codes generated by binary partitions of symmetric pointsets, IEEE Trans. Inform. Theory 41 (1995), 107–129, doi:10.1109/18.370114.
18⁢x−1
16 36 0.056002309435 Henry Cohn, 2023.
176⁢x2+8⁢x−1
16 38 0.065186804094 Henry Cohn, 2023.
7312⁢x4+864⁢x3−200⁢x2−8⁢x+1
16 39 0.074285234713 Henry Cohn, 2025.
16 40 0.077433436468 Henry Cohn, 2024.
16 41 0.078328485376 Henry Cohn, 2023.
16 42 0.085112299907 Henry Cohn, 2025.
16 44 0.085376587737 Henry Cohn, 2023.
512⁢x2−32⁢x−1
16 45 0.090651346396 Henry Cohn, 2023.
Minimal polynomial listed in plain text data
16 46 0.095440859515 Henry Cohn, 2025.
16 47 0.097443031003 Henry Cohn, 2025.
16 48 0.098771717854 Henry Cohn, 2023.
143⁢x2−4⁢x−1
16 49 0.105254154031 Henry Cohn, 2025.
16 50 0.108974791166 Henry Cohn, 2026.
16 51 0.111198306019 Henry Cohn, 2025.
16 52 0.111567586034 Henry Cohn, 2026.
16 54 0.112897448890 Henry Cohn, 2026.
16 55 0.113130733100 Henry Cohn, 2026, needs more optimization.
16 58 0.113835450316 Henry Cohn, 2026.
288⁢x2−24⁢x−1
16 59 0.115468708787 Henry Cohn, 2026, needs more optimization.
16 60 0.115470049065 Henry Cohn, 2026, needs more optimization.
16 61 0.119371454413 Henry Cohn, 2025.
16 62 0.125768177302 Henry Cohn, 2025.
16 63 0.127284448392 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
16 74 0.127284656799 Henry Cohn, 2023.
156⁢x2−12⁢x−1
16 75 0.142328493208 Henry Cohn, 2026, needs more optimization.
16 76 0.155906744058 Henry Cohn, 2026, needs more optimization.
16 77 0.156180532477 Henry Cohn, 2026, needs more optimization.
16 78 0.156308508153 Henry Cohn, 2026, needs more optimization.
16 79 0.156684907369 Henry Cohn, 2026, needs more optimization.
16 80 0.156933594040 Henry Cohn, 2026, needs more optimization.
16 81 0.157231026163 Henry Cohn, 2026, needs more optimization.
16 82 0.158312309770 Henry Cohn, 2026, needs more optimization.
16 83 0.158831583909 Henry Cohn, 2026, needs more optimization.
16 84 0.159473252852 Henry Cohn, 2026, needs more optimization.
16 85 0.161142075511 Henry Cohn, 2026, needs more optimization.
16 88 0.168668499420 Henry Cohn, 2025, needs more optimization.
16 89 0.168682927803 Henry Cohn, 2026, needs more optimization.
16 90 0.168683667206 Henry Cohn, 2026, needs more optimization.
16 92 0.168684604646 Henry Cohn, 2025, needs more optimization.
16 94 0.168684943107 Henry Cohn, 2025, needs more optimization.
16 95 0.168685569492 Henry Cohn, 2026, needs more optimization.
16 96 0.168685570157 Henry Cohn, 2026, needs more optimization.
16 97 0.169880683941 Henry Cohn, 2026, needs more optimization.
16 102 0.170753175474 Henry Cohn, 2026.
128⁢x2−16⁢x−1
16 103 0.174178397911 Henry Cohn, 2026.
16 104 0.179202077195 Henry Cohn, 2026, needs more optimization.
16 105 0.183402641544 Henry Cohn, 2026, needs more optimization.
16 106 0.185708759319 Henry Cohn, 2026, needs more optimization.
16 107 0.188005549055 Henry Cohn, 2026, needs more optimization.
16 108 0.190685071253 Henry Cohn, 2026, needs more optimization.
16 109 0.191584447293 Henry Cohn, 2026, needs more optimization.
16 110 0.192049208994 Henry Cohn, 2026, needs more optimization.
16 111 0.192381713999 Henry Cohn, 2026, needs more optimization.
16 112 0.192392774528 Henry Cohn, 2026, needs more optimization.
16 117 0.192450089730 Henry Cohn, 2026.
27⁢x2−1
16 118 0.192450164499 Henry Cohn, 2026, needs more optimization.
16 119 0.198881757541 Henry Cohn, 2026, needs more optimization.
16 120 0.199966090978 Henry Cohn, 2026, needs more optimization.
16 121 0.199966090985 Henry Cohn, 2026, needs more optimization.
16 122 0.199966090996 Henry Cohn, 2026, needs more optimization.
16 123 0.199988607136 Henry Cohn, 2026, needs more optimization.
16 124 0.199989165732 Henry Cohn, 2026, needs more optimization.
16 126 0.199993997090 Henry Cohn, 2026, needs more optimization.
16 127 0.199995845425 Henry Cohn, 2025, needs more optimization.
16 130 0.199999918321 Henry Cohn, 2025, needs more optimization.
16 131 0.200001028959 Henry Cohn, 2026, needs more optimization.
16 132 0.200001470662 Henry Cohn, 2026, needs more optimization.
16 133 0.202554133427 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
16 159 0.202913709779 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
44⁢x2−4⁢x−1
16 160 0.204974865153 Henry Cohn, 2026, needs more optimization.
16 161 0.221693168308 Henry Cohn, 2026, needs more optimization.
16 162 0.229546347447 Henry Cohn, 2026, needs more optimization.
16 165 0.230995927542 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
16 166 0.234433486339 Numaro AI Autoresearch, 11,000+ New Verified Spherical-Code Records from AI Autoresearch, Numaro Research Report NUMARO-2026-015 (2026), https://numaro.tech/research/spherical-codes-2026/.
16 169 0.236031010307 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
16 170 0.237449050255 Henry Cohn, 2026, needs more optimization.
16 171 0.240174282340 Henry Cohn, 2026, needs more optimization.
16 172 0.240961076187 Henry Cohn, 2026, needs more optimization.
16 173 0.241850347319 Henry Cohn, 2026, needs more optimization.
16 175 0.242225294068 Numaro AI Autoresearch, 11,000+ New Verified Spherical-Code Records from AI Autoresearch, Numaro Research Report NUMARO-2026-015 (2026), https://numaro.tech/research/spherical-codes-2026/.
16 176 0.244617595387 Henry Cohn, 2026, needs more optimization.
16 177 0.245302048762 Henry Cohn, 2026, needs more optimization.
16 178 0.245846854814 Henry Cohn, 2026, needs more optimization.
16 179 0.246244516104 Henry Cohn, 2026, needs more optimization.
16 180 0.246520321037 Henry Cohn, 2026, needs more optimization.
16 181 0.246838700705 Henry Cohn, 2026, needs more optimization.
16 182 0.247089285285 Henry Cohn, 2026, needs more optimization.
16 183 0.247330495791 Henry Cohn, 2026, needs more optimization.
16 184 0.247502758976 Henry Cohn, 2026, needs more optimization.
16 185 0.247619573276 Henry Cohn, 2026, needs more optimization.
16 186 0.247722496396 Henry Cohn, 2026, needs more optimization.
16 187 0.247805815091 Henry Cohn, 2026, needs more optimization.
16 188 0.247973749772 Henry Cohn, 2026, needs more optimization.
16 189 0.248088829660 Henry Cohn, 2026, needs more optimization.
16 190 0.248390608707 Henry Cohn, 2026, needs more optimization.
16 191 0.248617799777 Henry Cohn, 2026, needs more optimization.
16 192 0.248905692367 Henry Cohn, 2026, needs more optimization.
16 193 0.248965786250 Henry Cohn, 2026, needs more optimization.
16 194 0.249838015784 Henry Cohn, 2026, needs more optimization.
16 195 0.249848279692 Henry Cohn, 2026, needs more optimization.
16 196 0.249858768765 Henry Cohn, 2026, needs more optimization.
16 197 0.249881322692 Henry Cohn, 2026, needs more optimization.
16 198 0.249902175511 Henry Cohn, 2026, needs more optimization.
16 199 0.249977572292 Henry Cohn, 2026, needs more optimization.
16 288* 0.25 V. I. Levenšteĭn, Bounds for the maximal cardinality of a code with bounded modulus of the inner product (Russian), Dokl. Akad. Nauk SSSR 263 (1982), 1303–1308, English translation in Soviet Math. Dokl. 25 (1982), 526–531; H. Cohn, D. de Laat, and N. Leijenhorst, Optimality of spherical codes via exact semidefinite programming bounds, preprint, 2024, arXiv:2403.16874.
4⁢x−1
16 289 0.285672450987 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
16 290 0.288761813044 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
16 291 0.294686738699 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
16 294 0.296170673319 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
16 295 0.296948912691 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
16 296 0.298636139241 Henry Cohn, 2026, needs more optimization.
16 297 0.302628662752 Henry Cohn, 2026, needs more optimization.
16 299 0.302628682754 Henry Cohn, 2026, needs more optimization.
16 300 0.302628722040 Henry Cohn, 2026, needs more optimization.
16 302 0.302628916711 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
16 303 0.308229010927 Henry Cohn, 2026, needs more optimization.
16 310 0.308247103268 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
16 311 0.308247340713 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
16 312 0.308247407184 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
16 313 0.308887003374 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
16 314 0.310254251467 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
16 315 0.311958527330 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
16 316 0.313557858137 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
16 317 0.317288938011 Henry Cohn, 2026, needs more optimization.
16 318 0.319994972294 Henry Cohn, 2026, needs more optimization.
16 319 0.321893724667 Henry Cohn, 2026, needs more optimization.
16 320 0.324159552780 Henry Cohn, 2026, needs more optimization.
16 321 0.326120810377 Henry Cohn, 2026, needs more optimization.
16 322 0.326887405901 Henry Cohn, 2026, needs more optimization.
16 323 0.327980212062 Henry Cohn, 2026, needs more optimization.
16 324 0.328120233229 Henry Cohn, 2026, needs more optimization.
16 325 0.328353332564 Henry Cohn, 2026, needs more optimization.
16 326 0.328381689752 Henry Cohn, 2026, needs more optimization.
16 327 0.328596664656 Henry Cohn, 2026, needs more optimization.
16 328 0.328632195465 Henry Cohn, 2026, needs more optimization.
16 329 0.328727632621 Henry Cohn, 2026, needs more optimization.
16 330 0.328800543486 Henry Cohn, 2026, needs more optimization.
16 340 0.328947368422 Henry Cohn, 2026.
76⁢x−25
16 341 0.329842105372 A. Kravatsky, V. Khrulkov, and I. Oseledets, ImprovEvolve: basin-hopping meets LLM-guided evolutionary search, ICML 2026 AI4Math Workshop Poster, https://openreview.net/forum?id=nE1q0gRDNr, arXiv:2602.10233, after some further optimization.
16 342 0.329865971255 Henry Cohn, 2026, needs more optimization.
16 343 0.329977231353 Henry Cohn, 2026, needs more optimization.
16 344 0.330268455069 Henry Cohn, 2026, needs more optimization.
16 345 0.330437877403 Henry Cohn, 2026, needs more optimization.
16 346 0.330552441048 Henry Cohn, 2026, needs more optimization.
16 347 0.330595865520 Henry Cohn, 2026, needs more optimization.
16 348 0.330664617105 Henry Cohn, 2026, needs more optimization.
16 349 0.330749507871 Henry Cohn, 2026, needs more optimization.
16 350 0.330893098516 Henry Cohn, 2026, needs more optimization.
16 351 0.331027458725 Henry Cohn, 2026, needs more optimization.
16 352 0.331312288854 Henry Cohn, 2026, needs more optimization.
16 353 0.331426392088 Henry Cohn, 2026, needs more optimization.
16 354 0.331532838006 Henry Cohn, 2026, needs more optimization.
16 355 0.331679576492 Henry Cohn, 2026, needs more optimization.
16 356 0.331805619447 Henry Cohn, 2026, needs more optimization.
16 357 0.331824785305 Henry Cohn, 2026, needs more optimization.
16 358 0.332028665977 Henry Cohn, 2026, needs more optimization.
16 359 0.332084211809 Henry Cohn, 2026, needs more optimization.
16 360 0.332247983559 Henry Cohn, 2026, needs more optimization.
16 361 0.332492640029 Henry Cohn, 2026, needs more optimization.
16 362 0.332564629325 Henry Cohn, 2026, needs more optimization.
16 363 0.332720445806 Henry Cohn, 2026, needs more optimization.
16 364 0.332751038454 Henry Cohn, 2026, needs more optimization.
16 365 0.332909062161 Henry Cohn, 2026, needs more optimization.
16 366 0.333013492608 Henry Cohn, 2026, needs more optimization.
16 367 0.333036569583 Henry Cohn, 2026, needs more optimization.
16 368 0.333067959916 Henry Cohn, 2026, needs more optimization.
16 369 0.333177470788 Henry Cohn, 2026, needs more optimization.
16 370 0.333194954637 Henry Cohn, 2026, needs more optimization.
16 512 0.333333333334 T. Ericson and V. Zinoviev, Spherical codes generated by binary partitions of symmetric pointsets, IEEE Trans. Inform. Theory 41 (1995), 107–129, doi:10.1109/18.370114.
3⁢x−1
16 513 0.350752627625 Henry Cohn, 2026, needs more optimization.
16 514 0.351225079852 Henry Cohn, 2026, needs more optimization.
16 515 0.352910746657 Henry Cohn, 2026, needs more optimization.
16 516 0.356556314990 Henry Cohn, 2026, needs more optimization.
16 517 0.357826412773 Henry Cohn, 2026, needs more optimization.
16 518 0.358500155181 Henry Cohn, 2026, needs more optimization.
16 519 0.358883001531 Henry Cohn, 2026, needs more optimization.
16 520 0.359930449631 Henry Cohn, 2026, needs more optimization.
16 521 0.360637233994 Henry Cohn, 2026, needs more optimization.
16 522 0.360830312006 Henry Cohn, 2026, needs more optimization.
16 523 0.361224341012 Henry Cohn, 2026, needs more optimization.
16 524 0.362555292182 Henry Cohn, 2026, needs more optimization.
16 525 0.362991624007 Henry Cohn, 2026, needs more optimization.
16 526 0.363465279729 Henry Cohn, 2026, needs more optimization.
16 527 0.363996767571 Henry Cohn, 2026, needs more optimization.
16 528 0.364542752338 Henry Cohn, 2026, needs more optimization.
16 529 0.365192629968 Henry Cohn, 2026, needs more optimization.
16 530 0.365498715641 Henry Cohn, 2026, needs more optimization.
16 531 0.365822084990 Henry Cohn, 2026, needs more optimization.
16 532 0.366425382096 Henry Cohn, 2026, needs more optimization.
16 533 0.366970107402 Henry Cohn, 2026, needs more optimization.
16 534 0.367326144566 A. Kravatsky, V. Khrulkov, and I. Oseledets, ImprovEvolve: basin-hopping meets LLM-guided evolutionary search, ICML 2026 AI4Math Workshop Poster, https://openreview.net/forum?id=nE1q0gRDNr, arXiv:2602.10233, after some further optimization.
16 535 0.367806268443 Henry Cohn, 2026, needs more optimization.
16 536 0.368166411325 Henry Cohn, 2026, needs more optimization.
16 537 0.368727959057 Henry Cohn, 2026, needs more optimization.
16 538 0.369122618980 Henry Cohn, 2026, needs more optimization.
16 567 0.369248411466 Henry Cohn, 2026.
29⁢x2−8⁢x−1
16 575 0.375 C. Ma, T. Tao Z., P. Li, M. Liu, H. Chen, Z. Mao, Y. Cheng, Y. Qi, and Y. Yang, Finding kissing numbers with game-theoretic reinforcement learning, preprint, 2025, arXiv:2511.13391.
8⁢x−3
16 583 0.375 Henry Cohn, 2026.
8⁢x−3
16 593 0.378265794095 Henry Cohn, 2026, needs more optimization.
16 594 0.378266161447 Henry Cohn, 2026, needs more optimization.
16 595 0.378266228878 Henry Cohn, 2026, needs more optimization.
16 596 0.378397117481 Henry Cohn, 2026, needs more optimization.
16 597 0.378397543310 Henry Cohn, 2026, needs more optimization.
16 599 0.379362277068 Henry Cohn, 2026, needs more optimization.
16 601 0.380089227351 Henry Cohn, 2026, needs more optimization.
16 602 0.380182061357 Henry Cohn, 2026, needs more optimization.
16 603 0.380197986511 Henry Cohn, 2026, needs more optimization.
16 604 0.380633382026 Henry Cohn, 2026, needs more optimization.
16 605 0.380633547882 Henry Cohn, 2026, needs more optimization.
16 606 0.380714294300 Henry Cohn, 2026, needs more optimization.
16 607 0.381179151594 Henry Cohn, 2026, needs more optimization.
16 608 0.381179458923 Henry Cohn, 2026, needs more optimization.
16 609 0.381749856927 Henry Cohn, 2026, needs more optimization.
16 610 0.381990574904 Henry Cohn, 2026, needs more optimization.
16 611 0.382290440601 Henry Cohn, 2026, needs more optimization.
16 612 0.382737319710 Henry Cohn, 2026, needs more optimization.
16 613 0.383148875889 Henry Cohn, 2026, needs more optimization.
16 614 0.383459756206 Henry Cohn, 2026, needs more optimization.
16 615 0.383633336573 Henry Cohn, 2026, needs more optimization.
16 616 0.384232685808 Henry Cohn, 2026, needs more optimization.
16 617 0.384324047088 Henry Cohn, 2026, needs more optimization.
16 642 0.384615384616 C. Ma, T. Tao Z., P. Li, M. Liu, H. Chen, Z. Mao, Y. Cheng, Y. Qi, and Y. Yang, Finding kissing numbers with game-theoretic reinforcement learning, preprint, 2025, arXiv:2511.13391.
13⁢x−5
16 643 0.386118036398 Henry Cohn, 2026, needs more optimization.
16 680 0.392857142858 Henry Cohn, 2026.
28⁢x−11
16 681 0.394879531732 Henry Cohn, 2026, needs more optimization.
16 682 0.395905983031 Henry Cohn, 2026, needs more optimization.
16 683 0.396406838240 Henry Cohn, 2026, needs more optimization.
16 684 0.396849274198 Henry Cohn, 2026, needs more optimization.
16 685 0.397220538372 Henry Cohn, 2026, needs more optimization.
16 715 0.397260273973 C. Ma, T. Tao Z., P. Li, M. Liu, H. Chen, Z. Mao, Y. Cheng, Y. Qi, and Y. Yang, Finding kissing numbers with game-theoretic reinforcement learning, preprint, 2025, arXiv:2511.13391.
73⁢x−29
16 716 0.398933979682 Numaro AI Autoresearch, 11,000+ New Verified Spherical-Code Records from AI Autoresearch, Numaro Research Report NUMARO-2026-015 (2026), https://numaro.tech/research/spherical-codes-2026/.
16 768 0.4 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
5⁢x−2
16 769 0.4 Henry Cohn, 2025, by enlarging a code from T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
5⁢x−2
16 771 0.4 C. Ma, T. Tao Z., P. Li, M. Liu, H. Chen, Z. Mao, Y. Cheng, Y. Qi, and Y. Yang, Finding kissing numbers with game-theoretic reinforcement learning, preprint, 2025, arXiv:2511.13391.
5⁢x−2
16 772 0.400742606619 Henry Cohn, 2026, needs more optimization.
16 773 0.405991294659 Henry Cohn, 2026, needs more optimization.
16 775 0.405999149577 Henry Cohn, 2026, needs more optimization.
16 776 0.406145442902 Henry Cohn, 2026, needs more optimization.
16 780 0.406202766737 Henry Cohn, 2026, needs more optimization.
16 781 0.406407299954 Henry Cohn, 2026, needs more optimization.
16 782 0.407310780957 Henry Cohn, 2026, needs more optimization.
16 785 0.407559432732 Henry Cohn, 2026, needs more optimization.
16 787 0.407693990644 Henry Cohn, 2026, needs more optimization.
16 793 0.408465304233 Henry Cohn, 2026, needs more optimization.
16 795 0.408556420774 Henry Cohn, 2026, needs more optimization.
16 796 0.408780422325 Henry Cohn, 2026, needs more optimization.
16 797 0.408943278128 Henry Cohn, 2026, needs more optimization.
16 798 0.409038444317 Henry Cohn, 2026, needs more optimization.
16 799 0.409104721244 Henry Cohn, 2026, needs more optimization.
16 800 0.409156462709 Henry Cohn, 2026, needs more optimization.
16 801 0.409175590213 Henry Cohn, 2026, needs more optimization.
16 802 0.409205486793 Henry Cohn, 2026, needs more optimization.
16 803 0.409231252189 Henry Cohn, 2026, needs more optimization.
16 804 0.409294131160 Henry Cohn, 2026, needs more optimization.
16 805 0.409353416874 Henry Cohn, 2026, needs more optimization.
16 806 0.409365241702 Henry Cohn, 2026, needs more optimization.
16 807 0.409374344631 Henry Cohn, 2026, needs more optimization.
16 810 0.409374450250 Henry Cohn, 2026, needs more optimization.
16 811 0.411793610680 Henry Cohn, 2026, needs more optimization.
16 812 0.411876971000 Henry Cohn, 2026, needs more optimization.
16 813 0.411878563264 Henry Cohn, 2026, needs more optimization.
16 815 0.414310351429 Henry Cohn, 2026, needs more optimization.
16 816 0.414313338249 Henry Cohn, 2026, needs more optimization.
16 817 0.414319313861 Henry Cohn, 2026, needs more optimization.
16 818 0.414322925324 Henry Cohn, 2026, needs more optimization.
16 820 0.414346214473 Henry Cohn, 2026, needs more optimization.
16 823 0.414349923899 Henry Cohn, 2026, needs more optimization.
16 826 0.414684464048 Henry Cohn, 2026, needs more optimization.
16 827 0.414684912818 Henry Cohn, 2026, needs more optimization.
16 828 0.414688318465 Henry Cohn, 2026, needs more optimization.
16 829 0.414741718719 Henry Cohn, 2026, needs more optimization.
16 830 0.414747596807 Henry Cohn, 2026, needs more optimization.
16 831 0.414791486970 Henry Cohn, 2026, needs more optimization.
16 832 0.414858561022 Henry Cohn, 2026, needs more optimization.
16 833 0.414979613561 Henry Cohn, 2026, needs more optimization.
16 915 0.423076923077 C. Ma, T. Tao Z., P. Li, M. Liu, H. Chen, Z. Mao, Y. Cheng, Y. Qi, and Y. Yang, Finding kissing numbers with game-theoretic reinforcement learning, preprint, 2025, arXiv:2511.13391.
26⁢x−11
16 916 0.425366938015 Numaro AI Autoresearch, 11,000+ New Verified Spherical-Code Records from AI Autoresearch, Numaro Research Report NUMARO-2026-015 (2026), https://numaro.tech/research/spherical-codes-2026/.
16 1024 0.428571428572 Subcode of a code of size 1056 from T. Ericson and V. Zinoviev, Spherical codes generated by binary partitions of symmetric pointsets, IEEE Trans. Inform. Theory 41 (1995), 107–129, doi:10.1109/18.370114.
7⁢x−3
17 35 0.044915529038 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
3825⁢x3−289⁢x2−17⁢x+1
17 36 0.052701899358 Henry Cohn, 2025.
17 37 0.055949316790 Henry Cohn, 2026.
17 38 0.055983875620 Henry Cohn, 2025.
17 39 0.062879614874 Henry Cohn, 2024.
17 40 0.064964413617 Henry Cohn, 2025.
17 41 0.070153821556 Henry Cohn, 2025.
17 42 0.073269797523 Henry Cohn, 2025.
17 45 0.073591871415 Henry Cohn, 2023.
239⁢x2−4⁢x−1
17 46 0.080184930575 Henry Cohn, 2026.
17 52 0.084342587557 Henry Cohn, 2023.
188⁢x2−4⁢x−1
17 53 0.098937215086 Henry Cohn, 2024.
2304⁢x4−96⁢x3−95⁢x2−2⁢x+1
17 55 0.099686435548 Henry Cohn, 2026.
153⁢x4+480⁢x3−150⁢x2+1
17 56 0.102993455487 Henry Cohn, 2026.
17 64 0.111111111112 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
9⁢x−1
17 65 0.120819518077 Henry Cohn, 2026.
17 66 0.124823699080 Henry Cohn, 2026.
17 67 0.127087890038 Henry Cohn, 2026.
17 68 0.127206280067 Henry Cohn, 2026, needs more optimization.
17 69 0.127241105668 Henry Cohn, 2026.
17 71 0.127270310008 Henry Cohn, 2025.
17 74 0.127284404862 Henry Cohn, 2025.
17 76 0.127284594471 Henry Cohn, 2025.
17 77 0.127301957060 Numaro AI Autoresearch, 11,000+ New Verified Spherical-Code Records from AI Autoresearch, Numaro Research Report NUMARO-2026-015 (2026), https://numaro.tech/research/spherical-codes-2026/.
17 78 0.135230868852 Henry Cohn, 2026, needs more optimization.
17 79 0.142557325278 Henry Cohn, 2026, needs more optimization.
17 80 0.147987559048 Henry Cohn, 2026, needs more optimization.
17 81 0.149882877304 Henry Cohn, 2026, needs more optimization.
17 82 0.149951006483 Henry Cohn, 2026, needs more optimization.
17 86 0.149999887893 Henry Cohn, 2026, needs more optimization.
17 87 0.151340636611 Henry Cohn, 2026, needs more optimization.
17 88 0.156527134064 Henry Cohn, 2026, needs more optimization.
17 89 0.158629295135 Henry Cohn, 2026, needs more optimization.
17 90 0.163948884645 Henry Cohn, 2026, needs more optimization.
17 91 0.167225196650 Henry Cohn, 2026, needs more optimization.
17 92 0.167349745004 Henry Cohn, 2026, needs more optimization.
17 93 0.167542856459 Henry Cohn, 2026, needs more optimization.
17 94 0.167882242302 Henry Cohn, 2026, needs more optimization.
17 95 0.168038484713 Henry Cohn, 2026, needs more optimization.
17 96 0.168351689587 Henry Cohn, 2026, needs more optimization.
17 97 0.168526086272 Henry Cohn, 2026, needs more optimization.
17 98 0.168598787002 Henry Cohn, 2026, needs more optimization.
17 99 0.168667156246 Henry Cohn, 2026, needs more optimization.
17 100 0.168671171954 Henry Cohn, 2026, needs more optimization.
17 101 0.168688905386 Henry Cohn, 2026, needs more optimization.
17 102 0.169861601432 Henry Cohn, 2026, needs more optimization.
17 104 0.170751369934 Henry Cohn, 2026, needs more optimization.
17 105 0.170751990216 Henry Cohn, 2026, needs more optimization.
17 106 0.170751990218 Henry Cohn, 2026, needs more optimization.
17 107 0.170759868976 Henry Cohn, 2026, needs more optimization.
17 108 0.175086042960 Henry Cohn, 2026, needs more optimization.
17 109 0.179282322465 Henry Cohn, 2026, needs more optimization.
17 110 0.180269681176 Henry Cohn, 2026, needs more optimization.
17 111 0.182397368105 Henry Cohn, 2026, needs more optimization.
17 115 0.184252183279 Henry Cohn, 2026.
17 116 0.184847526050 Henry Cohn, 2026, needs more optimization.
17 117 0.186660513707 Henry Cohn, 2026, needs more optimization.
17 118 0.187738675204 Henry Cohn, 2026, needs more optimization.
17 119 0.189940926437 Henry Cohn, 2026, needs more optimization.
17 120 0.190640777156 Henry Cohn, 2026, needs more optimization.
17 121 0.192288823399 Henry Cohn, 2026, needs more optimization.
17 122 0.192374690043 Henry Cohn, 2026, needs more optimization.
17 123 0.192449021873 Henry Cohn, 2026, needs more optimization.
17 124 0.192956787193 Henry Cohn, 2026, needs more optimization.
17 125 0.192981578828 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
17 126 0.192986066279 Henry Cohn, 2026, needs more optimization.
17 127 0.193832467986 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
17 128 0.196253513622 Henry Cohn, 2026, needs more optimization.
17 129 0.196782248787 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
17 130 0.197511600008 Henry Cohn, 2026, needs more optimization.
17 131 0.198977672352 Henry Cohn, 2026, needs more optimization.
17 132 0.199042801573 Henry Cohn, 2026, needs more optimization.
17 133 0.199556912831 Henry Cohn, 2026, needs more optimization.
17 134 0.199787169005 Henry Cohn, 2026, needs more optimization.
17 135 0.199854745200 Henry Cohn, 2026, needs more optimization.
17 136 0.199968459080 Henry Cohn, 2026, needs more optimization.
17 137 0.199987855897 Henry Cohn, 2026, needs more optimization.
17 138 0.200011212765 Henry Cohn, 2026, needs more optimization.
17 139 0.200152204943 Henry Cohn, 2026, needs more optimization.
17 140 0.200232133822 Henry Cohn, 2026, needs more optimization.
17 141 0.202594126836 Henry Cohn, 2026, needs more optimization.
17 142 0.202849585090 Henry Cohn, 2026, needs more optimization.
17 143 0.202861012935 Henry Cohn, 2026, needs more optimization.
17 144 0.202881192849 Henry Cohn, 2026, needs more optimization.
17 146 0.202890799240 Henry Cohn, 2026, needs more optimization.
17 148 0.202893418199 Henry Cohn, 2026, needs more optimization.
17 150 0.202894858760 Henry Cohn, 2026, needs more optimization.
17 151 0.202899027493 Henry Cohn, 2026, needs more optimization.
17 153 0.202909339588 Henry Cohn, 2026, needs more optimization.
17 154 0.202910812292 Henry Cohn, 2026, needs more optimization.
17 155 0.202910812450 Henry Cohn, 2026, needs more optimization.
17 156 0.202911272393 Henry Cohn, 2026, needs more optimization.
17 162 0.202913709779 Henry Cohn, 2026.
44⁢x2−4⁢x−1
17 163 0.202914134197 Henry Cohn, 2026, needs more optimization.
17 164 0.202916943828 Henry Cohn, 2026, needs more optimization.
17 165 0.203269399084 Henry Cohn, 2026, needs more optimization.
17 166 0.209283255705 Henry Cohn, 2026, needs more optimization.
17 167 0.209413224661 Henry Cohn, 2026, needs more optimization.
17 168 0.209696026939 Numaro AI Autoresearch, 11,000+ New Verified Spherical-Code Records from AI Autoresearch, Numaro Research Report NUMARO-2026-015 (2026), https://numaro.tech/research/spherical-codes-2026/.
17 177 0.214580576913 Henry Cohn, 2026.
59⁢x2−8⁢x−1
17 178 0.215890681553 Henry Cohn, 2026, needs more optimization.
17 179 0.223732515947 Henry Cohn, 2026, needs more optimization.
17 180 0.224771021238 Henry Cohn, 2026, needs more optimization.
17 181 0.227587627788 Henry Cohn, 2026, needs more optimization.
17 190 0.228481712325 Henry Cohn, 2026.
17 192 0.228757976713 Henry Cohn, 2026, needs more optimization.
17 193 0.233272137280 Henry Cohn, 2026, needs more optimization.
17 194 0.234602059071 Henry Cohn, 2026, needs more optimization.
17 195 0.235727130757 Henry Cohn, 2026, needs more optimization.
17 196 0.237300483965 Henry Cohn, 2026, needs more optimization.
17 197 0.238196702840 Henry Cohn, 2026, needs more optimization.
17 198 0.238378801012 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
17 199 0.238938054670 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
17 200 0.239023495482 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
17 201 0.239112157750 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
17 202 0.241542281645 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
17 203 0.242192008905 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
17 204 0.242739552748 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
17 205 0.243415329961 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
17 206 0.243667302332 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
17 207 0.244118892310 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
17 208 0.244397078711 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
17 209 0.244643340249 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
17 210 0.244940057057 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
17 211 0.245278064719 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
17 212 0.245582618186 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
17 213 0.245851527019 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
17 214 0.246034556504 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
17 215 0.246279098490 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
17 216 0.246532016253 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
17 217 0.246983265880 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
17 218 0.247258273723 Henry Cohn, 2026, needs more optimization.
17 219 0.247619706453 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
17 220 0.247783315735 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
17 221 0.247925742931 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
17 222 0.248064216425 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
17 223 0.248258067474 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
17 224 0.248474834943 Henry Cohn, 2026, needs more optimization.
17 225 0.248624030131 Henry Cohn, 2026, needs more optimization.
17 226 0.248718096284 Henry Cohn, 2026, needs more optimization.
17 227 0.248832016658 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
17 228 0.248969585609 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
17 229 0.249070394037 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
17 230 0.249145161376 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
17 231 0.249197686655 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
17 232 0.249243989093 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
17 233 0.249291546034 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
17 234 0.249323062328 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
17 235 0.249399125092 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
17 236 0.249477718289 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
17 237 0.249507867256 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
17 238 0.249554115353 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
17 239 0.249642284193 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
17 240 0.249720646088 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
17 241 0.249785208056 Henry Cohn, 2026, needs more optimization.
17 242 0.249805618936 Henry Cohn, 2026, needs more optimization.
17 243 0.249837476374 Henry Cohn, 2026, needs more optimization.
17 244 0.249848693348 Henry Cohn, 2026, needs more optimization.
17 245 0.249861344609 Henry Cohn, 2026, needs more optimization.
17 246 0.249880365342 Henry Cohn, 2026, needs more optimization.
17 247 0.249901370817 Henry Cohn, 2026, needs more optimization.
17 248 0.249912002298 Henry Cohn, 2026, needs more optimization.
17 249 0.249924175537 Henry Cohn, 2026, needs more optimization.
17 250 0.249928135524 Henry Cohn, 2026, needs more optimization.
17 251 0.249975160148 Henry Cohn, 2026, needs more optimization.
17 253 0.249997107913 Henry Cohn, 2026, needs more optimization.
17 254 0.249997107920 Henry Cohn, 2026, needs more optimization.
17 255 0.249998856322 Henry Cohn, 2026, needs more optimization.
17 256 0.249998856332 Henry Cohn, 2026, needs more optimization.
17 257 0.249999029843 Henry Cohn, 2026, needs more optimization.
17 258 0.249999292042 Henry Cohn, 2026, needs more optimization.
17 259 0.249999292043 Henry Cohn, 2026, needs more optimization.
17 263 0.249999497844 Henry Cohn, 2026, needs more optimization.
17 264 0.249999497846 Henry Cohn, 2026, needs more optimization.
17 284 0.249999885378 Henry Cohn, 2026, needs more optimization.
17 285 0.249999889767 Henry Cohn, 2026, needs more optimization.
17 292 0.25 Henry Cohn, 2026.
4⁢x−1
17 293 0.250000009139 Henry Cohn, 2026, needs more optimization.
17 294 0.250000045919 Henry Cohn, 2026, needs more optimization.
17 295 0.250769447825 Henry Cohn, 2026, needs more optimization.
17 296 0.253950601432 Henry Cohn, 2026, needs more optimization.
17 297 0.255601475223 Henry Cohn, 2026, needs more optimization.
17 298 0.259856877518 Henry Cohn, 2026, needs more optimization.
17 299 0.261085318961 Henry Cohn, 2026, needs more optimization.
17 300 0.261086116134 Henry Cohn, 2026, needs more optimization.
17 301 0.261087158996 Henry Cohn, 2026, needs more optimization.
17 302 0.261087765066 Henry Cohn, 2026, needs more optimization.
17 303 0.261088441255 Henry Cohn, 2026, needs more optimization.
17 304 0.261089733804 Henry Cohn, 2026, needs more optimization.
17 305 0.261090762758 Henry Cohn, 2026, needs more optimization.
17 306 0.261091588230 Henry Cohn, 2026, needs more optimization.
17 307 0.261092231325 Henry Cohn, 2026, needs more optimization.
17 308 0.261094001700 Henry Cohn, 2026, needs more optimization.
17 309 0.261094114302 Henry Cohn, 2026, needs more optimization.
17 310 0.261094118382 Henry Cohn, 2026, needs more optimization.
17 311 0.261094123147 Henry Cohn, 2026, needs more optimization.
17 312 0.261094127870 Henry Cohn, 2026, needs more optimization.
17 313 0.261094127951 Henry Cohn, 2026, needs more optimization.
17 314 0.261094129727 Henry Cohn, 2026, needs more optimization.
17 315 0.261094129997 Henry Cohn, 2026, needs more optimization.
17 316 0.261094133378 Henry Cohn, 2026, needs more optimization.
17 317 0.261094135790 Henry Cohn, 2026, needs more optimization.
17 318 0.261094137455 Henry Cohn, 2026, needs more optimization.
17 319 0.261094140536 Henry Cohn, 2026, needs more optimization.
17 320 0.261094143848 Henry Cohn, 2026, needs more optimization.
17 321 0.281913036169 Henry Cohn, 2026, needs more optimization.
17 322 0.286550122965 Henry Cohn, 2026, needs more optimization.
17 323 0.289492000465 Henry Cohn, 2026, needs more optimization.
17 324 0.291642147986 Henry Cohn, 2026, needs more optimization.
17 325 0.293577577268 Henry Cohn, 2026, needs more optimization.
17 352 0.294117647059 C. Ma, T. Tao Z., P. Li, M. Liu, H. Chen, Z. Mao, Y. Cheng, Y. Qi, and Y. Yang, Finding kissing numbers with game-theoretic reinforcement learning, preprint, 2025, arXiv:2511.13391.
17⁢x−5
17 353 0.296535165409 C. Ma, T. Tao Z., P. Li, M. Liu, H. Chen, Z. Mao, Y. Cheng, Y. Qi, and Y. Yang, Finding kissing numbers with game-theoretic reinforcement learning, preprint, 2025, arXiv:2511.13391.
8⁢x2+x−1
17 354 0.303054210944 Henry Cohn, 2026, needs more optimization.
17 355 0.304366843817 Henry Cohn, 2026, needs more optimization.
17 356 0.305238436676 Henry Cohn, 2026, needs more optimization.
17 357 0.306093176694 Henry Cohn, 2026, needs more optimization.
17 358 0.306688821556 Henry Cohn, 2026, needs more optimization.
17 359 0.307431989275 Henry Cohn, 2026, needs more optimization.
17 360 0.308031916973 Henry Cohn, 2026, needs more optimization.
17 361 0.308321977495 Henry Cohn, 2026, needs more optimization.
17 362 0.308713746196 Henry Cohn, 2026, needs more optimization.
17 363 0.309147467592 Henry Cohn, 2026, needs more optimization.
17 364 0.309522584536 Henry Cohn, 2026, needs more optimization.
17 365 0.309893244928 Henry Cohn, 2026, needs more optimization.
17 366 0.310326698847 Henry Cohn, 2026, needs more optimization.
17 367 0.310570751029 Henry Cohn, 2026, needs more optimization.
17 368 0.310892865539 Henry Cohn, 2026, needs more optimization.
17 369 0.311196812673 Henry Cohn, 2026, needs more optimization.
17 370 0.311456278517 Henry Cohn, 2026, needs more optimization.
17 371 0.311796494659 Henry Cohn, 2026, needs more optimization.
17 372 0.312062592910 Henry Cohn, 2026, needs more optimization.
17 373 0.312278861220 Henry Cohn, 2026, needs more optimization.
17 374 0.312606521202 Henry Cohn, 2026, needs more optimization.
17 375 0.312911979586 Henry Cohn, 2026, needs more optimization.
17 376 0.313083595443 Henry Cohn, 2026, needs more optimization.
17 377 0.313357447443 Henry Cohn, 2026, needs more optimization.
17 378 0.313536738639 Henry Cohn, 2026, needs more optimization.
17 379 0.313732464800 Henry Cohn, 2026, needs more optimization.
17 380 0.313949573533 Henry Cohn, 2026, needs more optimization.
17 381 0.314179492414 Henry Cohn, 2026, needs more optimization.
17 382 0.314316910013 Henry Cohn, 2026, needs more optimization.
17 383 0.314496104585 Henry Cohn, 2026, needs more optimization.
17 384 0.314683590490 Henry Cohn, 2026, needs more optimization.
17 385 0.314908168456 Henry Cohn, 2026, needs more optimization.
17 386 0.315165460008 Henry Cohn, 2026, needs more optimization.
17 387 0.315312005663 Henry Cohn, 2026, needs more optimization.
17 388 0.315541064492 Henry Cohn, 2026, needs more optimization.
17 389 0.315791026034 Henry Cohn, 2026, needs more optimization.
17 390 0.316045379523 Henry Cohn, 2026, needs more optimization.
17 391 0.316325399990 Henry Cohn, 2026, needs more optimization.
17 392 0.316533322294 Henry Cohn, 2026, needs more optimization.
17 393 0.316765604715 Henry Cohn, 2026, needs more optimization.
17 394 0.317037733584 Henry Cohn, 2026, needs more optimization.
17 395 0.317455634187 Henry Cohn, 2026, needs more optimization.
17 396 0.317582782487 Henry Cohn, 2026, needs more optimization.
17 397 0.317677025939 Henry Cohn, 2026, needs more optimization.
17 398 0.317836887691 Henry Cohn, 2026, needs more optimization.
17 399 0.317871472497 Henry Cohn, 2026, needs more optimization.
17 400 0.318018885073 Henry Cohn, 2026, needs more optimization.
17 401 0.318071248408 Henry Cohn, 2026, needs more optimization.
17 402 0.318209695085 Henry Cohn, 2026, needs more optimization.
17 403 0.318264771224 Henry Cohn, 2026, needs more optimization.
17 404 0.318329129031 Henry Cohn, 2026, needs more optimization.
17 405 0.318359481109 Henry Cohn, 2026, needs more optimization.
17 406 0.318520583521 Henry Cohn, 2026, needs more optimization.
17 407 0.318577095696 Henry Cohn, 2026, needs more optimization.
17 408 0.318676544378 Henry Cohn, 2026, needs more optimization.
17 409 0.318766263332 Henry Cohn, 2026, needs more optimization.
17 410 0.318870411921 Henry Cohn, 2026, needs more optimization.
17 411 0.318942520152 Henry Cohn, 2026, needs more optimization.
17 412 0.318993706254 Henry Cohn, 2026, needs more optimization.
17 434 0.319025504452 Henry Cohn, 2026, needs more optimization.
17 435 0.320843412971 Henry Cohn, 2026, needs more optimization.
17 436 0.322285603017 Henry Cohn, 2026, needs more optimization.
17 437 0.322623839615 Henry Cohn, 2026, needs more optimization.
17 438 0.323530361415 Henry Cohn, 2026, needs more optimization.
17 439 0.323875331574 Henry Cohn, 2026, needs more optimization.
17 440 0.324304801178 Henry Cohn, 2026, needs more optimization.
17 441 0.324671092754 Henry Cohn, 2026, needs more optimization.
17 442 0.325040748627 Henry Cohn, 2026, needs more optimization.
17 443 0.325685307496 Henry Cohn, 2026, needs more optimization.
17 444 0.326566425656 Henry Cohn, 2026, needs more optimization.
17 446 0.327292624461 Henry Cohn, 2026, needs more optimization.
17 447 0.327506470220 Henry Cohn, 2026, needs more optimization.
17 448 0.327648888589 Henry Cohn, 2026, needs more optimization.
17 449 0.327798878247 Henry Cohn, 2026, needs more optimization.
17 450 0.329748484248 Henry Cohn, 2026, needs more optimization.
17 451 0.330606260298 Henry Cohn, 2026, needs more optimization.
17 452 0.331444024543 Henry Cohn, 2026, needs more optimization.
17 453 0.332563467409 Henry Cohn, 2026, needs more optimization.
17 546 0.333333333334 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
3⁢x−1
17 578 0.333333333334 C. Ma, T. Tao Z., P. Li, M. Liu, H. Chen, Z. Mao, Y. Cheng, Y. Qi, and Y. Yang, Finding kissing numbers with game-theoretic reinforcement learning, preprint, 2025, arXiv:2511.13391.
3⁢x−1
17 579 0.345190388486 Henry Cohn, 2026, needs more optimization.
17 580 0.345191408397 Henry Cohn, 2026, needs more optimization.
17 581 0.345192269899 Henry Cohn, 2026, needs more optimization.
17 582 0.345292988462 Henry Cohn, 2026, needs more optimization.
17 583 0.345295375957 Henry Cohn, 2026, needs more optimization.
17 586 0.345314016722 Henry Cohn, 2026, needs more optimization.
17 589 0.345318862835 Henry Cohn, 2026, needs more optimization.
17 591 0.345319819552 Henry Cohn, 2026, needs more optimization.
17 592 0.349709097860 Henry Cohn, 2026, needs more optimization.
17 594 0.349760453025 Henry Cohn, 2026, needs more optimization.
17 596 0.349766929116 Henry Cohn, 2026, needs more optimization.
17 597 0.349767253197 Henry Cohn, 2026, needs more optimization.
17 599 0.349791333080 Henry Cohn, 2026, needs more optimization.
17 600 0.350124818207 Henry Cohn, 2026, needs more optimization.
17 601 0.351971326767 Henry Cohn, 2026, needs more optimization.
17 603 0.352118258238 Henry Cohn, 2026, needs more optimization.
17 605 0.352142308247 Henry Cohn, 2026, needs more optimization.
17 606 0.352352882712 Henry Cohn, 2026, needs more optimization.
17 607 0.352366524506 Henry Cohn, 2026, needs more optimization.
17 608 0.352427782371 Henry Cohn, 2026, needs more optimization.
17 609 0.352558449531 Henry Cohn, 2026, needs more optimization.
17 610 0.352561589292 Henry Cohn, 2026, needs more optimization.
17 611 0.352566214929 Henry Cohn, 2026, needs more optimization.
17 612 0.352572233556 Henry Cohn, 2026, needs more optimization.
17 613 0.353050991954 Henry Cohn, 2026, needs more optimization.
17 614 0.353066863876 Henry Cohn, 2026, needs more optimization.
17 615 0.353184395538 Henry Cohn, 2026, needs more optimization.
17 616 0.353188688791 Henry Cohn, 2026, needs more optimization.
17 617 0.353196032368 Henry Cohn, 2026, needs more optimization.
17 618 0.353198973492 Henry Cohn, 2026, needs more optimization.
17 619 0.353213488423 Henry Cohn, 2026, needs more optimization.
17 620 0.353472050936 Henry Cohn, 2026, needs more optimization.
17 622 0.353511076336 Henry Cohn, 2026, needs more optimization.
17 623 0.353970660722 Henry Cohn, 2026, needs more optimization.
17 624 0.354864628941 Henry Cohn, 2026, needs more optimization.
17 625 0.354872894832 Henry Cohn, 2026, needs more optimization.
17 626 0.354875305799 Henry Cohn, 2026, needs more optimization.
17 628 0.354933920453 Henry Cohn, 2026, needs more optimization.
17 629 0.354937739664 Henry Cohn, 2026, needs more optimization.
17 630 0.354950212168 Henry Cohn, 2026, needs more optimization.
17 632 0.354964763403 Henry Cohn, 2026, needs more optimization.
17 633 0.354988753241 Henry Cohn, 2026, needs more optimization.
17 635 0.355036520661 Henry Cohn, 2026, needs more optimization.
17 636 0.362517681188 Henry Cohn, 2026, needs more optimization.
17 638 0.362549127048 Henry Cohn, 2026, needs more optimization.
17 640 0.362555477678 Henry Cohn, 2026, needs more optimization.
17 641 0.362557626826 Henry Cohn, 2026, needs more optimization.
17 643 0.362561996712 Henry Cohn, 2026, needs more optimization.
17 644 0.362565976580 Henry Cohn, 2026, needs more optimization.
17 645 0.362574997944 Henry Cohn, 2026, needs more optimization.
17 647 0.362604741960 Henry Cohn, 2026, needs more optimization.
17 648 0.362661763043 Henry Cohn, 2026, needs more optimization.
17 649 0.362670061280 Henry Cohn, 2026, needs more optimization.
17 650 0.362736935242 Henry Cohn, 2026, needs more optimization.
17 653 0.362794479554 Henry Cohn, 2026, needs more optimization.
17 657 0.362795588482 Henry Cohn, 2026, needs more optimization.
17 658 0.362828833871 Henry Cohn, 2026, needs more optimization.
17 659 0.362829755870 Henry Cohn, 2026, needs more optimization.
17 660 0.362832298797 Henry Cohn, 2026, needs more optimization.
17 664 0.362841628472 Henry Cohn, 2026, needs more optimization.
17 667 0.362860823068 Henry Cohn, 2026, needs more optimization.
17 668 0.362865193959 Henry Cohn, 2026, needs more optimization.
17 669 0.362867940888 Henry Cohn, 2026, needs more optimization.
17 672 0.362879113263 Henry Cohn, 2026, needs more optimization.
17 673 0.362903600886 Henry Cohn, 2026, needs more optimization.
17 674 0.362923529347 Henry Cohn, 2026, needs more optimization.
17 676 0.362954915166 Henry Cohn, 2026, needs more optimization.
17 682 0.363027094798 Henry Cohn, 2026, needs more optimization.
17 685 0.363092441815 Henry Cohn, 2026, needs more optimization.
17 687 0.363166777751 Henry Cohn, 2026, needs more optimization.
17 688 0.363196736552 Henry Cohn, 2026, needs more optimization.
17 691 0.363202995439 Henry Cohn, 2026, needs more optimization.
17 696 0.363215754111 Henry Cohn, 2026, needs more optimization.
17 701 0.363217621923 Henry Cohn, 2026, needs more optimization.
17 708 0.363226290847 Henry Cohn, 2026, needs more optimization.
17 709 0.363233470939 Henry Cohn, 2026, needs more optimization.
17 710 0.363235456882 Henry Cohn, 2026, needs more optimization.
17 711 0.363254471120 Henry Cohn, 2026, needs more optimization.
17 712 0.363266286707 Henry Cohn, 2026, needs more optimization.
17 714 0.363283073767 Henry Cohn, 2026, needs more optimization.
17 720 0.363290464487 Henry Cohn, 2026, needs more optimization.
17 724 0.363299377212 Henry Cohn, 2026, needs more optimization.
17 726 0.363306632362 Henry Cohn, 2026, needs more optimization.
17 727 0.363312719646 Henry Cohn, 2026, needs more optimization.
17 728 0.363317292873 Henry Cohn, 2026, needs more optimization.
17 729 0.363317448661 Henry Cohn, 2026, needs more optimization.
17 733 0.363319016203 Henry Cohn, 2026, needs more optimization.
17 734 0.363320702916 Henry Cohn, 2026, needs more optimization.
17 736 0.363321774392 Henry Cohn, 2026, needs more optimization.
17 737 0.363325666640 Henry Cohn, 2026, needs more optimization.
17 742 0.363327096415 Henry Cohn, 2026, needs more optimization.
17 744 0.363332306987 Henry Cohn, 2026, needs more optimization.
17 752 0.363338838232 Henry Cohn, 2026, needs more optimization.
17 754 0.363354451068 Henry Cohn, 2026, needs more optimization.
17 755 0.371240344009 Henry Cohn, 2026, needs more optimization.
17 757 0.371399751130 Henry Cohn, 2026, needs more optimization.
17 758 0.371470327078 Henry Cohn, 2026, needs more optimization.
17 759 0.371474870535 Henry Cohn, 2026, needs more optimization.
17 761 0.371612966574 Henry Cohn, 2026, needs more optimization.
17 765 0.371632217220 Henry Cohn, 2026, needs more optimization.
17 766 0.371636227364 Henry Cohn, 2026, needs more optimization.
17 768 0.378516413617 Henry Cohn, 2026, needs more optimization.
17 1024 0.384615384616 C. Ma, T. Tao Z., P. Li, M. Liu, H. Chen, Z. Mao, Y. Cheng, Y. Qi, and Y. Yang, Finding kissing numbers with game-theoretic reinforcement learning, preprint, 2025, arXiv:2511.13391.
13⁢x−5
18 37 0.042671058118 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
4608⁢x3−324⁢x2−18⁢x+1
18 38 0.050097352046 Henry Cohn, 2025.
18 39 0.055224148787 Henry Cohn, 2025.
18 40 0.055678193348 Henry Cohn, 2025.
1856⁢x4+736⁢x3+204⁢x2+4⁢x−1
18 41 0.060967744952 Henry Cohn, 2023.
18 42 0.063513513654 Henry Cohn, 2023.
18 43 0.066629754705 Henry Cohn, 2025.
18 44 0.066804066179 Henry Cohn, 2023.
18 45 0.071480323505 Henry Cohn, 2026.
18 46 0.073552043366 Henry Cohn, 2025.
18 47 0.073575768177 Henry Cohn, 2025.
Minimal polynomial listed in plain text data
18 48 0.074706792917 Henry Cohn, 2024.
49250304⁢x8−30019584⁢x7−3769088⁢x6−1665536⁢x5+436432⁢x4+8256⁢x3−3792⁢x2+9
18 50 0.078219048073 Henry Cohn, 2025.
368⁢x2−16⁢x−1
18 51 0.084307083931 Henry Cohn, 2026, needs more optimization.
18 54 0.084331772475 Henry Cohn, 2026, needs more optimization.
18 55 0.087707155784 Henry Cohn, 2025.
18 57 0.092724727985 Henry Cohn, 2025.
332⁢x2−20⁢x−1
18 59 0.096317631192 Henry Cohn, 2025.
18 60 0.096621974569 Henry Cohn, 2025.
1392⁢x5+5600⁢x4−2304⁢x3+152⁢x2+12⁢x−1
18 69 0.101456854890 Henry Cohn, 2024.
176⁢x2−8⁢x−1
18 71 0.107360417201 Henry Cohn, 2026.
18 72 0.109540130282 Henry Cohn, 2026.
18 73 0.117134464846 Henry Cohn, 2026, needs more optimization.
18 74 0.120049808519 Henry Cohn, 2026, needs more optimization.
18 75 0.120367585573 Henry Cohn, 2026, needs more optimization.
18 76 0.122043871163 Henry Cohn, 2026, needs more optimization.
18 77 0.123493542007 Henry Cohn, 2026, needs more optimization.
18 78 0.125804804449 Henry Cohn, 2026, needs more optimization.
18 80 0.126224060072 Henry Cohn, 2026, needs more optimization.
18 81 0.126904281672 Henry Cohn, 2026, needs more optimization.
18 82 0.127626483898 Henry Cohn, 2026, needs more optimization.
18 83 0.129098755666 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
18 84 0.130579477836 Henry Cohn, 2026, needs more optimization.
18 85 0.132293288623 Henry Cohn, 2026, needs more optimization.
18 86 0.132700025640 Henry Cohn, 2026, needs more optimization.
18 87 0.133639152637 Henry Cohn, 2026, needs more optimization.
18 88 0.134264346430 Henry Cohn, 2025.
18 96 0.142857142858 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
7⁢x−1
18 97 0.152402949200 Henry Cohn, 2026.
16⁢x2−9⁢x+1
18 98 0.155249851767 Henry Cohn, 2026.
18 100 0.157894736843 C. Ma, T. Tao Z., P. Li, M. Liu, H. Chen, Z. Mao, Y. Cheng, Y. Qi, and Y. Yang, Finding kissing numbers with game-theoretic reinforcement learning, preprint, 2025, arXiv:2511.13391.
19⁢x−3
18 101 0.161087011866 Henry Cohn, 2026.
52⁢x2−27⁢x+3
18 104 0.162407002682 Henry Cohn, 2026.
18 105 0.164921962691 Henry Cohn, 2026, needs more optimization.
18 106 0.166070837885 Henry Cohn, 2026, needs more optimization.
18 108 0.166586736179 Henry Cohn, 2026, needs more optimization.
18 109 0.167620540781 Henry Cohn, 2026, needs more optimization.
18 110 0.168468671425 Henry Cohn, 2026, needs more optimization.
18 111 0.169252748077 Henry Cohn, 2026, needs more optimization.
18 112 0.169845861244 Henry Cohn, 2026, needs more optimization.
18 113 0.170643157469 Henry Cohn, 2026, needs more optimization.
18 114 0.172123408342 Henry Cohn, 2026, needs more optimization.
18 115 0.172920397314 Henry Cohn, 2026, needs more optimization.
18 116 0.174475313522 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
18 117 0.177748575135 Numaro AI Autoresearch, 11,000+ New Verified Spherical-Code Records from AI Autoresearch, Numaro Research Report NUMARO-2026-015 (2026), https://numaro.tech/research/spherical-codes-2026/.
18 118 0.183010966175 Henry Cohn, 2026, needs more optimization.
18 119 0.184589005319 Henry Cohn, 2026, needs more optimization.
18 120 0.185137714594 Henry Cohn, 2026, needs more optimization.
18 121 0.185552099379 Henry Cohn, 2026, needs more optimization.
18 122 0.186958434117 Henry Cohn, 2026, needs more optimization.
18 123 0.188113485779 Henry Cohn, 2026, needs more optimization.
18 128 0.188405797102 C. Ma, T. Tao Z., P. Li, M. Liu, H. Chen, Z. Mao, Y. Cheng, Y. Qi, and Y. Yang, Finding kissing numbers with game-theoretic reinforcement learning, preprint, 2025, arXiv:2511.13391.
69⁢x−13
18 129 0.188801925845 Henry Cohn, 2026, needs more optimization.
18 130 0.188961019797 Henry Cohn, 2026, needs more optimization.
18 131 0.190523556591 Henry Cohn, 2026, needs more optimization.
18 132 0.191489361703 Henry Cohn, 2025, by enlarging a code from T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
47⁢x−9
18 133 0.193070622507 Henry Cohn, 2026, needs more optimization.
18 134 0.193719906753 Henry Cohn, 2026, needs more optimization.
18 135 0.194298207706 Henry Cohn, 2026, needs more optimization.
18 136 0.194621813477 Henry Cohn, 2026, needs more optimization.
18 137 0.194954296396 Henry Cohn, 2026, needs more optimization.
18 138 0.195229084001 Henry Cohn, 2026, needs more optimization.
18 140 0.195281232517 Henry Cohn, 2026, needs more optimization.
18 141 0.196394553473 Henry Cohn, 2026, needs more optimization.
18 142 0.196568686684 Henry Cohn, 2026, needs more optimization.
18 143 0.196782415799 Henry Cohn, 2026, needs more optimization.
18 144 0.197035852380 Henry Cohn, 2026, needs more optimization.
18 145 0.197324459260 Henry Cohn, 2026, needs more optimization.
18 146 0.197533592804 Henry Cohn, 2026, needs more optimization.
18 147 0.197851584019 Henry Cohn, 2026, needs more optimization.
18 148 0.198476047172 Henry Cohn, 2026, needs more optimization.
18 149 0.198690425828 Henry Cohn, 2026, needs more optimization.
18 150 0.199162220964 Henry Cohn, 2026, needs more optimization.
18 151 0.199542823326 Henry Cohn, 2026, needs more optimization.
18 152 0.200047290015 Henry Cohn, 2026, needs more optimization.
18 154 0.200209970019 Henry Cohn, 2026, needs more optimization.
18 155 0.200715301345 Henry Cohn, 2026, needs more optimization.
18 156 0.201466840595 Henry Cohn, 2026, needs more optimization.
18 157 0.201537057567 Henry Cohn, 2026, needs more optimization.
18 158 0.201574760752 Henry Cohn, 2026, needs more optimization.
18 159 0.201591813556 Numaro AI Autoresearch, 11,000+ New Verified Spherical-Code Records from AI Autoresearch, Numaro Research Report NUMARO-2026-015 (2026), https://numaro.tech/research/spherical-codes-2026/.
18 160 0.201667601115 Henry Cohn, 2026, needs more optimization.
18 161 0.202046884104 Henry Cohn, 2026, needs more optimization.
18 162 0.202215065383 Henry Cohn, 2026, needs more optimization.
18 163 0.202373950268 Henry Cohn, 2026, needs more optimization.
18 164 0.202373954343 Henry Cohn, 2026, needs more optimization.
18 165 0.202511862036 Henry Cohn, 2026, needs more optimization.
18 166 0.202838481565 Henry Cohn, 2026, needs more optimization.
18 167 0.202883134607 Henry Cohn, 2026, needs more optimization.
18 168 0.202914717799 Henry Cohn, 2026, needs more optimization.
18 169 0.202915400882 Henry Cohn, 2026, needs more optimization.
18 170 0.202915859443 Henry Cohn, 2026, needs more optimization.
18 171 0.203068311997 Henry Cohn, 2026, needs more optimization.
18 172 0.204247609846 Henry Cohn, 2026, needs more optimization.
18 173 0.205761439156 Henry Cohn, 2026, needs more optimization.
18 174 0.208697490607 Henry Cohn, 2026, needs more optimization.
18 175 0.211741836979 Henry Cohn, 2026, needs more optimization.
18 176 0.213036370120 Henry Cohn, 2026, needs more optimization.
18 177 0.214250084335 Henry Cohn, 2026, needs more optimization.
18 179 0.214580042766 Henry Cohn, 2026, needs more optimization.
18 180 0.214580042773 Henry Cohn, 2026, needs more optimization.
18 181 0.214580603161 Henry Cohn, 2026, needs more optimization.
18 184 0.214580882717 Henry Cohn, 2026, needs more optimization.
18 186 0.214580882720 Henry Cohn, 2026, needs more optimization.
18 187 0.214582420751 Henry Cohn, 2026, needs more optimization.
18 188 0.214752745580 Henry Cohn, 2026, needs more optimization.
18 189 0.217221147795 Henry Cohn, 2026, needs more optimization.
18 190 0.219692642117 Henry Cohn, 2026, needs more optimization.
18 191 0.221432690941 Henry Cohn, 2026, needs more optimization.
18 192 0.223214674781 Henry Cohn, 2026, needs more optimization.
18 210 0.224009237740 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
11⁢x2+2⁢x−1
18 211 0.225990499496 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
18 212 0.228848482488 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
18 213 0.230092987106 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
18 214 0.231934740043 Henry Cohn, 2026, needs more optimization.
18 215 0.231934817426 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
18 221 0.232007097535 Henry Cohn, 2026, needs more optimization.
18 222 0.232007098160 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
18 224 0.232010656772 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
18 225 0.232175156854 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
18 226 0.233054009359 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
18 227 0.236185963482 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
18 228 0.237259939982 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
18 229 0.237908637592 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
18 230 0.238378768928 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
18 231 0.238876657801 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
18 232 0.239457659826 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
18 233 0.239915070673 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
18 234 0.240478489947 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
18 235 0.240784504422 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
18 236 0.241275031509 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
18 237 0.241694790586 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
18 238 0.242146902152 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
18 239 0.242650374595 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
18 240 0.243099425080 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
18 241 0.243428750757 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
18 242 0.243740717321 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
18 243 0.244076205422 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
18 244 0.244437554898 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
18 245 0.244845083818 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
18 246 0.245058046151 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
18 247 0.245331662928 Henry Cohn, 2026, needs more optimization.
18 248 0.245387636514 Henry Cohn, 2026, needs more optimization.
18 249 0.245536656833 Henry Cohn, 2026, needs more optimization.
18 250 0.245627654677 Henry Cohn, 2026, needs more optimization.
18 251 0.245771017987 Henry Cohn, 2026, needs more optimization.
18 252 0.245833399556 Henry Cohn, 2026, needs more optimization.
18 253 0.245966762368 Henry Cohn, 2026, needs more optimization.
18 254 0.245968258489 Henry Cohn, 2026, needs more optimization.
18 255 0.246018611579 Henry Cohn, 2026, needs more optimization.
18 256 0.246066162321 Henry Cohn, 2026, needs more optimization.
18 257 0.246122779539 Henry Cohn, 2026, needs more optimization.
18 258 0.246134898446 Henry Cohn, 2026, needs more optimization.
18 259 0.246241211073 Henry Cohn, 2026, needs more optimization.
18 260 0.246316908953 Henry Cohn, 2026, needs more optimization.
18 261 0.246344426839 Henry Cohn, 2026, needs more optimization.
18 262 0.246402898694 Henry Cohn, 2026, needs more optimization.
18 263 0.246433997538 Henry Cohn, 2026, needs more optimization.
18 264 0.246478752342 Henry Cohn, 2026, needs more optimization.
18 265 0.246918202898 Henry Cohn, 2026, needs more optimization.
18 266 0.246951438378 Henry Cohn, 2026, needs more optimization.
18 267 0.246972076815 Henry Cohn, 2026, needs more optimization.
18 268 0.247076619076 Henry Cohn, 2026, needs more optimization.
18 269 0.247473172397 Henry Cohn, 2026, needs more optimization.
18 270 0.247484781302 Henry Cohn, 2026, needs more optimization.
18 271 0.247527103295 Henry Cohn, 2026, needs more optimization.
18 272 0.247574167266 Henry Cohn, 2026, needs more optimization.
18 273 0.247580689099 Henry Cohn, 2026, needs more optimization.
18 274 0.247594186788 Henry Cohn, 2026, needs more optimization.
18 275 0.247626131163 Henry Cohn, 2026, needs more optimization.
18 276 0.247646419025 Henry Cohn, 2026, needs more optimization.
18 277 0.247700627359 Henry Cohn, 2026, needs more optimization.
18 278 0.247719112859 Henry Cohn, 2026, needs more optimization.
18 279 0.247739345946 Henry Cohn, 2026, needs more optimization.
18 280 0.247741668984 Henry Cohn, 2026, needs more optimization.
18 281 0.247789219267 Henry Cohn, 2026, needs more optimization.
18 282 0.247800395597 Henry Cohn, 2026, needs more optimization.
18 283 0.247855354547 Henry Cohn, 2026, needs more optimization.
18 284 0.247855356407 Henry Cohn, 2026, needs more optimization.
18 285 0.247856117218 Henry Cohn, 2026, needs more optimization.
18 286 0.247856125798 Henry Cohn, 2026, needs more optimization.
18 287 0.248144191940 Henry Cohn, 2026, needs more optimization.
18 288 0.248878268629 Henry Cohn, 2026, needs more optimization.
18 289 0.248922015437 Henry Cohn, 2026, needs more optimization.
18 290 0.249110620459 Henry Cohn, 2026, needs more optimization.
18 291 0.249395484503 Henry Cohn, 2026, needs more optimization.
18 292 0.249395484710 Henry Cohn, 2026, needs more optimization.
18 293 0.249622433495 Henry Cohn, 2026, needs more optimization.
18 294 0.249873852154 Henry Cohn, 2026, needs more optimization.
18 295 0.249874859088 Henry Cohn, 2026, needs more optimization.
18 296 0.249928492611 Henry Cohn, 2026, needs more optimization.
18 297 0.250003019177 Henry Cohn, 2026, needs more optimization.
18 298 0.250003021639 Henry Cohn, 2026, needs more optimization.
18 299 0.250003022988 Henry Cohn, 2026, needs more optimization.
18 302 0.250003678229 Henry Cohn, 2026, needs more optimization.
18 303 0.250008678872 Henry Cohn, 2026, needs more optimization.
18 304 0.250009255812 Henry Cohn, 2026, needs more optimization.
18 305 0.250019508673 Henry Cohn, 2026, needs more optimization.
18 306 0.250117452624 Henry Cohn, 2026, needs more optimization.
18 307 0.251207489942 Henry Cohn, 2026, needs more optimization.
18 308 0.251969388095 Henry Cohn, 2026, needs more optimization.
18 309 0.252613053013 Henry Cohn, 2026, needs more optimization.
18 310 0.253759006378 Henry Cohn, 2026, needs more optimization.
18 311 0.254809338887 Henry Cohn, 2026, needs more optimization.
18 312 0.256213816402 Henry Cohn, 2026, needs more optimization.
18 313 0.256826791517 Henry Cohn, 2026, needs more optimization.
18 314 0.258091019543 Henry Cohn, 2026, needs more optimization.
18 315 0.258817632748 Henry Cohn, 2026, needs more optimization.
18 316 0.258834366682 Henry Cohn, 2026, needs more optimization.
18 317 0.258928475395 Henry Cohn, 2026, needs more optimization.
18 318 0.258932597526 Henry Cohn, 2026, needs more optimization.
18 319 0.259041690530 Henry Cohn, 2026, needs more optimization.
18 320 0.259157489650 Henry Cohn, 2026, needs more optimization.
18 321 0.259163156512 Henry Cohn, 2026, needs more optimization.
18 322 0.259173494309 Henry Cohn, 2026, needs more optimization.
18 323 0.259181175220 Henry Cohn, 2026, needs more optimization.
18 324 0.259354188758 Henry Cohn, 2026, needs more optimization.
18 325 0.259840750699 Henry Cohn, 2026, needs more optimization.
18 326 0.259912688948 Henry Cohn, 2026, needs more optimization.
18 327 0.260096832994 Henry Cohn, 2026, needs more optimization.
18 328 0.260214021724 Henry Cohn, 2026, needs more optimization.
18 329 0.260395772980 Henry Cohn, 2026, needs more optimization.
18 330 0.260709405513 Henry Cohn, 2026, needs more optimization.
18 331 0.260710788726 Henry Cohn, 2026, needs more optimization.
18 332 0.260712669793 Henry Cohn, 2026, needs more optimization.
18 333 0.260730743783 Henry Cohn, 2026, needs more optimization.
18 334 0.260749068159 Henry Cohn, 2026, needs more optimization.
18 335 0.260766810238 Henry Cohn, 2026, needs more optimization.
18 336 0.260776238562 Henry Cohn, 2026, needs more optimization.
18 337 0.260822386154 Henry Cohn, 2026, needs more optimization.
18 338 0.260823540325 Henry Cohn, 2026, needs more optimization.
18 339 0.260834749561 Henry Cohn, 2026, needs more optimization.
18 340 0.260836480836 Henry Cohn, 2026, needs more optimization.
18 341 0.260868053541 Henry Cohn, 2026, needs more optimization.
18 342 0.260868798962 Henry Cohn, 2026, needs more optimization.
18 343 0.260878440076 Henry Cohn, 2026, needs more optimization.
18 344 0.260910521919 Henry Cohn, 2026, needs more optimization.
18 345 0.260928271866 Henry Cohn, 2026, needs more optimization.
18 346 0.260938858854 Henry Cohn, 2026, needs more optimization.
18 347 0.260942878347 Henry Cohn, 2026, needs more optimization.
18 348 0.260957767680 Henry Cohn, 2026, needs more optimization.
18 349 0.260961870760 Henry Cohn, 2026, needs more optimization.
18 350 0.260988790151 Henry Cohn, 2026, needs more optimization.
18 352 0.261013578769 Henry Cohn, 2026, needs more optimization.
18 353 0.262945969973 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
18 354 0.277835032990 Henry Cohn, 2026, needs more optimization.
18 355 0.280365583999 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
18 356 0.284677619291 Henry Cohn, 2026, needs more optimization.
18 357 0.287869003393 Henry Cohn, 2026, needs more optimization.
18 358 0.290324074061 Henry Cohn, 2026, needs more optimization.
18 359 0.291541488075 Henry Cohn, 2026, needs more optimization.
18 360 0.292837949312 Henry Cohn, 2026, needs more optimization.
18 374 0.294118378911 Henry Cohn, 2026, needs more optimization.
18 379 0.294118399809 Henry Cohn, 2026, needs more optimization.
18 399 0.294118475997 Henry Cohn, 2026, needs more optimization.
18 402 0.294118478695 Henry Cohn, 2026, needs more optimization.
18 411 0.294118496257 Henry Cohn, 2026, needs more optimization.
18 413 0.294119936152 Henry Cohn, 2026, needs more optimization.
18 414 0.294163845247 Henry Cohn, 2026, needs more optimization.
18 415 0.295538239529 Henry Cohn, 2026, needs more optimization.
18 416 0.295538317517 Henry Cohn, 2026, needs more optimization.
18 417 0.295876274618 Henry Cohn, 2026, needs more optimization.
18 419 0.295911304702 Henry Cohn, 2026, needs more optimization.
18 420 0.295923675013 Henry Cohn, 2026, needs more optimization.
18 480 0.296296296297 Henry Cohn, 2025, by enlarging a code from T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
27⁢x−8
18 481 0.298381039896 Henry Cohn, 2026, needs more optimization.
18 482 0.300181449869 Henry Cohn, 2026, needs more optimization.
18 483 0.301456013084 Henry Cohn, 2026, needs more optimization.
18 484 0.302682594026 Henry Cohn, 2026, needs more optimization.
18 485 0.303478200320 Henry Cohn, 2026, needs more optimization.
18 486 0.305662838512 Henry Cohn, 2026, needs more optimization.
18 487 0.307359527544 Henry Cohn, 2026, needs more optimization.
18 488 0.309212791229 Henry Cohn, 2026, needs more optimization.
18 489 0.309480416750 Henry Cohn, 2026, needs more optimization.
18 490 0.309601876583 Henry Cohn, 2026, needs more optimization.
18 491 0.309882098976 Henry Cohn, 2026, needs more optimization.
18 492 0.310035493759 Henry Cohn, 2026, needs more optimization.
18 493 0.311325631241 Henry Cohn, 2026, needs more optimization.
18 494 0.312263559519 Henry Cohn, 2026, needs more optimization.
18 495 0.312956809283 Henry Cohn, 2026, needs more optimization.
18 496 0.313613704614 Henry Cohn, 2026, needs more optimization.
18 497 0.313673431672 Henry Cohn, 2026, needs more optimization.
18 498 0.313742704588 Henry Cohn, 2026, needs more optimization.
18 499 0.313936364574 Henry Cohn, 2026, needs more optimization.
18 500 0.315403617347 Henry Cohn, 2026, needs more optimization.
18 501 0.315952140128 Henry Cohn, 2026, needs more optimization.
18 502 0.316367524225 Henry Cohn, 2026, needs more optimization.
18 503 0.316619445698 Henry Cohn, 2026, needs more optimization.
18 504 0.316735149492 Henry Cohn, 2026, needs more optimization.
18 505 0.317102993793 Henry Cohn, 2026, needs more optimization.
18 506 0.317419556623 Henry Cohn, 2026, needs more optimization.
18 507 0.317883231222 Henry Cohn, 2026, needs more optimization.
18 508 0.318370576142 Henry Cohn, 2026, needs more optimization.
18 509 0.318705984867 Henry Cohn, 2026, needs more optimization.
18 510 0.318835744326 Henry Cohn, 2026, needs more optimization.
18 511 0.318929642853 Henry Cohn, 2026, needs more optimization.
18 512 0.319257735385 Henry Cohn, 2026, needs more optimization.
18 513 0.319284492363 Henry Cohn, 2026, needs more optimization.
18 514 0.319628971536 Henry Cohn, 2026, needs more optimization.
18 515 0.319681000768 Henry Cohn, 2026, needs more optimization.
18 516 0.320212107986 Henry Cohn, 2026, needs more optimization.
18 517 0.320463663166 Henry Cohn, 2026, needs more optimization.
18 518 0.321004890660 Henry Cohn, 2026, needs more optimization.
18 519 0.321650252393 Henry Cohn, 2026, needs more optimization.
18 520 0.321836381429 Henry Cohn, 2026, needs more optimization.
18 521 0.321862883299 Henry Cohn, 2026, needs more optimization.
18 522 0.323073025853 Henry Cohn, 2026, needs more optimization.
18 523 0.323106569680 Henry Cohn, 2026, needs more optimization.
18 524 0.323167104481 Henry Cohn, 2026, needs more optimization.
18 525 0.323734367371 Henry Cohn, 2026, needs more optimization.
18 526 0.323938628922 Henry Cohn, 2026, needs more optimization.
18 527 0.324353574267 Henry Cohn, 2026, needs more optimization.
18 528 0.324641201384 Henry Cohn, 2026, needs more optimization.
18 529 0.324922154974 Henry Cohn, 2026, needs more optimization.
18 530 0.324930796419 Henry Cohn, 2026, needs more optimization.
18 531 0.325262399933 Henry Cohn, 2026, needs more optimization.
18 532 0.325685907264 Henry Cohn, 2026, needs more optimization.
18 533 0.326007409218 Henry Cohn, 2026, needs more optimization.
18 534 0.326333342710 Henry Cohn, 2026, needs more optimization.
18 535 0.326574834409 Henry Cohn, 2026, needs more optimization.
18 536 0.326875250227 Henry Cohn, 2026, needs more optimization.
18 537 0.327103232434 Henry Cohn, 2026, needs more optimization.
18 538 0.327724004012 Henry Cohn, 2026, needs more optimization.
18 539 0.327903942910 Henry Cohn, 2026, needs more optimization.
18 540 0.328307501984 Henry Cohn, 2026, needs more optimization.
18 541 0.328713435928 Henry Cohn, 2026, needs more optimization.
18 542 0.328990685954 Henry Cohn, 2026, needs more optimization.
18 543 0.329066212639 Henry Cohn, 2026, needs more optimization.
18 544 0.329516122111 Henry Cohn, 2026, needs more optimization.
18 545 0.329665024391 Henry Cohn, 2026, needs more optimization.
18 546 0.330029469640 Henry Cohn, 2026, needs more optimization.
18 547 0.330236319649 Henry Cohn, 2026, needs more optimization.
18 548 0.330494625983 Henry Cohn, 2026, needs more optimization.
18 549 0.330846313400 Henry Cohn, 2026, needs more optimization.
18 550 0.331282412099 Henry Cohn, 2026, needs more optimization.
18 551 0.331636388358 Henry Cohn, 2026, needs more optimization.
18 552 0.331922735514 Henry Cohn, 2026, needs more optimization.
18 553 0.332346176032 Henry Cohn, 2026, needs more optimization.
18 554 0.332422021346 Henry Cohn, 2026, needs more optimization.
18 555 0.332557909307 Henry Cohn, 2026, needs more optimization.
18 556 0.332845475007 Henry Cohn, 2026, needs more optimization.
18 557 0.332965880408 Henry Cohn, 2026, needs more optimization.
18 558 0.333149042029 Henry Cohn, 2026, needs more optimization.
18 672 0.333333333334 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
3⁢x−1
18 704 0.333333333334 C. Ma, T. Tao Z., P. Li, M. Liu, H. Chen, Z. Mao, Y. Cheng, Y. Qi, and Y. Yang, Finding kissing numbers with game-theoretic reinforcement learning, preprint, 2025, arXiv:2511.13391.
3⁢x−1
18 705 0.342198384693 Henry Cohn, 2026, needs more optimization.
18 706 0.343271262968 Henry Cohn, 2026, needs more optimization.
18 707 0.344648334009 Henry Cohn, 2026, needs more optimization.
18 708 0.345475324461 Henry Cohn, 2026, needs more optimization.
18 709 0.346116740551 Henry Cohn, 2026, needs more optimization.
18 710 0.346663821830 Henry Cohn, 2026, needs more optimization.
18 711 0.347192037772 Henry Cohn, 2026, needs more optimization.
18 712 0.347589080825 Henry Cohn, 2026, needs more optimization.
18 713 0.348059120096 Henry Cohn, 2026, needs more optimization.
18 714 0.348511069184 Henry Cohn, 2026, needs more optimization.
18 715 0.348818407929 Henry Cohn, 2026, needs more optimization.
18 716 0.348920320880 Henry Cohn, 2026, needs more optimization.
18 717 0.349210319309 Henry Cohn, 2026, needs more optimization.
18 718 0.349479657649 Henry Cohn, 2026, needs more optimization.
18 719 0.349807739921 Henry Cohn, 2026, needs more optimization.
18 720 0.350025372387 Henry Cohn, 2026, needs more optimization.
18 721 0.350297065398 Henry Cohn, 2026, needs more optimization.
18 722 0.350569895816 Henry Cohn, 2026, needs more optimization.
18 723 0.350624106108 Henry Cohn, 2026, needs more optimization.
18 724 0.350843544366 Henry Cohn, 2026, needs more optimization.
18 725 0.350966184375 Henry Cohn, 2026, needs more optimization.
18 726 0.351034034181 Henry Cohn, 2026, needs more optimization.
18 727 0.351243288318 Henry Cohn, 2026, needs more optimization.
18 728 0.351395965803 Henry Cohn, 2026, needs more optimization.
18 729 0.351531892560 Henry Cohn, 2026, needs more optimization.
18 730 0.351721574025 Henry Cohn, 2026, needs more optimization.
18 731 0.351791322885 Henry Cohn, 2026, needs more optimization.
18 733 0.351905771508 Henry Cohn, 2026, needs more optimization.
18 734 0.351912424563 Henry Cohn, 2026, needs more optimization.
18 737 0.351916296306 Henry Cohn, 2026, needs more optimization.
18 740 0.351921896780 Henry Cohn, 2026, needs more optimization.
18 742 0.351922999486 Henry Cohn, 2026, needs more optimization.
18 743 0.351927986271 Henry Cohn, 2026, needs more optimization.
18 744 0.351947314025 Henry Cohn, 2026, needs more optimization.
18 746 0.351949629986 Henry Cohn, 2026, needs more optimization.
18 747 0.351966507930 Henry Cohn, 2026, needs more optimization.
18 749 0.351979599313 Henry Cohn, 2026, needs more optimization.
18 750 0.351990021190 Henry Cohn, 2026, needs more optimization.
18 752 0.351990465867 Henry Cohn, 2026, needs more optimization.
18 753 0.351995823518 Henry Cohn, 2026, needs more optimization.
18 754 0.352000678755 Henry Cohn, 2026, needs more optimization.
18 755 0.352005827789 Henry Cohn, 2026, needs more optimization.
18 756 0.352007167540 Henry Cohn, 2026, needs more optimization.
18 757 0.352009054559 Henry Cohn, 2026, needs more optimization.
18 758 0.352015943098 Henry Cohn, 2026, needs more optimization.
18 760 0.352019883693 Henry Cohn, 2026, needs more optimization.
18 761 0.352031165903 Henry Cohn, 2026, needs more optimization.
18 762 0.352034988547 Henry Cohn, 2026, needs more optimization.
18 764 0.352035363487 Henry Cohn, 2026, needs more optimization.
18 765 0.352036235221 Henry Cohn, 2026, needs more optimization.
18 767 0.352038865003 Henry Cohn, 2026, needs more optimization.
18 768 0.352039023107 Numaro AI Autoresearch, 11,000+ New Verified Spherical-Code Records from AI Autoresearch, Numaro Research Report NUMARO-2026-015 (2026), https://numaro.tech/research/spherical-codes-2026/.
18 769 0.352040252849 Henry Cohn, 2026, needs more optimization.
18 771 0.352047345930 Henry Cohn, 2026, needs more optimization.
18 772 0.356479170867 Henry Cohn, 2026, needs more optimization.
18 773 0.356637963969 Henry Cohn, 2026, needs more optimization.
18 774 0.356817986973 Henry Cohn, 2026, needs more optimization.
18 775 0.356968120983 Henry Cohn, 2026, needs more optimization.
18 776 0.357116865677 Henry Cohn, 2026, needs more optimization.
18 867 0.357142857143 Henry Cohn, 2025, by modifying a construction from C. Ma, T. Tao Z., P. Li, M. Liu, H. Chen, Z. Mao, Y. Cheng, Y. Qi, and Y. Yang, Finding kissing numbers with game-theoretic reinforcement learning, preprint, 2025, arXiv:2511.13391.
14⁢x−5
18 868 0.373242698022 Numaro AI Autoresearch, 11,000+ New Verified Spherical-Code Records from AI Autoresearch, Numaro Research Report NUMARO-2026-015 (2026), https://numaro.tech/research/spherical-codes-2026/.
18 869 0.373254115239 Henry Cohn, 2026, needs more optimization.
18 1024 0.375 C. Ma, T. Tao Z., P. Li, M. Liu, H. Chen, Z. Mao, Y. Cheng, Y. Qi, and Y. Yang, Finding kissing numbers with game-theoretic reinforcement learning, preprint, 2025, arXiv:2511.13391.
8⁢x−3
19 39 0.040648168399 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
5491⁢x3−361⁢x2−19⁢x+1
19 40 0.047619047620 T. Ericson and V. Zinoviev, Spherical codes generated by binary partitions of symmetric pointsets, IEEE Trans. Inform. Theory 41 (1995), 107–129, doi:10.1109/18.370114.
21⁢x−1
19 41 0.053165944699 Henry Cohn, 2023.
19 42 0.053978364917 Henry Cohn, 2025.
19 43 0.058551084358 Henry Cohn, 2025.
19 44 0.059131790994 Henry Cohn, 2023.
19 45 0.059418524383 Henry Cohn, 2023.
Minimal polynomial listed in plain text data
19 48 0.063706690497 Henry Cohn, 2023.
215⁢x2+2⁢x−1
19 50 0.069767441861 Henry Cohn, 2023.
43⁢x−3
19 51 0.075275141543 Henry Cohn, 2025.
19 52 0.077597142083 Henry Cohn, 2026.
19 53 0.080493593475 Henry Cohn, 2026.
19 54 0.081604760576 Henry Cohn, 2026, needs more optimization.
19 55 0.082178889828 Henry Cohn, 2025.
19 56 0.083233613334 Henry Cohn, 2026.
19 57 0.084523221985 Henry Cohn, 2026, needs more optimization.
19 58 0.088502538618 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
19 60 0.090909090910 Kissing configuration of 81 points in 20 dimensions from A. E. Brouwer and W. H. Haemers, Structure and uniqueness of the (81,20,1,6) strongly regular graph, Discrete Math. 106/107 (1992), 77–82, doi:10.1016/0012-365X(92)90532-K.
11⁢x−1
19 62 0.093346164763 Henry Cohn, 2026.
479⁢x2−34⁢x−1
19 66 0.097744360903 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
133⁢x−13
19 69 0.101319957446 Henry Cohn, 2026, needs more optimization.
19 70 0.101392647883 Henry Cohn, 2025, needs more optimization.
19 71 0.101456853395 Henry Cohn, 2026, needs more optimization.
19 72 0.101838513947 Henry Cohn, 2026, needs more optimization.
19 73 0.102201317334 Henry Cohn, 2026.
311⁢x2−22⁢x−1
19 74 0.104236915651 Henry Cohn, 2026, needs more optimization.
19 75 0.107816370262 Henry Cohn, 2026, needs more optimization.
19 76 0.111553284797 Henry Cohn, 2026.
19 77 0.112762714951 Henry Cohn, 2026, needs more optimization.
19 89 0.112912613537 Henry Cohn, 2023.
167⁢x2−10⁢x−1
19 90 0.121308037796 Henry Cohn, 2024.
2809⁢x4−192⁢x3−86⁢x2+1
19 91 0.128902034018 Henry Cohn, 2026, needs more optimization.
19 92 0.133859604087 Henry Cohn, 2026, needs more optimization.
19 93 0.142506259847 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
19 100 0.142857142858 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
7⁢x−1
19 102 0.142857142858 Henry Cohn, 2023, by enlarging a code from T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
7⁢x−1
19 103 0.149928121676 Henry Cohn, 2026.
19 104 0.150748959688 Henry Cohn, 2026.
19 105 0.152679567208 Henry Cohn, 2026, needs more optimization.
19 106 0.152679567278 Henry Cohn, 2026, needs more optimization.
19 107 0.153846307095 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
19 108 0.156351981287 Henry Cohn, 2026, needs more optimization.
19 132 0.157894736843 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
19⁢x−3
19 133 0.168802199651 Henry Cohn, 2026.
19 134 0.174620105369 Henry Cohn, 2026, needs more optimization.
19 135 0.175005075648 Henry Cohn, 2026, needs more optimization.
19 136 0.175550938988 Henry Cohn, 2026, needs more optimization.
19 137 0.176552072145 Henry Cohn, 2026, needs more optimization.
19 138 0.177160791714 Henry Cohn, 2026, needs more optimization.
19 139 0.177607145165 Henry Cohn, 2026, needs more optimization.
19 140 0.178022647099 Henry Cohn, 2026, needs more optimization.
19 141 0.178306253389 Henry Cohn, 2026, needs more optimization.
19 142 0.178659456328 Henry Cohn, 2026, needs more optimization.
19 143 0.179124259783 Henry Cohn, 2026, needs more optimization.
19 144 0.179750083872 Henry Cohn, 2026, needs more optimization.
19 145 0.180428426406 Henry Cohn, 2026, needs more optimization.
19 146 0.180708623307 Henry Cohn, 2026, needs more optimization.
19 147 0.182330408346 Henry Cohn, 2026, needs more optimization.
19 148 0.183293302892 Henry Cohn, 2026, needs more optimization.
19 149 0.183922068892 Henry Cohn, 2026, needs more optimization.
19 150 0.184646543855 Henry Cohn, 2026, needs more optimization.
19 151 0.186861702854 Henry Cohn, 2026, needs more optimization.
19 166 0.189189189190 Henry Cohn, 2026.
37⁢x−7
19 176 0.191919191920 Henry Cohn, 2025, by enlarging a code from T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
99⁢x−19
19 177 0.193637369253 Henry Cohn, 2026.
19 178 0.194663251780 Henry Cohn, 2026, needs more optimization.
19 179 0.195466927374 Henry Cohn, 2026, needs more optimization.
19 180 0.195821119719 Henry Cohn, 2026, needs more optimization.
19 181 0.196900143928 Henry Cohn, 2026, needs more optimization.
19 182 0.197578676212 Henry Cohn, 2026, needs more optimization.
19 183 0.198453416125 Henry Cohn, 2026, needs more optimization.
19 184 0.199206619499 Henry Cohn, 2026, needs more optimization.
19 185 0.199766909588 Henry Cohn, 2026, needs more optimization.
19 192 0.2 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
5⁢x−1
19 193 0.203357314598 Henry Cohn, 2026.
19 194 0.205905415936 Henry Cohn, 2026, needs more optimization.
19 195 0.207107870178 Henry Cohn, 2026, needs more optimization.
19 196 0.208039035510 Henry Cohn, 2026, needs more optimization.
19 197 0.208691101910 Henry Cohn, 2026, needs more optimization.
19 198 0.209389192438 Henry Cohn, 2026, needs more optimization.
19 199 0.209806575429 Henry Cohn, 2026, needs more optimization.
19 202 0.210526315790 C. Ma, T. Tao Z., P. Li, M. Liu, H. Chen, Z. Mao, Y. Cheng, Y. Qi, and Y. Yang, Finding kissing numbers with game-theoretic reinforcement learning, preprint, 2025, arXiv:2511.13391.
19⁢x−4
19 203 0.212022013635 Henry Cohn, 2026, needs more optimization.
19 204 0.212309120939 Henry Cohn, 2026, needs more optimization.
19 205 0.212684657796 Henry Cohn, 2026, needs more optimization.
19 206 0.212895489764 Henry Cohn, 2026, needs more optimization.
19 207 0.213596186334 Henry Cohn, 2026, needs more optimization.
19 208 0.214189897369 Henry Cohn, 2026, needs more optimization.
19 209 0.214622274059 Henry Cohn, 2026, needs more optimization.
19 210 0.214960664771 Henry Cohn, 2026, needs more optimization.
19 211 0.215403215476 Henry Cohn, 2026, needs more optimization.
19 212 0.215584842347 Henry Cohn, 2026, needs more optimization.
19 213 0.216093435233 Henry Cohn, 2026, needs more optimization.
19 214 0.216350940872 Henry Cohn, 2026, needs more optimization.
19 215 0.216856755301 Henry Cohn, 2026, needs more optimization.
19 216 0.217388128163 Henry Cohn, 2026, needs more optimization.
19 217 0.217552839292 Henry Cohn, 2026, needs more optimization.
19 218 0.218606447832 Henry Cohn, 2026, needs more optimization.
19 219 0.219121059321 Henry Cohn, 2026, needs more optimization.
19 220 0.219981252182 Henry Cohn, 2026, needs more optimization.
19 221 0.221044730586 Henry Cohn, 2026, needs more optimization.
19 222 0.222157282794 Henry Cohn, 2026, needs more optimization.
19 223 0.222363676452 Henry Cohn, 2026, needs more optimization.
19 224 0.222481880013 Henry Cohn, 2026, needs more optimization.
19 225 0.223293099278 Henry Cohn, 2026, needs more optimization.
19 226 0.223540656352 Henry Cohn, 2026, needs more optimization.
19 227 0.223954670750 Henry Cohn, 2026, needs more optimization.
19 228 0.224159412271 Henry Cohn, 2026, needs more optimization.
19 229 0.224194070242 Henry Cohn, 2026, needs more optimization.
19 230 0.224312771734 Henry Cohn, 2026, needs more optimization.
19 231 0.224470119509 Henry Cohn, 2026, needs more optimization.
19 232 0.224533692917 Henry Cohn, 2026, needs more optimization.
19 233 0.224686957679 Henry Cohn, 2026, needs more optimization.
19 234 0.224739920657 Henry Cohn, 2026, needs more optimization.
19 235 0.225173621315 Henry Cohn, 2026, needs more optimization.
19 236 0.225829136549 Henry Cohn, 2026, needs more optimization.
19 237 0.225934294866 Henry Cohn, 2026, needs more optimization.
19 238 0.225960619822 Henry Cohn, 2026, needs more optimization.
19 239 0.225980935019 Henry Cohn, 2026, needs more optimization.
19 240 0.226446633888 Henry Cohn, 2026, needs more optimization.
19 241 0.226625810579 Henry Cohn, 2026, needs more optimization.
19 242 0.226789078585 Henry Cohn, 2026, needs more optimization.
19 243 0.227019622689 Henry Cohn, 2026, needs more optimization.
19 244 0.227635840562 Henry Cohn, 2026, needs more optimization.
19 245 0.228801342816 Henry Cohn, 2026, needs more optimization.
19 246 0.229502790249 Henry Cohn, 2026, needs more optimization.
19 247 0.229935142353 Henry Cohn, 2026, needs more optimization.
19 248 0.230600575811 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
19 277 0.230769230770 Henry Cohn, 2025, by enlarging a code from T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
13⁢x−3
19 278 0.235886985005 Henry Cohn, 2026, needs more optimization.
19 279 0.237014772071 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
19 280 0.237995421719 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
19 291 0.238519273263 Henry Cohn, 2026, needs more optimization.
19 292 0.240704635744 Henry Cohn, 2026, needs more optimization.
19 293 0.242301435199 Henry Cohn, 2026, needs more optimization.
19 294 0.243938302165 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
19 295 0.244482855555 Henry Cohn, 2026, needs more optimization.
19 296 0.244756092001 Henry Cohn, 2026, needs more optimization.
19 297 0.245792687070 Henry Cohn, 2026, needs more optimization.
19 298 0.246151731610 Henry Cohn, 2026, needs more optimization.
19 299 0.246659944898 Henry Cohn, 2026, needs more optimization.
19 300 0.246660631785 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
19 301 0.247931355454 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
19 302 0.248412224186 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
19 303 0.249093268395 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
19 304 0.249388060562 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
19 305 0.249572932143 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
19 306 0.249892722624 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
19 307 0.249929924675 Henry Cohn, 2026, needs more optimization.
19 308 0.249930332971 Henry Cohn, 2026, needs more optimization.
19 309 0.249933195930 Henry Cohn, 2026, needs more optimization.
19 311 0.249935361232 Henry Cohn, 2026, needs more optimization.
19 312 0.249947708810 Henry Cohn, 2026, needs more optimization.
19 313 0.249947790084 Henry Cohn, 2026, needs more optimization.
19 314 0.249950108395 Henry Cohn, 2026, needs more optimization.
19 315 0.249952577353 Henry Cohn, 2026, needs more optimization.
19 318 0.249963764413 Henry Cohn, 2026, needs more optimization.
19 319 0.249967165980 Henry Cohn, 2026, needs more optimization.
19 320 0.249988819083 Henry Cohn, 2026, needs more optimization.
19 321 0.249995104371 Henry Cohn, 2026, needs more optimization.
19 322 0.250000789385 Henry Cohn, 2026, needs more optimization.
19 323 0.250002929300 Henry Cohn, 2026, needs more optimization.
19 324 0.250017872056 Henry Cohn, 2026, needs more optimization.
19 325 0.250054454271 Henry Cohn, 2026, needs more optimization.
19 326 0.250149576999 Henry Cohn, 2026, needs more optimization.
19 327 0.250727023360 Henry Cohn, 2026, needs more optimization.
19 328 0.251781786204 Henry Cohn, 2026, needs more optimization.
19 329 0.252746238548 Henry Cohn, 2026, needs more optimization.
19 330 0.253217192515 Henry Cohn, 2026, needs more optimization.
19 331 0.254209170467 Henry Cohn, 2026, needs more optimization.
19 332 0.255661161903 Henry Cohn, 2026, needs more optimization.
19 333 0.256788881214 Henry Cohn, 2026, needs more optimization.
19 334 0.257980131566 Henry Cohn, 2026, needs more optimization.
19 335 0.258029579372 Henry Cohn, 2026, needs more optimization.
19 336 0.258113644701 Henry Cohn, 2026, needs more optimization.
19 337 0.258203390843 Henry Cohn, 2026, needs more optimization.
19 338 0.258251084814 Henry Cohn, 2026, needs more optimization.
19 339 0.258358001215 Henry Cohn, 2026, needs more optimization.
19 340 0.258480000728 Henry Cohn, 2026, needs more optimization.
19 341 0.258540542868 Henry Cohn, 2026, needs more optimization.
19 342 0.258640462513 Henry Cohn, 2026, needs more optimization.
19 343 0.258804716765 Henry Cohn, 2026, needs more optimization.
19 345 0.258818445340 Henry Cohn, 2026, needs more optimization.
19 346 0.258828529225 Henry Cohn, 2026, needs more optimization.
19 347 0.258869544352 Henry Cohn, 2026, needs more optimization.
19 348 0.258874082690 Henry Cohn, 2026, needs more optimization.
19 349 0.258925944609 Henry Cohn, 2026, needs more optimization.
19 350 0.259055755292 Henry Cohn, 2026, needs more optimization.
19 351 0.259175660992 Henry Cohn, 2026, needs more optimization.
19 352 0.259230367281 Henry Cohn, 2026, needs more optimization.
19 353 0.259307756464 Henry Cohn, 2026, needs more optimization.
19 354 0.259361427168 Henry Cohn, 2026, needs more optimization.
19 355 0.259430524757 Henry Cohn, 2026, needs more optimization.
19 356 0.259507446267 Henry Cohn, 2026, needs more optimization.
19 357 0.259545483839 Henry Cohn, 2026, needs more optimization.
19 358 0.259869359958 Henry Cohn, 2026, needs more optimization.
19 359 0.259957069924 Henry Cohn, 2026, needs more optimization.
19 360 0.260589687841 Henry Cohn, 2026, needs more optimization.
19 361 0.261503162698 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
19 362 0.263803628501 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
19 363 0.265639077728 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
19 364 0.267119495412 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
19 367 0.268540691304 Henry Cohn, 2026, needs more optimization.
19 368 0.270348286989 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
19 369 0.271660319184 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
19 404 0.272727272728 C. Ma, T. Tao Z., P. Li, M. Liu, H. Chen, Z. Mao, Y. Cheng, Y. Qi, and Y. Yang, Finding kissing numbers with game-theoretic reinforcement learning, preprint, 2025, arXiv:2511.13391.
11⁢x−3
19 405 0.278180715130 Henry Cohn, 2026, needs more optimization.
19 406 0.279647385064 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
19 407 0.281131452886 Henry Cohn, 2026, needs more optimization.
19 408 0.281654060252 Henry Cohn, 2026, needs more optimization.
19 409 0.282094571487 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
19 410 0.282455904294 Henry Cohn, 2026, needs more optimization.
19 411 0.282665893882 Henry Cohn, 2026, needs more optimization.
19 412 0.282900032948 Henry Cohn, 2026, needs more optimization.
19 413 0.283124640223 Henry Cohn, 2026, needs more optimization.
19 414 0.283380491940 Henry Cohn, 2026, needs more optimization.
19 415 0.286038313848 Henry Cohn, 2026, needs more optimization.
19 416 0.286354872971 Henry Cohn, 2026, needs more optimization.
19 417 0.287128783204 Henry Cohn, 2026, needs more optimization.
19 464 0.287671232877 Henry Cohn, 2026.
73⁢x−21
19 465 0.287673623805 Henry Cohn, 2026, needs more optimization.
19 466 0.287758305044 Henry Cohn, 2026, needs more optimization.
19 468 0.287862066704 Henry Cohn, 2026, needs more optimization.
19 469 0.287887488317 Henry Cohn, 2026, needs more optimization.
19 470 0.287889377660 Henry Cohn, 2026, needs more optimization.
19 471 0.287891516177 Henry Cohn, 2026, needs more optimization.
19 472 0.287899511306 Henry Cohn, 2026, needs more optimization.
19 473 0.287901922453 Henry Cohn, 2026, needs more optimization.
19 474 0.287903996769 Henry Cohn, 2026, needs more optimization.
19 476 0.287907345145 Henry Cohn, 2026, needs more optimization.
19 477 0.287908498069 Henry Cohn, 2026, needs more optimization.
19 478 0.287914247274 Henry Cohn, 2026, needs more optimization.
19 479 0.287919831215 Henry Cohn, 2026, needs more optimization.
19 480 0.287925976337 Henry Cohn, 2026, needs more optimization.
19 569 0.294117647059 C. Ma, T. Tao Z., P. Li, M. Liu, H. Chen, Z. Mao, Y. Cheng, Y. Qi, and Y. Yang, Finding kissing numbers with game-theoretic reinforcement learning, preprint, 2025, arXiv:2511.13391.
17⁢x−5
19 578 0.294117647059 Henry Cohn, 2026.
17⁢x−5
19 579 0.295154604839 Henry Cohn, 2026, needs more optimization.
19 580 0.296103691093 Henry Cohn, 2026, needs more optimization.
19 581 0.296709917468 Henry Cohn, 2026, needs more optimization.
19 582 0.296711245934 Henry Cohn, 2026, needs more optimization.
19 583 0.296714177068 Henry Cohn, 2026, needs more optimization.
19 584 0.296835051269 Henry Cohn, 2026, needs more optimization.
19 585 0.296934346206 Henry Cohn, 2026, needs more optimization.
19 586 0.297170050634 Henry Cohn, 2026, needs more optimization.
19 587 0.297366008063 Henry Cohn, 2026, needs more optimization.
19 588 0.297835407985 Henry Cohn, 2026, needs more optimization.
19 589 0.298138110516 Henry Cohn, 2026, needs more optimization.
19 590 0.298503962680 Henry Cohn, 2026, needs more optimization.
19 591 0.298843492557 Henry Cohn, 2026, needs more optimization.
19 592 0.299187685855 Henry Cohn, 2026, needs more optimization.
19 593 0.299286049335 Henry Cohn, 2026, needs more optimization.
19 594 0.299540168181 Henry Cohn, 2026, needs more optimization.
19 595 0.299674110183 Henry Cohn, 2026, needs more optimization.
19 596 0.299852851753 Henry Cohn, 2026, needs more optimization.
19 597 0.300024580749 Henry Cohn, 2026, needs more optimization.
19 598 0.300229918437 Henry Cohn, 2026, needs more optimization.
19 599 0.300366938937 Henry Cohn, 2026, needs more optimization.
19 600 0.300489564404 Henry Cohn, 2026, needs more optimization.
19 601 0.300634560264 Henry Cohn, 2026, needs more optimization.
19 602 0.300851168532 Henry Cohn, 2026, needs more optimization.
19 603 0.301013105968 Henry Cohn, 2026, needs more optimization.
19 604 0.301359916338 Henry Cohn, 2026, needs more optimization.
19 605 0.301633320629 Henry Cohn, 2026, needs more optimization.
19 606 0.301896399288 Henry Cohn, 2026, needs more optimization.
19 607 0.302100663500 Henry Cohn, 2026, needs more optimization.
19 608 0.302342670407 Henry Cohn, 2026, needs more optimization.
19 609 0.302592847548 Henry Cohn, 2026, needs more optimization.
19 610 0.302849030632 Henry Cohn, 2026, needs more optimization.
19 611 0.303037738505 Henry Cohn, 2026, needs more optimization.
19 612 0.303235070007 Henry Cohn, 2026, needs more optimization.
19 613 0.303376536483 Henry Cohn, 2026, needs more optimization.
19 614 0.303607925345 Henry Cohn, 2026, needs more optimization.
19 615 0.303762566861 Henry Cohn, 2026, needs more optimization.
19 616 0.303865112752 Henry Cohn, 2026, needs more optimization.
19 617 0.304053344775 Henry Cohn, 2026, needs more optimization.
19 618 0.304180230839 Henry Cohn, 2026, needs more optimization.
19 619 0.304248759553 Henry Cohn, 2026, needs more optimization.
19 620 0.304346597417 Henry Cohn, 2026, needs more optimization.
19 621 0.304449035962 Henry Cohn, 2026, needs more optimization.
19 622 0.304551578839 Henry Cohn, 2026, needs more optimization.
19 623 0.305092672472 Henry Cohn, 2026, needs more optimization.
19 624 0.305096054564 Henry Cohn, 2026, needs more optimization.
19 625 0.305097264289 Henry Cohn, 2026, needs more optimization.
19 626 0.305106744677 Henry Cohn, 2026, needs more optimization.
19 627 0.305114271210 Henry Cohn, 2026, needs more optimization.
19 628 0.305118243953 Henry Cohn, 2026, needs more optimization.
19 629 0.305123988522 Henry Cohn, 2026, needs more optimization.
19 630 0.305129372313 Henry Cohn, 2026, needs more optimization.
19 631 0.305137759018 Henry Cohn, 2026, needs more optimization.
19 632 0.305144691121 Henry Cohn, 2026, needs more optimization.
19 633 0.305147833857 Henry Cohn, 2026, needs more optimization.
19 634 0.305152516227 Henry Cohn, 2026, needs more optimization.
19 635 0.305155460487 Henry Cohn, 2026, needs more optimization.
19 636 0.305160776333 Henry Cohn, 2026, needs more optimization.
19 637 0.305164392791 Henry Cohn, 2026, needs more optimization.
19 638 0.305168575491 Henry Cohn, 2026, needs more optimization.
19 639 0.305172403604 Henry Cohn, 2026, needs more optimization.
19 640 0.305174505900 Henry Cohn, 2026, needs more optimization.
19 642 0.308281154932 Henry Cohn, 2026, needs more optimization.
19 643 0.308281162052 Henry Cohn, 2026, needs more optimization.
19 644 0.309142057181 Henry Cohn, 2026, needs more optimization.
19 645 0.309755538134 Henry Cohn, 2026, needs more optimization.
19 646 0.309756138442 Henry Cohn, 2026, needs more optimization.
19 647 0.310676765312 Henry Cohn, 2026, needs more optimization.
19 648 0.310959430401 Henry Cohn, 2026, needs more optimization.
19 649 0.311339338280 Henry Cohn, 2026, needs more optimization.
19 650 0.311459531206 Henry Cohn, 2026, needs more optimization.
19 651 0.311956775081 Henry Cohn, 2026, needs more optimization.
19 652 0.312211582642 Henry Cohn, 2026, needs more optimization.
19 653 0.312267868337 Henry Cohn, 2026, needs more optimization.
19 654 0.312731790547 Henry Cohn, 2026, needs more optimization.
19 655 0.312977301204 Henry Cohn, 2026, needs more optimization.
19 656 0.313150692719 Henry Cohn, 2026, needs more optimization.
19 657 0.313578769232 Henry Cohn, 2026, needs more optimization.
19 658 0.313799806699 Henry Cohn, 2026, needs more optimization.
19 659 0.314009865858 Henry Cohn, 2026, needs more optimization.
19 660 0.314163260228 Henry Cohn, 2026, needs more optimization.
19 661 0.314393087561 Henry Cohn, 2026, needs more optimization.
19 662 0.314544357347 Henry Cohn, 2026, needs more optimization.
19 663 0.314809529389 Henry Cohn, 2026, needs more optimization.
19 664 0.314972916489 Henry Cohn, 2026, needs more optimization.
19 665 0.315218722464 Henry Cohn, 2026, needs more optimization.
19 666 0.315351879871 Henry Cohn, 2026, needs more optimization.
19 667 0.315390597286 Henry Cohn, 2026, needs more optimization.
19 668 0.315672913361 Henry Cohn, 2026, needs more optimization.
19 669 0.315850914070 Henry Cohn, 2026, needs more optimization.
19 670 0.316102855892 Henry Cohn, 2026, needs more optimization.
19 671 0.316452540181 Henry Cohn, 2026, needs more optimization.
19 672 0.316543820140 Henry Cohn, 2026, needs more optimization.
19 673 0.316700078845 Henry Cohn, 2026, needs more optimization.
19 674 0.316961204865 Henry Cohn, 2026, needs more optimization.
19 675 0.317116660245 Henry Cohn, 2026, needs more optimization.
19 676 0.317245361489 Henry Cohn, 2026, needs more optimization.
19 677 0.317315499248 Henry Cohn, 2026, needs more optimization.
19 678 0.317572778729 Henry Cohn, 2026, needs more optimization.
19 679 0.317928004938 Henry Cohn, 2026, needs more optimization.
19 680 0.318232335495 Henry Cohn, 2026, needs more optimization.
19 681 0.318366747185 Henry Cohn, 2026, needs more optimization.
19 682 0.318722774651 Henry Cohn, 2026, needs more optimization.
19 683 0.318984896490 Henry Cohn, 2026, needs more optimization.
19 684 0.319315918326 Henry Cohn, 2026, needs more optimization.
19 685 0.319451549791 Henry Cohn, 2026, needs more optimization.
19 686 0.319674906551 Henry Cohn, 2026, needs more optimization.
19 687 0.319786032982 Henry Cohn, 2026, needs more optimization.
19 688 0.320174055722 Henry Cohn, 2026, needs more optimization.
19 689 0.320281614059 Henry Cohn, 2026, needs more optimization.
19 690 0.320489438882 Henry Cohn, 2026, needs more optimization.
19 691 0.320723941847 Henry Cohn, 2026, needs more optimization.
19 692 0.321068314486 Henry Cohn, 2026, needs more optimization.
19 693 0.321286850695 Henry Cohn, 2026, needs more optimization.
19 694 0.321406597400 Henry Cohn, 2026, needs more optimization.
19 695 0.321757384410 Henry Cohn, 2026, needs more optimization.
19 696 0.321903844562 Henry Cohn, 2026, needs more optimization.
19 697 0.322134038196 Henry Cohn, 2026, needs more optimization.
19 698 0.322371052373 Henry Cohn, 2026, needs more optimization.
19 699 0.322542485785 Henry Cohn, 2026, needs more optimization.
19 700 0.322608934837 Henry Cohn, 2026, needs more optimization.
19 701 0.322685628702 Henry Cohn, 2026, needs more optimization.
19 702 0.322920357339 Henry Cohn, 2026, needs more optimization.
19 703 0.323187053355 Henry Cohn, 2026, needs more optimization.
19 704 0.323563632254 Henry Cohn, 2026, needs more optimization.
19 705 0.323707263974 Numaro AI Autoresearch, 11,000+ New Verified Spherical-Code Records from AI Autoresearch, Numaro Research Report NUMARO-2026-015 (2026), https://numaro.tech/research/spherical-codes-2026/.
19 706 0.323801373305 Henry Cohn, 2026, needs more optimization.
19 707 0.323987956586 Henry Cohn, 2026, needs more optimization.
19 708 0.324132840243 Henry Cohn, 2026, needs more optimization.
19 709 0.324304487774 Henry Cohn, 2026, needs more optimization.
19 710 0.324380088754 Henry Cohn, 2026, needs more optimization.
19 711 0.324469706112 Henry Cohn, 2026, needs more optimization.
19 712 0.324548905807 Henry Cohn, 2026, needs more optimization.
19 713 0.324821105727 Henry Cohn, 2026, needs more optimization.
19 714 0.324918622844 Henry Cohn, 2026, needs more optimization.
19 715 0.325140105734 Henry Cohn, 2026, needs more optimization.
19 716 0.325361772429 Henry Cohn, 2026, needs more optimization.
19 717 0.325612486791 Henry Cohn, 2026, needs more optimization.
19 718 0.325804063848 Henry Cohn, 2026, needs more optimization.
19 719 0.326036487594 Henry Cohn, 2026, needs more optimization.
19 720 0.326204072954 Henry Cohn, 2026, needs more optimization.
19 721 0.326323767553 Henry Cohn, 2026, needs more optimization.
19 722 0.326526207445 Henry Cohn, 2026, needs more optimization.
19 723 0.326633888423 Henry Cohn, 2026, needs more optimization.
19 724 0.326711245314 Henry Cohn, 2026, needs more optimization.
19 725 0.326817430192 Henry Cohn, 2026, needs more optimization.
19 726 0.326985174460 Henry Cohn, 2026, needs more optimization.
19 727 0.327093641905 Henry Cohn, 2026, needs more optimization.
19 728 0.327249660785 Henry Cohn, 2026, needs more optimization.
19 729 0.327400884409 Henry Cohn, 2026, needs more optimization.
19 730 0.327702833769 Henry Cohn, 2026, needs more optimization.
19 731 0.327798601734 Henry Cohn, 2026, needs more optimization.
19 732 0.327934670384 Henry Cohn, 2026, needs more optimization.
19 733 0.328128533169 Henry Cohn, 2026, needs more optimization.
19 734 0.328247608391 Henry Cohn, 2026, needs more optimization.
19 735 0.328425193076 Henry Cohn, 2026, needs more optimization.
19 736 0.328566456406 Henry Cohn, 2026, needs more optimization.
19 737 0.328755751574 Henry Cohn, 2026, needs more optimization.
19 738 0.328944412276 Henry Cohn, 2026, needs more optimization.
19 739 0.329136895277 Henry Cohn, 2026, needs more optimization.
19 740 0.329436816574 Henry Cohn, 2026, needs more optimization.
19 741 0.329750950905 Henry Cohn, 2026, needs more optimization.
19 742 0.329870986856 Henry Cohn, 2026, needs more optimization.
19 743 0.330128119018 Henry Cohn, 2026, needs more optimization.
19 744 0.330398557387 Henry Cohn, 2026, needs more optimization.
19 745 0.330484348658 Henry Cohn, 2026, needs more optimization.
19 746 0.330737807555 Henry Cohn, 2026, needs more optimization.
19 747 0.330830691098 Henry Cohn, 2026, needs more optimization.
19 748 0.331084402515 Henry Cohn, 2026, needs more optimization.
19 749 0.331220906849 Henry Cohn, 2026, needs more optimization.
19 750 0.331413210585 Henry Cohn, 2026, needs more optimization.
19 751 0.331645372866 Henry Cohn, 2026, needs more optimization.
19 752 0.331878563118 Henry Cohn, 2026, needs more optimization.
19 753 0.332141225434 Henry Cohn, 2026, needs more optimization.
19 754 0.332340496708 Henry Cohn, 2026, needs more optimization.
19 755 0.332672572816 Henry Cohn, 2026, needs more optimization.
19 756 0.332848255152 Henry Cohn, 2026, needs more optimization.
19 757 0.333055242123 Henry Cohn, 2026, needs more optimization.
19 896 0.333333333334 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
3⁢x−1
19 897 0.339468324593 Henry Cohn, 2026, needs more optimization.
19 898 0.341203713242 Henry Cohn, 2026, needs more optimization.
19 899 0.342631010324 Henry Cohn, 2026, needs more optimization.
19 900 0.344028104125 Henry Cohn, 2026, needs more optimization.
19 901 0.345531003484 Henry Cohn, 2026, needs more optimization.
19 902 0.346047725513 Henry Cohn, 2026, needs more optimization.
19 903 0.346834070519 Henry Cohn, 2026, needs more optimization.
19 904 0.347400503071 Henry Cohn, 2026, needs more optimization.
19 905 0.347928810537 Henry Cohn, 2026, needs more optimization.
19 906 0.348379224612 Henry Cohn, 2026, needs more optimization.
19 907 0.349035573101 Henry Cohn, 2026, needs more optimization.
19 908 0.349287865151 Henry Cohn, 2026, needs more optimization.
19 909 0.349719652081 Henry Cohn, 2026, needs more optimization.
19 910 0.350000097962 Henry Cohn, 2026, needs more optimization.
19 911 0.350106005277 Henry Cohn, 2026, needs more optimization.
19 912 0.350850577298 Henry Cohn, 2026, needs more optimization.
19 913 0.350981308904 Henry Cohn, 2026, needs more optimization.
19 914 0.351378878550 Henry Cohn, 2026, needs more optimization.
19 915 0.351463325568 Henry Cohn, 2026, needs more optimization.
19 916 0.351524305288 Henry Cohn, 2026, needs more optimization.
19 917 0.351612396672 Henry Cohn, 2026, needs more optimization.
19 918 0.351656671548 Henry Cohn, 2026, needs more optimization.
19 919 0.351793204729 Henry Cohn, 2026, needs more optimization.
19 920 0.351910961663 Henry Cohn, 2026, needs more optimization.
19 921 0.352102430180 Henry Cohn, 2026, needs more optimization.
19 922 0.352185323279 Henry Cohn, 2026, needs more optimization.
19 923 0.352263487152 Henry Cohn, 2026, needs more optimization.
19 924 0.352459822737 Henry Cohn, 2026, needs more optimization.
19 925 0.352529707642 Henry Cohn, 2026, needs more optimization.
19 926 0.352730017259 Henry Cohn, 2026, needs more optimization.
19 927 0.352981167612 Henry Cohn, 2026, needs more optimization.
19 928 0.353075914658 Henry Cohn, 2026, needs more optimization.
19 929 0.353213936073 Henry Cohn, 2026, needs more optimization.
19 930 0.353417750581 Henry Cohn, 2026, needs more optimization.
19 931 0.353667864459 Henry Cohn, 2026, needs more optimization.
19 932 0.353766627158 Henry Cohn, 2026, needs more optimization.
19 933 0.353855500090 Henry Cohn, 2026, needs more optimization.
19 934 0.354022271479 Henry Cohn, 2026, needs more optimization.
19 935 0.354183310956 Henry Cohn, 2026, needs more optimization.
19 936 0.354326491002 Henry Cohn, 2026, needs more optimization.
19 937 0.354508428207 Henry Cohn, 2026, needs more optimization.
19 938 0.354673902179 Henry Cohn, 2026, needs more optimization.
19 1024 0.354838709678 Henry Cohn, 2026, subcode of a code of size 1040.
31⁢x−11
20 41 0.038815055717 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
6480⁢x3−400⁢x2−20⁢x+1
20 42 0.045454545455 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
22⁢x−1
20 43 0.050117159654 Henry Cohn, 2024.
6493504⁢x6+4442432⁢x5−359919⁢x4−90844⁢x3+13006⁢x2−588⁢x+9
20 44 0.051781487230 Henry Cohn, 2023.
20 45 0.053400898990 Henry Cohn, 2023.
Minimal polynomial listed in plain text data
20 46 0.053968966531 Henry Cohn, 2025.
20 47 0.053993355922 Henry Cohn, 2023.
120⁢x2−25⁢x+1
20 48 0.055838151510 Henry Cohn, 2023.
464⁢x2−8⁢x−1
20 49 0.060513303142 Henry Cohn, 2023.
Minimal polynomial listed in plain text data
20 50 0.063702950432 Henry Cohn, 2025.
20 56* 0.066666666667 T. Ericson and V. Zinoviev, Spherical codes generated by binary partitions of symmetric pointsets, IEEE Trans. Inform. Theory 41 (1995), 107–129, doi:10.1109/18.370114; H. Cohn, D. de Laat, and N. Leijenhorst, Optimality of spherical codes via exact semidefinite programming bounds, preprint, 2024, arXiv:2403.16874.
15⁢x−1
20 60 0.076923076924 Kissing configuration of 77 points in 21 dimensions.
13⁢x−1
20 63 0.081967213115 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
61⁢x−5
20 64 0.087282748333 Henry Cohn, 2026.
20 65 0.087640553689 Henry Cohn, 2026, needs more optimization.
20 66 0.089602007874 Henry Cohn, 2026.
20 67 0.090150903490 Henry Cohn, 2026.
2103⁢x4−1376⁢x3+230⁢x2−1
20 68 0.092978419163 Henry Cohn, 2026.
20 69 0.096785945467 Henry Cohn, 2026, needs more optimization.
20 70 0.097921327696 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
20 81 0.1 A. E. Brouwer and W. H. Haemers, Structure and uniqueness of the (81,20,1,6) strongly regular graph, Discrete Math. 106/107 (1992), 77–82, doi:10.1016/0012-365X(92)90532-K.
10⁢x−1
20 82 0.111111111112 Henry Cohn, 2026.
9⁢x−1
20 83 0.112895349919 Henry Cohn, 2026, needs more optimization.
20 84 0.112895349921 Henry Cohn, 2026, needs more optimization.
20 85 0.112902505491 Henry Cohn, 2026, needs more optimization.
20 86 0.112908499193 Henry Cohn, 2026, needs more optimization.
20 87 0.112912074804 Henry Cohn, 2025, needs more optimization.
20 88 0.112912612812 Henry Cohn, 2025, needs more optimization.
20 89 0.112912613185 Henry Cohn, 2025, needs more optimization.
20 92 0.112912613537 Henry Cohn, 2025.
167⁢x2−10⁢x−1
20 93 0.118699001808 Henry Cohn, 2026, needs more optimization.
20 105 0.125 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
8⁢x−1
20 106 0.136915269061 Henry Cohn, 2026.
7225⁢x4−990⁢x3−480⁢x2+9
20 120 0.142857142858 T. Ericson and V. Zinoviev, Spherical codes generated by binary partitions of symmetric pointsets, IEEE Trans. Inform. Theory 41 (1995), 107–129, doi:10.1109/18.370114.
7⁢x−1
20 124 0.145853791080 Henry Cohn, 2026, needs more optimization.
20 125 0.147670835572 Henry Cohn, 2026.
20 126 0.149455666198 Henry Cohn, 2026, needs more optimization.
20 127 0.149702280564 Henry Cohn, 2026, needs more optimization.
20 128 0.149900399825 Henry Cohn, 2026, needs more optimization.
20 129 0.150190421521 Henry Cohn, 2026, needs more optimization.
20 130 0.150479191679 Henry Cohn, 2026, needs more optimization.
20 131 0.150513257025 Henry Cohn, 2026, needs more optimization.
20 132 0.150513448214 Henry Cohn, 2026, needs more optimization.
20 133 0.151452462029 Henry Cohn, 2026, needs more optimization.
20 135 0.151500526296 Henry Cohn, 2026, needs more optimization.
20 136 0.151500526411 Henry Cohn, 2026, needs more optimization.
20 137 0.153058909203 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
20 138 0.154375391677 Henry Cohn, 2026, needs more optimization.
20 139 0.154944920631 Henry Cohn, 2026, needs more optimization.
20 140 0.156027125137 Henry Cohn, 2026, needs more optimization.
20 141 0.157229456154 Henry Cohn, 2026, needs more optimization.
20 142 0.161809087523 Henry Cohn, 2026, needs more optimization.
20 143 0.166621820001 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
20 170 0.166666666667 E. Bannai and N. J. A. Sloane, Uniqueness of certain spherical codes, Canadian J. Math. 33 (1981), 437–449, doi:10.4153/CJM-1981-038-7.
6⁢x−1
20 171 0.181540268746 Henry Cohn, 2026, needs more optimization.
20 172 0.187883205761 Henry Cohn, 2026, needs more optimization.
20 173 0.189189891596 Henry Cohn, 2026, needs more optimization.
20 174 0.189189899944 Henry Cohn, 2026, needs more optimization.
20 176 0.189189906510 Henry Cohn, 2026, needs more optimization.
20 177 0.189189914434 Henry Cohn, 2026, needs more optimization.
20 178 0.189189921283 Henry Cohn, 2026, needs more optimization.
20 179 0.189189925912 Henry Cohn, 2026, needs more optimization.
20 180 0.189189938690 Henry Cohn, 2026, needs more optimization.
20 181 0.189189939125 Henry Cohn, 2026, needs more optimization.
20 183 0.189189939407 Henry Cohn, 2026, needs more optimization.
20 184 0.189189939555 Henry Cohn, 2026, needs more optimization.
20 185 0.189190097900 Henry Cohn, 2026, needs more optimization.
20 186 0.189190101286 Henry Cohn, 2026, needs more optimization.
20 187 0.189190102094 Henry Cohn, 2026, needs more optimization.
20 188 0.189190794573 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
20 189 0.189190795539 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
20 190 0.189190796509 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
20 191 0.189270513933 Henry Cohn, 2026, needs more optimization.
20 195 0.191919195360 Henry Cohn, 2026, needs more optimization.
20 196 0.191919195361 Henry Cohn, 2026, needs more optimization.
20 201 0.191919201146 Henry Cohn, 2026, needs more optimization.
20 202 0.191919229689 Henry Cohn, 2026, needs more optimization.
20 203 0.191919308153 Henry Cohn, 2026, needs more optimization.
20 204 0.192071600350 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
20 231 0.192307692308 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
26⁢x−5
20 256 0.2 T. Ericson and V. Zinoviev, Spherical codes generated by binary partitions of symmetric pointsets, IEEE Trans. Inform. Theory 41 (1995), 107–129, doi:10.1109/18.370114.
5⁢x−1
20 257 0.203357314598 Henry Cohn, 2026.
20 258 0.205766147850 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
20 259 0.206645270202 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
20 260 0.208082004091 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
20 262 0.208386799892 Henry Cohn, 2026, needs more optimization.
20 263 0.208832042722 Henry Cohn, 2026, needs more optimization.
20 264 0.208834164080 Henry Cohn, 2026, needs more optimization.
20 265 0.212156207286 Henry Cohn, 2026, needs more optimization.
20 266 0.212391710072 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
20 267 0.212660728203 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
20 268 0.212959272996 Henry Cohn, 2026, needs more optimization.
20 269 0.213323556637 Henry Cohn, 2026, needs more optimization.
20 270 0.213404385982 Henry Cohn, 2026, needs more optimization.
20 271 0.213464402770 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
20 272 0.213912404564 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
20 273 0.214306305478 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
20 274 0.214691938549 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
20 275 0.214991543339 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
20 276 0.215453245779 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
20 277 0.215838431358 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
20 278 0.216144517636 Henry Cohn, 2026, needs more optimization.
20 279 0.216302083757 Henry Cohn, 2026, needs more optimization.
20 280 0.216538910374 Henry Cohn, 2026, needs more optimization.
20 281 0.216758871476 Henry Cohn, 2026, needs more optimization.
20 282 0.217056699370 Henry Cohn, 2026, needs more optimization.
20 283 0.217406627212 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
20 284 0.217575880683 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
20 285 0.217804101437 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
20 286 0.217926336343 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
20 287 0.218050459820 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
20 288 0.219346869756 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
20 289 0.219982696474 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
20 290 0.220302291130 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
20 291 0.220615141198 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
20 293 0.220690241676 Henry Cohn, 2026, needs more optimization.
20 294 0.220691806500 Henry Cohn, 2026, needs more optimization.
20 301 0.222222222223 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
9⁢x−2
20 322 0.222222222223 Henry Cohn, 2025, by enlarging a code from T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
9⁢x−2
20 323 0.232387029873 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
20 324 0.236122066567 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
20 378 0.236363636364 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
55⁢x−13
20 379 0.242464091180 Henry Cohn, 2026, needs more optimization.
20 380 0.242509745068 Henry Cohn, 2026, needs more optimization.
20 381 0.242573763508 Henry Cohn, 2026, needs more optimization.
20 382 0.242648822467 Henry Cohn, 2026, needs more optimization.
20 383 0.242713791848 Henry Cohn, 2026, needs more optimization.
20 384 0.242785869848 Henry Cohn, 2026, needs more optimization.
20 385 0.242877690448 Henry Cohn, 2026, needs more optimization.
20 386 0.242965624892 Henry Cohn, 2026, needs more optimization.
20 387 0.242987302817 Henry Cohn, 2026, needs more optimization.
20 388 0.243020606257 Henry Cohn, 2026, needs more optimization.
20 389 0.243111653501 Henry Cohn, 2026, needs more optimization.
20 390 0.243171239031 Henry Cohn, 2026, needs more optimization.
20 391 0.243219020327 Henry Cohn, 2026, needs more optimization.
20 392 0.243332229098 C. Ma, T. Tao Z., P. Li, M. Liu, H. Chen, Z. Mao, Y. Cheng, Y. Qi, and Y. Yang, Finding kissing numbers with game-theoretic reinforcement learning, preprint, 2025, arXiv:2511.13391.
Minimal polynomial listed in plain text data
20 393 0.247798396078 Henry Cohn, 2026, needs more optimization.
20 405 0.25 C. Ma, T. Tao Z., P. Li, M. Liu, H. Chen, Z. Mao, Y. Cheng, Y. Qi, and Y. Yang, Finding kissing numbers with game-theoretic reinforcement learning, preprint, 2025, arXiv:2511.13391.
4⁢x−1
20 406 0.262172700766 Henry Cohn, 2026, needs more optimization.
20 407 0.264976401006 Henry Cohn, 2026, needs more optimization.
20 473 0.266666666667 Henry Cohn, 2025.
15⁢x−4
20 474 0.269855642213 Henry Cohn, 2026, needs more optimization.
20 475 0.270933959731 Henry Cohn, 2026, needs more optimization.
20 476 0.272595503772 Henry Cohn, 2026, needs more optimization.
20 524 0.272727272728 C. Ma, T. Tao Z., P. Li, M. Liu, H. Chen, Z. Mao, Y. Cheng, Y. Qi, and Y. Yang, Finding kissing numbers with game-theoretic reinforcement learning, preprint, 2025, arXiv:2511.13391.
11⁢x−3
20 567 0.273861278753 C. Ma, T. Tao Z., P. Li, M. Liu, H. Chen, Z. Mao, Y. Cheng, Y. Qi, and Y. Yang, Finding kissing numbers with game-theoretic reinforcement learning, preprint, 2025, arXiv:2511.13391.
40⁢x2−3
20 568 0.280556241918 Henry Cohn, 2026, needs more optimization.
20 640 0.285714285715 C. Ma, T. Tao Z., P. Li, M. Liu, H. Chen, Z. Mao, Y. Cheng, Y. Qi, and Y. Yang, Finding kissing numbers with game-theoretic reinforcement learning, preprint, 2025, arXiv:2511.13391.
7⁢x−2
20 641 0.292028046770 Henry Cohn, 2026, needs more optimization.
20 840 0.3 C. Ma, T. Tao Z., P. Li, M. Liu, H. Chen, Z. Mao, Y. Cheng, Y. Qi, and Y. Yang, Finding kissing numbers with game-theoretic reinforcement learning, preprint, 2025, arXiv:2511.13391.
10⁢x−3
20 841 0.303064566389 Henry Cohn, 2026, needs more optimization.
20 1002 0.307692307693 C. Ma, T. Tao Z., P. Li, M. Liu, H. Chen, Z. Mao, Y. Cheng, Y. Qi, and Y. Yang, Finding kissing numbers with game-theoretic reinforcement learning, preprint, 2025, arXiv:2511.13391.
13⁢x−4
20 1003 0.315496048152 Henry Cohn, 2026, needs more optimization.
20 1006 0.323084306383 Numaro AI Autoresearch, 11,000+ New Verified Spherical-Code Records from AI Autoresearch, Numaro Research Report NUMARO-2026-015 (2026), https://numaro.tech/research/spherical-codes-2026/.
20 1007 0.323177283459 Numaro AI Autoresearch, 11,000+ New Verified Spherical-Code Records from AI Autoresearch, Numaro Research Report NUMARO-2026-015 (2026), https://numaro.tech/research/spherical-codes-2026/.
20 1008 0.323177381053 Numaro AI Autoresearch, 11,000+ New Verified Spherical-Code Records from AI Autoresearch, Numaro Research Report NUMARO-2026-015 (2026), https://numaro.tech/research/spherical-codes-2026/.
20 1010 0.323472587190 Numaro AI Autoresearch, 11,000+ New Verified Spherical-Code Records from AI Autoresearch, Numaro Research Report NUMARO-2026-015 (2026), https://numaro.tech/research/spherical-codes-2026/.
20 1011 0.323874848855 Numaro AI Autoresearch, 11,000+ New Verified Spherical-Code Records from AI Autoresearch, Numaro Research Report NUMARO-2026-015 (2026), https://numaro.tech/research/spherical-codes-2026/.
20 1012 0.323878371715 Numaro AI Autoresearch, 11,000+ New Verified Spherical-Code Records from AI Autoresearch, Numaro Research Report NUMARO-2026-015 (2026), https://numaro.tech/research/spherical-codes-2026/.
20 1013 0.323879016535 Henry Cohn, 2026, needs more optimization.
20 1014 0.323879019845 Numaro AI Autoresearch, 11,000+ New Verified Spherical-Code Records from AI Autoresearch, Numaro Research Report NUMARO-2026-015 (2026), https://numaro.tech/research/spherical-codes-2026/.
20 1015 0.323879653034 Numaro AI Autoresearch, 11,000+ New Verified Spherical-Code Records from AI Autoresearch, Numaro Research Report NUMARO-2026-015 (2026), https://numaro.tech/research/spherical-codes-2026/.
20 1017 0.323975424158 Numaro AI Autoresearch, 11,000+ New Verified Spherical-Code Records from AI Autoresearch, Numaro Research Report NUMARO-2026-015 (2026), https://numaro.tech/research/spherical-codes-2026/.
20 1019 0.324107005397 Numaro AI Autoresearch, 11,000+ New Verified Spherical-Code Records from AI Autoresearch, Numaro Research Report NUMARO-2026-015 (2026), https://numaro.tech/research/spherical-codes-2026/.
20 1020 0.324108368852 Numaro AI Autoresearch, 11,000+ New Verified Spherical-Code Records from AI Autoresearch, Numaro Research Report NUMARO-2026-015 (2026), https://numaro.tech/research/spherical-codes-2026/.
20 1021 0.324194688420 Numaro AI Autoresearch, 11,000+ New Verified Spherical-Code Records from AI Autoresearch, Numaro Research Report NUMARO-2026-015 (2026), https://numaro.tech/research/spherical-codes-2026/.
20 1022 0.324195083672 Numaro AI Autoresearch, 11,000+ New Verified Spherical-Code Records from AI Autoresearch, Numaro Research Report NUMARO-2026-015 (2026), https://numaro.tech/research/spherical-codes-2026/.
20 1024 0.324712629095 Numaro AI Autoresearch, 11,000+ New Verified Spherical-Code Records from AI Autoresearch, Numaro Research Report NUMARO-2026-015 (2026), https://numaro.tech/research/spherical-codes-2026/.
21 43 0.037145782135 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
7581⁢x3−441⁢x2−21⁢x+1
21 44 0.043532808199 Henry Cohn, 2023.
21 50* 0.047619047620 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001; H. Cohn, D. de Laat, and N. Leijenhorst, Optimality of spherical codes via exact semidefinite programming bounds, preprint, 2024, arXiv:2403.16874.
21⁢x−1
21 51 0.058803648698 Henry Cohn, 2024.
21 52 0.062635030303 Henry Cohn, 2026.
21 53 0.066664743840 Henry Cohn, 2026, needs more optimization.
21 54 0.066665400631 Henry Cohn, 2026, needs more optimization.
21 55 0.066666409280 Henry Cohn, 2025.
21 56 0.066666653891 Henry Cohn, 2025, needs more optimization.
21 57 0.066666662289 Henry Cohn, 2025, needs more optimization.
21 58 0.066666666335 Henry Cohn, 2026, needs more optimization.
21 59 0.072019011748 Henry Cohn, 2025.
21 60 0.074662292991 Henry Cohn, 2026.
21 61 0.076923073145 Henry Cohn, 2025, needs more optimization.
21 62 0.076923075369 Henry Cohn, 2025, needs more optimization.
21 63 0.078689325834 Henry Cohn, 2026.
9⁢x2+12⁢x−1
21 64 0.080216778694 Henry Cohn, 2026.
14481⁢x4−18000⁢x3+4848⁢x2−480⁢x+16
21 65 0.081966984741 Henry Cohn, 2026.
21 77* 0.083333333334 T. Ericson and V. Zinoviev, Spherical codes generated by binary partitions of symmetric pointsets, IEEE Trans. Inform. Theory 41 (1995), 107–129, doi:10.1109/18.370114; H. Cohn, D. de Laat, and N. Leijenhorst, Optimality of spherical codes via exact semidefinite programming bounds, preprint, 2024, arXiv:2403.16874.
12⁢x−1
21 78 0.093247656078 Henry Cohn, 2026.
21 82 0.093297851017 Henry Cohn, 2026.
144⁢x4−840⁢x3+192⁢x2−1
21 83 0.095523255230 Henry Cohn, 2026, needs more optimization.
21 84 0.096073235105 Henry Cohn, 2026, needs more optimization.
21 85 0.097702080330 Henry Cohn, 2026, needs more optimization.
21 86 0.104649382361 Henry Cohn, 2026, needs more optimization.
21 88 0.106199014100 Henry Cohn, 2026, needs more optimization.
21 89 0.108845760578 Henry Cohn, 2026, needs more optimization.
21 90 0.109639633905 Henry Cohn, 2026, needs more optimization.
21 92 0.109918568059 Henry Cohn, 2026, needs more optimization.
21 93 0.110695598499 Henry Cohn, 2026, needs more optimization.
21 112* 0.111111111112 P. Delsarte, J. M. Goethals, and J. J. Seidel, Spherical codes and designs, Geometriae Dedicata 6 (1977), 363–388, doi:10.1007/bf03187604; V. I. Levenšteĭn, On bounds for packings in n-dimensional Euclidean space (Russian), Dokl. Akad. Nauk SSSR 245 (1979), 1299–1303, English translation in Soviet Math. Dokl. 20 (1979), 417–421.
9⁢x−1
21 113 0.127363959709 Henry Cohn, 2026.
21 119 0.131782945737 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
129⁢x−17
21 120 0.139344936865 Henry Cohn, 2026, needs more optimization.
21 121 0.139344936970 Henry Cohn, 2026, needs more optimization.
21 122 0.139344956937 Henry Cohn, 2026, needs more optimization.
21 123 0.139385702539 Henry Cohn, 2026, needs more optimization.
21 124 0.140535690921 Henry Cohn, 2026, needs more optimization.
21 162* 0.142857142858 P. Delsarte, J. M. Goethals, and J. J. Seidel, Spherical codes and designs, Geometriae Dedicata 6 (1977), 363–388, doi:10.1007/bf03187604; V. I. Levenšteĭn, On bounds for packings in n-dimensional Euclidean space (Russian), Dokl. Akad. Nauk SSSR 245 (1979), 1299–1303, English translation in Soviet Math. Dokl. 20 (1979), 417–421.
7⁢x−1
21 163 0.153926281042 Henry Cohn, 2026.
21 164 0.160001004685 Henry Cohn, 2026, needs more optimization.
21 165 0.160002653209 Henry Cohn, 2026, needs more optimization.
21 166 0.160894264689 Henry Cohn, 2026, needs more optimization.
21 198 0.161904761905 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
105⁢x−17
21 199 0.172187000249 Henry Cohn, 2026.
21 200 0.174789246224 Henry Cohn, 2026, needs more optimization.
21 201 0.174789524364 Henry Cohn, 2026, needs more optimization.
21 217 0.174875298960 C. Ma, T. Tao Z., P. Li, M. Liu, H. Chen, Z. Mao, Y. Cheng, Y. Qi, and Y. Yang, Finding kissing numbers with game-theoretic reinforcement learning, preprint, 2025, arXiv:2511.13391.
119⁢x4+580⁢x3+42⁢x2−20⁢x−1
21 218 0.177286556402 Henry Cohn, 2026, needs more optimization.
21 219 0.177401695417 Henry Cohn, 2026, needs more optimization.
21 220 0.177459656457 Henry Cohn, 2026, needs more optimization.
21 221 0.177479980767 Henry Cohn, 2026, needs more optimization.
21 224 0.177492046263 Henry Cohn, 2026, needs more optimization.
21 225 0.178085751307 Henry Cohn, 2026, needs more optimization.
21 226 0.185484136393 Henry Cohn, 2026.
21 227 0.190599361553 Henry Cohn, 2026, needs more optimization.
21 233 0.192307692308 Code with 231 points in 20 dimensions, together with two antipodal points orthogonal to it; T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
26⁢x−5
21 234 0.192307929309 Henry Cohn, 2026, needs more optimization.
21 235 0.192308006431 Henry Cohn, 2026, needs more optimization.
21 236 0.194538259040 Henry Cohn, 2026, needs more optimization.
21 237 0.195347439432 Henry Cohn, 2026, needs more optimization.
21 336 0.2 E. Bannai and N. J. A. Sloane, Uniqueness of certain spherical codes, Canadian J. Math. 33 (1981), 437–449, doi:10.4153/CJM-1981-038-7.
5⁢x−1
21 352 0.214285714286 Henry Cohn, 2026.
14⁢x−3
21 353 0.222395820677 Henry Cohn, 2026.
21 373 0.227586206897 C. Ma, T. Tao Z., P. Li, M. Liu, H. Chen, Z. Mao, Y. Cheng, Y. Qi, and Y. Yang, Finding kissing numbers with game-theoretic reinforcement learning, preprint, 2025, arXiv:2511.13391.
145⁢x−33
21 379 0.227586206897 Henry Cohn, 2026.
145⁢x−33
21 380 0.228028264629 Henry Cohn, 2026, needs more optimization.
21 381 0.228383442125 Henry Cohn, 2026, needs more optimization.
21 383 0.228659151903 Henry Cohn, 2026, needs more optimization.
21 384 0.228720535994 Henry Cohn, 2026, needs more optimization.
21 385 0.228907547079 Henry Cohn, 2026, needs more optimization.
21 386 0.228986660608 Henry Cohn, 2026, needs more optimization.
21 387 0.228997003640 Henry Cohn, 2026, needs more optimization.
21 388 0.229054574511 Henry Cohn, 2026, needs more optimization.
21 394 0.230769230770 Henry Cohn, 2026.
13⁢x−3
21 395 0.230770690659 Henry Cohn, 2026, needs more optimization.
21 396 0.232285518710 Henry Cohn, 2026, needs more optimization.
21 397 0.237323451236 Henry Cohn, 2026, needs more optimization.
21 554 0.238095238096 T. Ericson and V. Zinoviev, Spherical codes generated by binary partitions of symmetric pointsets, IEEE Trans. Inform. Theory 41 (1995), 107–129, doi:10.1109/18.370114.
21⁢x−5
21 567 0.25 C. Ma, T. Tao Z., P. Li, M. Liu, H. Chen, Z. Mao, Y. Cheng, Y. Qi, and Y. Yang, Finding kissing numbers with game-theoretic reinforcement learning, preprint, 2025, arXiv:2511.13391.
4⁢x−1
21 568 0.253536497622 Henry Cohn, 2026, needs more optimization.
21 569 0.254499432066 Henry Cohn, 2026, needs more optimization.
21 570 0.255064892889 Henry Cohn, 2026, needs more optimization.
21 571 0.255477440567 Henry Cohn, 2026, needs more optimization.
21 572 0.255805547252 Henry Cohn, 2026, needs more optimization.
21 573 0.256122279505 Henry Cohn, 2026, needs more optimization.
21 574 0.256383960890 Henry Cohn, 2026, needs more optimization.
21 575 0.256601173160 Henry Cohn, 2026, needs more optimization.
21 576 0.256818535779 Henry Cohn, 2026, needs more optimization.
21 577 0.257065151531 Henry Cohn, 2026, needs more optimization.
21 578 0.257277708461 Henry Cohn, 2026, needs more optimization.
21 579 0.257423073114 Henry Cohn, 2026, needs more optimization.
21 580 0.257574590261 Henry Cohn, 2026, needs more optimization.
21 581 0.257695093577 Henry Cohn, 2026, needs more optimization.
21 582 0.257814789188 Henry Cohn, 2026, needs more optimization.
21 583 0.257901499264 Henry Cohn, 2026, needs more optimization.
21 584 0.258015677459 Henry Cohn, 2026, needs more optimization.
21 585 0.258106841974 Henry Cohn, 2026, needs more optimization.
21 586 0.258234376485 Henry Cohn, 2026, needs more optimization.
21 587 0.258300390675 Henry Cohn, 2026, needs more optimization.
21 588 0.258372949610 Henry Cohn, 2026, needs more optimization.
21 589 0.258443914878 Henry Cohn, 2026, needs more optimization.
21 590 0.258598881671 Henry Cohn, 2026, needs more optimization.
21 591 0.258699060034 Henry Cohn, 2026, needs more optimization.
21 592 0.258733586059 Henry Cohn, 2026, needs more optimization.
21 593 0.258970559401 Henry Cohn, 2026, needs more optimization.
21 594 0.259204623864 Henry Cohn, 2026, needs more optimization.
21 595 0.259316104056 Henry Cohn, 2026, needs more optimization.
21 596 0.259390878248 Henry Cohn, 2026, needs more optimization.
21 597 0.259458572371 Henry Cohn, 2026, needs more optimization.
21 598 0.259597267752 Henry Cohn, 2026, needs more optimization.
21 599 0.259670832111 Henry Cohn, 2026, needs more optimization.
21 600 0.259737000547 Henry Cohn, 2026, needs more optimization.
21 601 0.259788371777 Henry Cohn, 2026, needs more optimization.
21 602 0.259827614316 Henry Cohn, 2026, needs more optimization.
21 603 0.259903555235 Henry Cohn, 2026, needs more optimization.
21 604 0.259937022563 Henry Cohn, 2026, needs more optimization.
21 605 0.260041541420 Henry Cohn, 2026, needs more optimization.
21 606 0.260130757849 Henry Cohn, 2026, needs more optimization.
21 607 0.260226389784 Henry Cohn, 2026, needs more optimization.
21 608 0.260272892330 Henry Cohn, 2026, needs more optimization.
21 609 0.260313808741 Henry Cohn, 2026, needs more optimization.
21 610 0.260493677987 Henry Cohn, 2026, needs more optimization.
21 611 0.260597991598 Henry Cohn, 2026, needs more optimization.
21 612 0.260661889768 Henry Cohn, 2026, needs more optimization.
21 613 0.260783590934 Henry Cohn, 2026, needs more optimization.
21 614 0.260874766671 Henry Cohn, 2026, needs more optimization.
21 615 0.260931947436 Henry Cohn, 2026, needs more optimization.
21 616 0.261024564360 Henry Cohn, 2026, needs more optimization.
21 617 0.261082046838 Henry Cohn, 2026, needs more optimization.
21 618 0.261158101643 Henry Cohn, 2026, needs more optimization.
21 619 0.261226671897 Henry Cohn, 2026, needs more optimization.
21 620 0.261266511020 Henry Cohn, 2026, needs more optimization.
21 621 0.261304921862 Henry Cohn, 2026, needs more optimization.
21 622 0.261344837484 Henry Cohn, 2026, needs more optimization.
21 623 0.261388989855 Henry Cohn, 2026, needs more optimization.
21 624 0.261423941749 Henry Cohn, 2026, needs more optimization.
21 625 0.261459591088 Henry Cohn, 2026, needs more optimization.
21 626 0.261499968219 Henry Cohn, 2026, needs more optimization.
21 627 0.261571994166 Henry Cohn, 2026, needs more optimization.
21 628 0.261627098893 Henry Cohn, 2026, needs more optimization.
21 629 0.261682623053 Henry Cohn, 2026, needs more optimization.
21 630 0.262074421160 Henry Cohn, 2026, needs more optimization.
21 631 0.262324783096 Henry Cohn, 2026, needs more optimization.
21 632 0.262514531671 Henry Cohn, 2026, needs more optimization.
21 633 0.262613948178 Henry Cohn, 2026, needs more optimization.
21 634 0.262684582118 Henry Cohn, 2026, needs more optimization.
21 635 0.262734906138 Henry Cohn, 2026, needs more optimization.
21 636 0.262885748869 Henry Cohn, 2026, needs more optimization.
21 637 0.263006223425 Henry Cohn, 2026, needs more optimization.
21 638 0.263137959104 Henry Cohn, 2026, needs more optimization.
21 639 0.263227165384 Henry Cohn, 2026, needs more optimization.
21 640 0.263327551383 Henry Cohn, 2026, needs more optimization.
21 641 0.263415342893 Henry Cohn, 2026, needs more optimization.
21 642 0.263576863887 Henry Cohn, 2026, needs more optimization.
21 643 0.263702484243 Henry Cohn, 2026, needs more optimization.
21 644 0.263825001137 Henry Cohn, 2026, needs more optimization.
21 645 0.263933545749 Henry Cohn, 2026, needs more optimization.
21 646 0.263971446383 Henry Cohn, 2026, needs more optimization.
21 647 0.264048016665 Henry Cohn, 2026, needs more optimization.
21 648 0.264123753322 Henry Cohn, 2026, needs more optimization.
21 649 0.264185360564 Henry Cohn, 2026, needs more optimization.
21 650 0.264291747908 Henry Cohn, 2026, needs more optimization.
21 651 0.264364712598 Henry Cohn, 2026, needs more optimization.
21 652 0.264436395535 Henry Cohn, 2026, needs more optimization.
21 653 0.264503974722 Henry Cohn, 2026, needs more optimization.
21 654 0.264557776273 Henry Cohn, 2026, needs more optimization.
21 655 0.264633959709 Henry Cohn, 2026, needs more optimization.
21 656 0.264732823703 Henry Cohn, 2026, needs more optimization.
21 657 0.264801557039 Henry Cohn, 2026, needs more optimization.
21 658 0.264893800109 Henry Cohn, 2026, needs more optimization.
21 659 0.264987741102 Henry Cohn, 2026, needs more optimization.
21 660 0.265122411240 Henry Cohn, 2026, needs more optimization.
21 661 0.265178191126 Henry Cohn, 2026, needs more optimization.
21 662 0.265230371464 Henry Cohn, 2026, needs more optimization.
21 663 0.265294817475 Henry Cohn, 2026, needs more optimization.
21 664 0.265373996086 Henry Cohn, 2026, needs more optimization.
21 665 0.265446085077 Henry Cohn, 2026, needs more optimization.
21 666 0.265519635434 Henry Cohn, 2026, needs more optimization.
21 667 0.265557393097 Henry Cohn, 2026, needs more optimization.
21 668 0.265602724388 Henry Cohn, 2026, needs more optimization.
21 669 0.265630801425 Henry Cohn, 2026, needs more optimization.
21 670 0.265666538119 Henry Cohn, 2026, needs more optimization.
21 671 0.265729924830 Henry Cohn, 2026, needs more optimization.
21 672 0.265768345343 Henry Cohn, 2026, needs more optimization.
21 673 0.265851510787 Henry Cohn, 2026, needs more optimization.
21 674 0.265900199822 Henry Cohn, 2026, needs more optimization.
21 675 0.265958485908 Henry Cohn, 2026, needs more optimization.
21 676 0.266025761635 Henry Cohn, 2026, needs more optimization.
21 677 0.266078423519 Henry Cohn, 2026, needs more optimization.
21 678 0.266134816439 Henry Cohn, 2026, needs more optimization.
21 679 0.266165734384 Henry Cohn, 2026, needs more optimization.
21 680 0.266222539814 Henry Cohn, 2026, needs more optimization.
21 681 0.266278310358 Henry Cohn, 2026, needs more optimization.
21 682 0.266341772355 Henry Cohn, 2026, needs more optimization.
21 683 0.266503176546 Henry Cohn, 2026, needs more optimization.
21 684 0.266585313002 Henry Cohn, 2026, needs more optimization.
21 715 0.266666666667 C. Ma, T. Tao Z., P. Li, M. Liu, H. Chen, Z. Mao, Y. Cheng, Y. Qi, and Y. Yang, Finding kissing numbers with game-theoretic reinforcement learning, preprint, 2025, arXiv:2511.13391.
15⁢x−4
21 728 0.267171850610 Henry Cohn, 2026, needs more optimization.
21 729 0.267261241913 Henry Cohn, 2026.
14⁢x2−1
21 730 0.277220707390 Henry Cohn, 2026, needs more optimization.
21 731 0.282340308442 Henry Cohn, 2026, needs more optimization.
21 732 0.284690760597 Henry Cohn, 2026, needs more optimization.
21 850 0.285714285715 Henry Cohn, 2026.
7⁢x−2
21 851 0.290297039336 Numaro AI Autoresearch, 11,000+ New Verified Spherical-Code Records from AI Autoresearch, Numaro Research Report NUMARO-2026-015 (2026), https://numaro.tech/research/spherical-codes-2026/.
21 852 0.291094975721 Numaro AI Autoresearch, 11,000+ New Verified Spherical-Code Records from AI Autoresearch, Numaro Research Report NUMARO-2026-015 (2026), https://numaro.tech/research/spherical-codes-2026/.
21 853 0.291722481993 Numaro AI Autoresearch, 11,000+ New Verified Spherical-Code Records from AI Autoresearch, Numaro Research Report NUMARO-2026-015 (2026), https://numaro.tech/research/spherical-codes-2026/.
21 854 0.292104584573 Numaro AI Autoresearch, 11,000+ New Verified Spherical-Code Records from AI Autoresearch, Numaro Research Report NUMARO-2026-015 (2026), https://numaro.tech/research/spherical-codes-2026/.
21 855 0.292429903745 Numaro AI Autoresearch, 11,000+ New Verified Spherical-Code Records from AI Autoresearch, Numaro Research Report NUMARO-2026-015 (2026), https://numaro.tech/research/spherical-codes-2026/.
21 856 0.292762689880 Numaro AI Autoresearch, 11,000+ New Verified Spherical-Code Records from AI Autoresearch, Numaro Research Report NUMARO-2026-015 (2026), https://numaro.tech/research/spherical-codes-2026/.
21 857 0.293056704975 Numaro AI Autoresearch, 11,000+ New Verified Spherical-Code Records from AI Autoresearch, Numaro Research Report NUMARO-2026-015 (2026), https://numaro.tech/research/spherical-codes-2026/.
21 858 0.293321772530 Numaro AI Autoresearch, 11,000+ New Verified Spherical-Code Records from AI Autoresearch, Numaro Research Report NUMARO-2026-015 (2026), https://numaro.tech/research/spherical-codes-2026/.
21 859 0.293634218618 Numaro AI Autoresearch, 11,000+ New Verified Spherical-Code Records from AI Autoresearch, Numaro Research Report NUMARO-2026-015 (2026), https://numaro.tech/research/spherical-codes-2026/.
21 974 0.294117647059 C. Ma, T. Tao Z., P. Li, M. Liu, H. Chen, Z. Mao, Y. Cheng, Y. Qi, and Y. Yang, Finding kissing numbers with game-theoretic reinforcement learning, preprint, 2025, arXiv:2511.13391.
17⁢x−5
21 975 0.299221206750 Numaro AI Autoresearch, 11,000+ New Verified Spherical-Code Records from AI Autoresearch, Numaro Research Report NUMARO-2026-015 (2026), https://numaro.tech/research/spherical-codes-2026/.
21 1024 0.3 C. Ma, T. Tao Z., P. Li, M. Liu, H. Chen, Z. Mao, Y. Cheng, Y. Qi, and Y. Yang, Finding kissing numbers with game-theoretic reinforcement learning, preprint, 2025, arXiv:2511.13391.
10⁢x−3
22 45 0.035618974680 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
8800⁢x3−484⁢x2−22⁢x+1
22 46 0.041709010468 Henry Cohn, 2026.
22 47 0.046962270332 Henry Cohn, 2026, continuous family of codes without rattlers.
736⁢x3+236⁢x2−34⁢x+1
22 48 0.047524915294 Henry Cohn, 2025, continuous family of codes without rattlers.
64⁢x2+18⁢x−1
22 49 0.047603596724 Henry Cohn, 2026.
22 50 0.047618606209 Henry Cohn, 2025, needs more optimization.
22 52 0.047619047316 Henry Cohn, 2025, needs more optimization.
22 53 0.057560345703 Henry Cohn, 2024.
22 54 0.060108874148 Henry Cohn, 2025.
22 55 0.064358001899 Henry Cohn, 2026.
22 56 0.066435789676 Henry Cohn, 2026, needs more optimization.
22 57 0.066559109857 Henry Cohn, 2026.
22 58 0.066625280626 Henry Cohn, 2026, needs more optimization.
22 59 0.066652771147 Henry Cohn, 2026, needs more optimization.
22 60 0.066661306762 Henry Cohn, 2026, needs more optimization.
22 61 0.069638781740 Henry Cohn, 2026, needs more optimization.
22 62 0.071702992547 Henry Cohn, 2026, needs more optimization.
22 63 0.076903597971 Henry Cohn, 2026, needs more optimization.
22 64 0.076918163843 Henry Cohn, 2026, needs more optimization.
22 65 0.076924075517 Henry Cohn, 2026, needs more optimization.
22 66 0.078243584883 Henry Cohn, 2026.
22 67 0.079295758513 Henry Cohn, 2026, needs more optimization.
22 68 0.080927905651 Henry Cohn, 2026.
22 69 0.083018488609 Henry Cohn, 2026, needs more optimization.
22 70 0.083309827283 Henry Cohn, 2025, needs more optimization.
22 71 0.083331871272 Henry Cohn, 2025, needs more optimization.
22 72 0.083333305430 Henry Cohn, 2026, needs more optimization.
22 73 0.083333332773 Henry Cohn, 2025, needs more optimization.
22 79 0.083333333334 Code with 77 points in 21 dimensions, together with two antipodal points orthogonal to it; T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
12⁢x−1
22 80 0.086876541301 Henry Cohn, 2026.
22 100* 0.090909090910 P. Delsarte, J. M. Goethals, and J. J. Seidel, Spherical codes and designs, Geometriae Dedicata 6 (1977), 363–388, doi:10.1007/bf03187604; V. I. Levenšteĭn, On bounds for packings in n-dimensional Euclidean space (Russian), Dokl. Akad. Nauk SSSR 245 (1979), 1299–1303, English translation in Soviet Math. Dokl. 20 (1979), 417–421.
11⁢x−1
22 101 0.109433688331 Henry Cohn, 2026.
6912⁢x4−560⁢x3−272⁢x2+3
22 114 0.111111111112 Code with 112 points in 21 dimensions, together with two antipodal points orthogonal to it; T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
9⁢x−1
22 115 0.112789665003 Henry Cohn, 2026.
68⁢x2−52⁢x+5
22 116 0.117359909647 Henry Cohn, 2026.
30⁢x2+5⁢x−1
22 117 0.122749959678 Henry Cohn, 2026, needs more optimization.
22 118 0.126503630021 Henry Cohn, 2026, needs more optimization.
22 119 0.126740173095 Henry Cohn, 2026, needs more optimization.
22 120 0.131231549706 Henry Cohn, 2026, needs more optimization.
22 127 0.131782945737 Henry Cohn, 2026.
129⁢x−17
22 136 0.135135135136 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
37⁢x−5
22 141 0.135135135136 Henry Cohn, 2026.
37⁢x−5
22 142 0.135517368455 Henry Cohn, 2026, needs more optimization.
22 143 0.137953428332 Henry Cohn, 2026, needs more optimization.
22 144 0.139623936242 Henry Cohn, 2026, needs more optimization.
22 166 0.142857142858 Henry Cohn, 2026.
7⁢x−1
22 167 0.144948974279 Henry Cohn, 2026.
20⁢x2+4⁢x−1
22 169 0.149071198500 Henry Cohn, 2026.
45⁢x2−1
22 170 0.153808582906 Henry Cohn, 2026.
22 171 0.156572050095 Henry Cohn, 2026.
22 172 0.158304782726 Henry Cohn, 2026, needs more optimization.
22 173 0.159107132818 Henry Cohn, 2026, needs more optimization.
22 174 0.161501329557 Henry Cohn, 2026, needs more optimization.
22 201 0.161904761905 Henry Cohn, 2026.
105⁢x−17
22 202 0.161905113244 Henry Cohn, 2026, needs more optimization.
22 203 0.165615111681 Henry Cohn, 2026, needs more optimization.
22 275* 0.166666666667 P. Delsarte, J. M. Goethals, and J. J. Seidel, Spherical codes and designs, Geometriae Dedicata 6 (1977), 363–388, doi:10.1007/bf03187604; V. I. Levenšteĭn, On bounds for packings in n-dimensional Euclidean space (Russian), Dokl. Akad. Nauk SSSR 245 (1979), 1299–1303, English translation in Soviet Math. Dokl. 20 (1979), 417–421.
6⁢x−1
22 276 0.178506323194 Henry Cohn, 2026.
22 277 0.185913607789 Henry Cohn, 2026, needs more optimization.
22 278 0.189283234640 Henry Cohn, 2026, needs more optimization.
22 279 0.191581549902 Henry Cohn, 2026, needs more optimization.
22 280 0.193234500613 Henry Cohn, 2026, needs more optimization.
22 281 0.194512977456 Henry Cohn, 2026, needs more optimization.
22 282 0.195694470998 Henry Cohn, 2026, needs more optimization.
22 283 0.196333225377 Henry Cohn, 2026, needs more optimization.
22 284 0.196353279594 Henry Cohn, 2026, needs more optimization.
22 286 0.196362023436 Henry Cohn, 2026, needs more optimization.
22 287 0.199244821770 Henry Cohn, 2026, needs more optimization.
22 352 0.2 C. Ma, T. Tao Z., P. Li, M. Liu, H. Chen, Z. Mao, Y. Cheng, Y. Qi, and Y. Yang, Finding kissing numbers with game-theoretic reinforcement learning, preprint, 2025, arXiv:2511.13391.
5⁢x−1
22 353 0.201777989818 Henry Cohn, 2026.
22 354 0.202832443486 Numaro AI Autoresearch, 11,000+ New Verified Spherical-Code Records from AI Autoresearch, Numaro Research Report NUMARO-2026-015 (2026), https://numaro.tech/research/spherical-codes-2026/.
22 355 0.203727072273 Henry Cohn, 2026, needs more optimization.
22 356 0.204034193781 Henry Cohn, 2026, needs more optimization.
22 357 0.204058223592 Henry Cohn, 2026, needs more optimization.
22 358 0.204059171295 Henry Cohn, 2026, needs more optimization.
22 359 0.204488590084 Henry Cohn, 2026, needs more optimization.
22 374 0.204624019941 Henry Cohn, 2026.
22 375 0.205718448770 Henry Cohn, 2026, needs more optimization.
22 376 0.206395598566 Henry Cohn, 2026, needs more optimization.
22 377 0.206695251640 Henry Cohn, 2026, needs more optimization.
22 378 0.206884606303 Henry Cohn, 2026, needs more optimization.
22 379 0.207057776180 Henry Cohn, 2026, needs more optimization.
22 380 0.207118971078 Henry Cohn, 2026, needs more optimization.
22 381 0.207165729959 Henry Cohn, 2026, needs more optimization.
22 382 0.207172528046 Henry Cohn, 2026, needs more optimization.
22 387 0.207172542358 Henry Cohn, 2026, needs more optimization.
22 389 0.207173003748 Henry Cohn, 2026, needs more optimization.
22 390 0.207173532979 Henry Cohn, 2026, needs more optimization.
22 391 0.208463217107 Henry Cohn, 2026, needs more optimization.
22 392 0.208815802216 Henry Cohn, 2026, needs more optimization.
22 393 0.209019444823 Henry Cohn, 2026, needs more optimization.
22 394 0.209060231953 Henry Cohn, 2026, needs more optimization.
22 395 0.209386077957 Henry Cohn, 2026, needs more optimization.
22 396 0.209524317342 Henry Cohn, 2026, needs more optimization.
22 397 0.209574946501 Henry Cohn, 2026, needs more optimization.
22 398 0.209589648533 Henry Cohn, 2026, needs more optimization.
22 399 0.209592406373 Henry Cohn, 2026, needs more optimization.
22 400 0.209594050128 Henry Cohn, 2026, needs more optimization.
22 401 0.209595120004 Henry Cohn, 2026, needs more optimization.
22 402 0.209599157254 Henry Cohn, 2026, needs more optimization.
22 403 0.209600440117 Henry Cohn, 2026, needs more optimization.
22 404 0.209686857167 Henry Cohn, 2026, needs more optimization.
22 405 0.209705577938 Henry Cohn, 2026, needs more optimization.
22 415 0.209711457926 Henry Cohn, 2026, needs more optimization.
22 416 0.209814456873 Henry Cohn, 2026, needs more optimization.
22 430 0.209817069797 Henry Cohn, 2026.
22 431 0.210993089892 Henry Cohn, 2026, needs more optimization.
22 432 0.211661635422 Henry Cohn, 2026, needs more optimization.
22 433 0.212032939829 Henry Cohn, 2026, needs more optimization.
22 436 0.212148697334 Henry Cohn, 2026, needs more optimization.
22 437 0.212406691088 Henry Cohn, 2026, needs more optimization.
22 438 0.212505211637 Henry Cohn, 2026, needs more optimization.
22 439 0.212505214875 Henry Cohn, 2026, needs more optimization.
22 440 0.212505214877 Henry Cohn, 2026, needs more optimization.
22 441 0.212505214879 Henry Cohn, 2026, needs more optimization.
22 442 0.212505214885 Henry Cohn, 2026, needs more optimization.
22 451 0.212653226480 Henry Cohn, 2026.
22 452 0.213200716356 Henry Cohn, 2026.
22⁢x2−1
22 485 0.229650347182 Henry Cohn, 2026, needs more optimization.
22 505 0.229926564594 Henry Cohn, 2026, needs more optimization.
22 506 0.231137104549 Henry Cohn, 2026, needs more optimization.
22 529 0.233333333334 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
30⁢x−7
22 556 0.238095238096 Orthogonal union of 554 points in 21 dimensions and 2 points in 1 dimension.
21⁢x−5
22 557 0.238095351437 Henry Cohn, 2026, needs more optimization.
22 558 0.238097213136 Henry Cohn, 2026, needs more optimization.
22 559 0.238211131327 Henry Cohn, 2026, needs more optimization.
22 560 0.238514924763 Henry Cohn, 2026, needs more optimization.
22 561 0.240687787996 Henry Cohn, 2026, needs more optimization.
22 562 0.244013244622 Henry Cohn, 2026, needs more optimization.
22 563 0.246119690767 Henry Cohn, 2026, needs more optimization.
22 564 0.248007452356 Henry Cohn, 2026, needs more optimization.
22 565 0.249744520705 Henry Cohn, 2026, needs more optimization.
22 891* 0.25 P. Delsarte, J. M. Goethals, and J. J. Seidel, Spherical codes and designs, Geometriae Dedicata 6 (1977), 363–388, doi:10.1007/bf03187604; V. I. Levenšteĭn, On bounds for packings in n-dimensional Euclidean space (Russian), Dokl. Akad. Nauk SSSR 245 (1979), 1299–1303, English translation in Soviet Math. Dokl. 20 (1979), 417–421.
4⁢x−1
22 1024 0.272727272728 T. Ericson and V. Zinoviev, Spherical codes generated by binary partitions of symmetric pointsets, IEEE Trans. Inform. Theory 41 (1995), 107–129, doi:10.1109/18.370114.
11⁢x−3
23 47 0.034216857253 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
10143⁢x3−529⁢x2−23⁢x+1
23 48 0.040044233015 Henry Cohn, 2025.
23 49 0.045954913455 Henry Cohn, 2026.
23 50 0.046749604258 Henry Cohn, 2025, continuous family of codes without rattlers.
713⁢x3+215⁢x2−33⁢x+1
23 51 0.047343031571 Henry Cohn, 2026.
23 52 0.047477902076 Henry Cohn, 2026, needs more optimization.
23 53 0.047579301640 Henry Cohn, 2026, needs more optimization.
23 54 0.047608667748 Henry Cohn, 2026.
23 55 0.055365527542 Henry Cohn, 2026.
23 56 0.057275984127 Henry Cohn, 2025.
23 57 0.061654200859 Henry Cohn, 2026.
23 58 0.064487742999 Henry Cohn, 2026, needs more optimization.
23 59 0.065947075206 Henry Cohn, 2026, needs more optimization.
23 60 0.066273220340 Henry Cohn, 2026, needs more optimization.
23 61 0.066456405073 Henry Cohn, 2026, needs more optimization.
23 62 0.066559758683 Henry Cohn, 2026, needs more optimization.
23 63 0.067249405088 Henry Cohn, 2026.
23 64 0.069716146261 Henry Cohn, 2026.
23 65 0.073130743225 Henry Cohn, 2026.
23 66 0.075359392650 Henry Cohn, 2026, needs more optimization.
23 67 0.076883023372 Henry Cohn, 2026, needs more optimization.
23 68 0.076894792665 Henry Cohn, 2026, needs more optimization.
23 69 0.077605236851 Henry Cohn, 2026, needs more optimization.
23 70 0.077985593068 Henry Cohn, 2026, needs more optimization.
23 71 0.079522620309 Henry Cohn, 2026.
23 72 0.080064660878 Henry Cohn, 2026.
23 73 0.081988639816 Henry Cohn, 2026, needs more optimization.
23 74 0.083305685093 Henry Cohn, 2026, needs more optimization.
23 75 0.083307304283 Henry Cohn, 2026, needs more optimization.
23 76 0.083319580451 Henry Cohn, 2026, needs more optimization.
23 77 0.083330983512 Henry Cohn, 2026, needs more optimization.
23 79 0.083333145471 Henry Cohn, 2026, needs more optimization.
23 81 0.083333222004 Henry Cohn, 2025, needs more optimization.
23 82 0.083365060180 Henry Cohn, 2026, needs more optimization.
23 83 0.087272831288 Henry Cohn, 2026, needs more optimization.
23 84 0.089248232030 Henry Cohn, 2026, needs more optimization.
23 102 0.090909090910 Code with 100 points in 22 dimensions, together with two antipodal points orthogonal to it; T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
11⁢x−1
23 103 0.094789393423 Henry Cohn, 2026.
67⁢x2−38⁢x+3
23 104 0.102473100453 Henry Cohn, 2026, needs more optimization.
23 106 0.109392443214 Henry Cohn, 2026.
2175⁢x2+210⁢x−49
23 107 0.111111109507 Henry Cohn, 2026, needs more optimization.
23 108 0.111111109515 Henry Cohn, 2026, needs more optimization.
23 111 0.111111109519 Henry Cohn, 2026, needs more optimization.
23 113 0.111111109682 Henry Cohn, 2026, needs more optimization.
23 115 0.111111109683 Henry Cohn, 2026, needs more optimization.
23 116 0.111111109684 Henry Cohn, 2026, needs more optimization.
23 117 0.111111529863 Henry Cohn, 2026, needs more optimization.
23 118 0.111111531356 Henry Cohn, 2026, needs more optimization.
23 119 0.115910206677 Henry Cohn, 2026, needs more optimization.
23 120 0.119778745465 Henry Cohn, 2026, needs more optimization.
23 121 0.124476982465 Henry Cohn, 2026, needs more optimization.
23 122 0.124526838717 Henry Cohn, 2026, needs more optimization.
23 123 0.130470283541 Henry Cohn, 2026, needs more optimization.
23 129 0.131782945737 Orthogonal union of 127 points in 22 dimensions and 2 points in 1 dimension.
129⁢x−17
23 130 0.131783417809 Henry Cohn, 2026, needs more optimization.
23 131 0.132067119443 Henry Cohn, 2026, needs more optimization.
23 132 0.134161317610 Henry Cohn, 2026, needs more optimization.
23 133 0.134703323566 Henry Cohn, 2026, needs more optimization.
23 134 0.135029159654 Henry Cohn, 2026, needs more optimization.
23 147 0.135135135136 Henry Cohn, 2026.
37⁢x−5
23 148 0.135305749471 Henry Cohn, 2026, needs more optimization.
23 149 0.136611841248 Henry Cohn, 2026, needs more optimization.
23 150 0.136642662956 Henry Cohn, 2026, needs more optimization.
23 151 0.137557808169 Henry Cohn, 2026, needs more optimization.
23 152 0.138673551832 Henry Cohn, 2026, needs more optimization.
23 168 0.142857142858 Orthogonal union of 166 points in 22 dimensions and 2 points in 1 dimension.
7⁢x−1
23 169 0.142857630115 Henry Cohn, 2026, needs more optimization.
23 170 0.142857630117 Henry Cohn, 2026, needs more optimization.
23 171 0.145096804730 Henry Cohn, 2026, needs more optimization.
23 172 0.145383795939 Henry Cohn, 2026, needs more optimization.
23 173 0.145383795957 Henry Cohn, 2026, needs more optimization.
23 174 0.146719215200 Henry Cohn, 2026, needs more optimization.
23 175 0.150592523247 Henry Cohn, 2026, needs more optimization.
23 176 0.153571024236 Henry Cohn, 2026, needs more optimization.
23 177 0.154899110495 Henry Cohn, 2026, needs more optimization.
23 178 0.155965300059 Henry Cohn, 2026, needs more optimization.
23 179 0.156306715649 Henry Cohn, 2026, needs more optimization.
23 180 0.158773058610 Henry Cohn, 2026, needs more optimization.
23 181 0.159255831194 Henry Cohn, 2026, needs more optimization.
23 182 0.160918538099 Henry Cohn, 2026, needs more optimization.
23 183 0.161390084751 Henry Cohn, 2026, needs more optimization.
23 203 0.161904761905 Orthogonal union of 201 points in 22 dimensions and 2 points in 1 dimension.
105⁢x−17
23 204 0.161904891178 Henry Cohn, 2026, needs more optimization.
23 205 0.161904895839 Henry Cohn, 2026, needs more optimization.
23 206 0.161907076292 Henry Cohn, 2026, needs more optimization.
23 207 0.161918513785 Henry Cohn, 2026, needs more optimization.
23 208 0.161957300108 Henry Cohn, 2026, needs more optimization.
23 209 0.164060791821 Henry Cohn, 2026, needs more optimization.
23 210 0.164949114289 Henry Cohn, 2026, needs more optimization.
23 211 0.165496552786 Henry Cohn, 2026, needs more optimization.
23 212 0.166122583861 Henry Cohn, 2026, needs more optimization.
23 213 0.166454985198 Henry Cohn, 2026, needs more optimization.
23 214 0.166587977818 Henry Cohn, 2026, needs more optimization.
23 278 0.166666666667 Henry Cohn, 2026.
6⁢x−1
23 279 0.168164328629 Henry Cohn, 2026, needs more optimization.
23 280 0.174223846133 Henry Cohn, 2026, needs more optimization.
23 281 0.178760842521 Henry Cohn, 2026, needs more optimization.
23 282 0.181917179801 Henry Cohn, 2026, needs more optimization.
23 283 0.183303364149 Henry Cohn, 2026, needs more optimization.
23 284 0.185710494989 Henry Cohn, 2026, needs more optimization.
23 285 0.186029348849 Henry Cohn, 2026, needs more optimization.
23 286 0.187582465144 Henry Cohn, 2026, needs more optimization.
23 287 0.188050785770 Henry Cohn, 2026, needs more optimization.
23 288 0.188291960606 Henry Cohn, 2026, needs more optimization.
23 289 0.189180116210 Henry Cohn, 2026, needs more optimization.
23 290 0.189363558282 Henry Cohn, 2026, needs more optimization.
23 291 0.189500931810 Henry Cohn, 2026, needs more optimization.
23 292 0.189580006076 Henry Cohn, 2026, needs more optimization.
23 293 0.189621928479 Henry Cohn, 2026, needs more optimization.
23 294 0.189656251012 Henry Cohn, 2026, needs more optimization.
23 295 0.189656253197 Henry Cohn, 2026, needs more optimization.
23 296 0.189656269416 Henry Cohn, 2026, needs more optimization.
23 297 0.189656372977 Henry Cohn, 2026, needs more optimization.
23 298 0.189656378476 Henry Cohn, 2026, needs more optimization.
23 299 0.189656380739 Henry Cohn, 2026, needs more optimization.
23 300 0.189657892523 Henry Cohn, 2026, needs more optimization.
23 301 0.190658498794 Henry Cohn, 2026, needs more optimization.
23 302 0.193044183846 Henry Cohn, 2026, needs more optimization.
23 303 0.194180527571 Henry Cohn, 2026, needs more optimization.
23 304 0.195440261896 Henry Cohn, 2026, needs more optimization.
23 305 0.196304794465 Henry Cohn, 2026, needs more optimization.
23 306 0.197473252744 Henry Cohn, 2026, needs more optimization.
23 307 0.198603084621 Henry Cohn, 2026, needs more optimization.
23 308 0.199006017618 Henry Cohn, 2026, needs more optimization.
23 309 0.199259131687 Henry Cohn, 2026, needs more optimization.
23 552* 0.2 P. Delsarte, J. M. Goethals, and J. J. Seidel, Spherical codes and designs, Geometriae Dedicata 6 (1977), 363–388, doi:10.1007/bf03187604; V. I. Levenšteĭn, On bounds for packings in n-dimensional Euclidean space (Russian), Dokl. Akad. Nauk SSSR 245 (1979), 1299–1303, English translation in Soviet Math. Dokl. 20 (1979), 417–421.
5⁢x−1
23 553 0.232851959963 Henry Cohn, 2026, needs more optimization.
23 554 0.235338473108 Henry Cohn, 2026, needs more optimization.
23 558 0.238095238096 Orthogonal union of 554 points in 21 dimensions and 4 points in 2 dimensions.
21⁢x−5
23 559 0.238095351403 Henry Cohn, 2026, needs more optimization.
23 560 0.238096151989 Henry Cohn, 2026, needs more optimization.
23 562 0.238096283359 Henry Cohn, 2026, needs more optimization.
23 563 0.238096558294 Henry Cohn, 2026, needs more optimization.
23 566 0.238100030295 Henry Cohn, 2026, needs more optimization.
23 570 0.238777810887 Henry Cohn, 2026, needs more optimization.
23 571 0.238783000100 Henry Cohn, 2026, needs more optimization.
23 572 0.238783700138 Henry Cohn, 2026, needs more optimization.
23 573 0.239234959225 Henry Cohn, 2026, needs more optimization.
23 574 0.240065458765 Henry Cohn, 2026, needs more optimization.
23 575 0.241013578729 Henry Cohn, 2026, needs more optimization.
23 576 0.241358393919 Henry Cohn, 2026, needs more optimization.
23 577 0.241575675375 Henry Cohn, 2026, needs more optimization.
23 578 0.242523718007 Henry Cohn, 2026, needs more optimization.
23 579 0.242821406283 Henry Cohn, 2026, needs more optimization.
23 581 0.243305846351 Henry Cohn, 2026, needs more optimization.
23 582 0.243558265462 Henry Cohn, 2026, needs more optimization.
23 583 0.244213847827 Henry Cohn, 2026, needs more optimization.
23 584 0.244885272933 Henry Cohn, 2026, needs more optimization.
23 585 0.245312247456 Henry Cohn, 2026, needs more optimization.
23 586 0.245505736406 Henry Cohn, 2026, needs more optimization.
23 587 0.245871385733 Henry Cohn, 2026, needs more optimization.
23 588 0.245919004766 Henry Cohn, 2026, needs more optimization.
23 590 0.246156085436 Henry Cohn, 2026, needs more optimization.
23 591 0.246456968366 Henry Cohn, 2026, needs more optimization.
23 592 0.246489297305 Henry Cohn, 2026, needs more optimization.
23 593 0.247102987768 Henry Cohn, 2026, needs more optimization.
23 594 0.247156056308 Henry Cohn, 2026, needs more optimization.
23 595 0.247308831888 Henry Cohn, 2026, needs more optimization.
23 596 0.247665416873 Henry Cohn, 2026, needs more optimization.
23 597 0.247973385691 Henry Cohn, 2026, needs more optimization.
23 598 0.248470314343 Henry Cohn, 2026, needs more optimization.
23 599 0.248730800759 Henry Cohn, 2026, needs more optimization.
23 600 0.248899226963 Henry Cohn, 2026, needs more optimization.
23 601 0.249302185592 Henry Cohn, 2026, needs more optimization.
23 602 0.249458852392 Henry Cohn, 2026, needs more optimization.
23 603 0.249618451927 Henry Cohn, 2026, needs more optimization.
23 604 0.249623669597 Henry Cohn, 2026, needs more optimization.
23 605 0.249806521031 Henry Cohn, 2026, needs more optimization.
23 894 0.25 Henry Cohn, 2026.
4⁢x−1
23 895 0.250001006530 Numaro AI Autoresearch, 11,000+ New Verified Spherical-Code Records from AI Autoresearch, Numaro Research Report NUMARO-2026-015 (2026), https://numaro.tech/research/spherical-codes-2026/.
23 896 0.252693959928 Henry Cohn, 2026, needs more optimization.
23 897 0.254297683924 Numaro AI Autoresearch, 11,000+ New Verified Spherical-Code Records from AI Autoresearch, Numaro Research Report NUMARO-2026-015 (2026), https://numaro.tech/research/spherical-codes-2026/.
23 898 0.255385789253 Numaro AI Autoresearch, 11,000+ New Verified Spherical-Code Records from AI Autoresearch, Numaro Research Report NUMARO-2026-015 (2026), https://numaro.tech/research/spherical-codes-2026/.
23 899 0.256375948656 Numaro AI Autoresearch, 11,000+ New Verified Spherical-Code Records from AI Autoresearch, Numaro Research Report NUMARO-2026-015 (2026), https://numaro.tech/research/spherical-codes-2026/.
23 900 0.256477369157 Henry Cohn, 2026, needs more optimization.
23 901 0.256477369165 Henry Cohn, 2026, needs more optimization.
23 902 0.256933008903 Numaro AI Autoresearch, 11,000+ New Verified Spherical-Code Records from AI Autoresearch, Numaro Research Report NUMARO-2026-015 (2026), https://numaro.tech/research/spherical-codes-2026/.
23 903 0.257961299555 Numaro AI Autoresearch, 11,000+ New Verified Spherical-Code Records from AI Autoresearch, Numaro Research Report NUMARO-2026-015 (2026), https://numaro.tech/research/spherical-codes-2026/.
23 904 0.258523102932 Numaro AI Autoresearch, 11,000+ New Verified Spherical-Code Records from AI Autoresearch, Numaro Research Report NUMARO-2026-015 (2026), https://numaro.tech/research/spherical-codes-2026/.
23 905 0.259254205784 Numaro AI Autoresearch, 11,000+ New Verified Spherical-Code Records from AI Autoresearch, Numaro Research Report NUMARO-2026-015 (2026), https://numaro.tech/research/spherical-codes-2026/.
23 906 0.259361955147 Henry Cohn, 2026, needs more optimization.
23 907 0.261480139135 Henry Cohn, 2026, needs more optimization.
23 908 0.264858079786 Henry Cohn, 2026, needs more optimization.
23 909 0.265174591312 Numaro AI Autoresearch, 11,000+ New Verified Spherical-Code Records from AI Autoresearch, Numaro Research Report NUMARO-2026-015 (2026), https://numaro.tech/research/spherical-codes-2026/.
23 910 0.265378479103 Numaro AI Autoresearch, 11,000+ New Verified Spherical-Code Records from AI Autoresearch, Numaro Research Report NUMARO-2026-015 (2026), https://numaro.tech/research/spherical-codes-2026/.
23 911 0.266013569187 Numaro AI Autoresearch, 11,000+ New Verified Spherical-Code Records from AI Autoresearch, Numaro Research Report NUMARO-2026-015 (2026), https://numaro.tech/research/spherical-codes-2026/.
23 912 0.267146427086 Henry Cohn, 2026, needs more optimization.
23 913 0.268029013370 Henry Cohn, 2026, needs more optimization.
23 914 0.268685179314 Henry Cohn, 2026, needs more optimization.
23 915 0.268789506298 Numaro AI Autoresearch, 11,000+ New Verified Spherical-Code Records from AI Autoresearch, Numaro Research Report NUMARO-2026-015 (2026), https://numaro.tech/research/spherical-codes-2026/.
23 916 0.269609811619 Henry Cohn, 2026, needs more optimization.
23 917 0.270148057511 Henry Cohn, 2026, needs more optimization.
23 918 0.270686134659 Henry Cohn, 2026, needs more optimization.
23 919 0.271126274437 Henry Cohn, 2026, needs more optimization.
23 920 0.271420519869 Henry Cohn, 2026, needs more optimization.
23 921 0.272114151685 Henry Cohn, 2026, needs more optimization.
23 1024 0.272727272728 Code with 1024 points in 22 dimensions.
11⁢x−3
23 4600* 0.333333333334 P. Delsarte, J. M. Goethals, and J. J. Seidel, Spherical codes and designs, Geometriae Dedicata 6 (1977), 363–388, doi:10.1007/bf03187604; V. I. Levenšteĭn, On bounds for packings in n-dimensional Euclidean space (Russian), Dokl. Akad. Nauk SSSR 245 (1979), 1299–1303, English translation in Soviet Math. Dokl. 20 (1979), 417–421.
3⁢x−1
24 49 0.032924519945 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
11616⁢x3−576⁢x2−24⁢x+1
24 50 0.038461538462 T. Ericson and V. Zinoviev, Spherical codes generated by binary partitions of symmetric pointsets, IEEE Trans. Inform. Theory 41 (1995), 107–129, doi:10.1109/18.370114.
26⁢x−1
24 51 0.045537713846 Henry Cohn, 2025.
24 52 0.046377212908 Henry Cohn, 2025.
24 53 0.046712202497 Henry Cohn, 2025.
24 54 0.047284571428 Henry Cohn, 2025.
24 55 0.047381601960 Henry Cohn, 2024.
24 56 0.047562533008 Henry Cohn, 2026.
24 57 0.053295295011 Henry Cohn, 2026.
24 58 0.054361642549 Henry Cohn, 2026.
24 59 0.057903810057 Henry Cohn, 2026.
24 60 0.061561217808 Henry Cohn, 2026.
24 61 0.064589747421 Henry Cohn, 2026.
24 62 0.065059060779 Henry Cohn, 2026, needs more optimization.
24 63 0.065490776858 Henry Cohn, 2026, needs more optimization.
24 64 0.065895168399 Henry Cohn, 2026, needs more optimization.
24 65 0.066584832783 Henry Cohn, 2026, needs more optimization.
24 66 0.068178739965 Henry Cohn, 2026, needs more optimization.
24 67 0.070762396841 Henry Cohn, 2026.
24 68 0.072116568734 Henry Cohn, 2026.
24 69 0.073247042433 Henry Cohn, 2026.
24 70 0.076551769514 Henry Cohn, 2026, needs more optimization.
24 71 0.076919863374 Henry Cohn, 2026, needs more optimization.
24 72 0.077408481482 Henry Cohn, 2026, needs more optimization.
24 73 0.077739710165 Henry Cohn, 2026, needs more optimization.
24 74 0.077908661685 Henry Cohn, 2026, needs more optimization.
24 75 0.078506895697 Henry Cohn, 2026, needs more optimization.
24 76 0.078850061999 Henry Cohn, 2026, needs more optimization.
24 77 0.081772396260 Henry Cohn, 2026, needs more optimization.
24 78 0.082752962267 Henry Cohn, 2026, needs more optimization.
24 79 0.083132289703 Henry Cohn, 2026, needs more optimization.
24 80 0.083243851890 Henry Cohn, 2026, needs more optimization.
24 81 0.083290447292 Henry Cohn, 2026, needs more optimization.
24 82 0.083315861506 Henry Cohn, 2026, needs more optimization.
24 83 0.083315861531 Henry Cohn, 2026, needs more optimization.
24 84 0.083327202550 Henry Cohn, 2026, needs more optimization.
24 85 0.083328479334 Henry Cohn, 2026, needs more optimization.
24 86 0.086216676467 Henry Cohn, 2026, needs more optimization.
24 87 0.088123588881 Henry Cohn, 2026, needs more optimization.
24 88 0.089529920991 Henry Cohn, 2026, needs more optimization.
24 89 0.090146324176 Henry Cohn, 2026, needs more optimization.
24 90 0.090524192223 Henry Cohn, 2026, needs more optimization.
24 91 0.090706242039 Henry Cohn, 2026, needs more optimization.
24 92 0.090827423650 Henry Cohn, 2026, needs more optimization.
24 93 0.090884059839 Henry Cohn, 2026, needs more optimization.
24 97 0.090909090540 Henry Cohn, 2026, needs more optimization.
24 98 0.090909090558 Henry Cohn, 2026, needs more optimization.
24 103 0.090909090571 Henry Cohn, 2026, needs more optimization.
24 104 0.090909090572 Henry Cohn, 2026, needs more optimization.
24 105 0.091487374084 Henry Cohn, 2026, needs more optimization.
24 106 0.095233114698 Henry Cohn, 2026, needs more optimization.
24 107 0.100951897476 Henry Cohn, 2026, needs more optimization.
24 108 0.105645382604 Henry Cohn, 2026, needs more optimization.
24 109 0.110674455116 Henry Cohn, 2026, needs more optimization.
24 110 0.110674461290 Henry Cohn, 2026, needs more optimization.
24 111 0.110685646663 Henry Cohn, 2026, needs more optimization.
24 112 0.110685655917 Henry Cohn, 2026, needs more optimization.
24 113 0.110865973543 Henry Cohn, 2026, needs more optimization.
24 118 0.111099565428 Henry Cohn, 2025, needs more optimization.
24 121 0.111111111112 Henry Cohn, 2026.
9⁢x−1
24 122 0.112098401692 Henry Cohn, 2026, needs more optimization.
24 123 0.116165160709 Henry Cohn, 2026, needs more optimization.
24 124 0.117892096044 Henry Cohn, 2026, needs more optimization.
24 125 0.122807017544 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
57⁢x−7
24 126 0.131751193083 Henry Cohn, 2026, needs more optimization.
24 127 0.131762644046 Henry Cohn, 2026, needs more optimization.
24 128 0.131762644167 Henry Cohn, 2026, needs more optimization.
24 130 0.131764727411 Henry Cohn, 2026, needs more optimization.
24 131 0.131774465876 Henry Cohn, 2026, needs more optimization.
24 132 0.131777155384 Henry Cohn, 2026, needs more optimization.
24 133 0.131781799209 Henry Cohn, 2026, needs more optimization.
24 134 0.131784003351 Henry Cohn, 2026, needs more optimization.
24 135 0.131946347090 Henry Cohn, 2026, needs more optimization.
24 136 0.132201450377 Henry Cohn, 2026, needs more optimization.
24 137 0.132919808972 Henry Cohn, 2026, needs more optimization.
24 138 0.133265101255 Henry Cohn, 2026, needs more optimization.
24 139 0.134214457704 Henry Cohn, 2026, needs more optimization.
24 140 0.134394038005 Henry Cohn, 2026, needs more optimization.
24 141 0.134777360954 Henry Cohn, 2026, needs more optimization.
24 142 0.134934452612 Henry Cohn, 2026, needs more optimization.
24 143 0.135094557535 Henry Cohn, 2026, needs more optimization.
24 149 0.135135135136 Orthogonal union of 147 points in 23 dimensions and 2 points in 1 dimension.
37⁢x−5
24 152 0.135135665735 Henry Cohn, 2026, needs more optimization.
24 153 0.136258642069 Henry Cohn, 2026, needs more optimization.
24 154 0.136258672568 Henry Cohn, 2026, needs more optimization.
24 155 0.137111104343 Henry Cohn, 2026, needs more optimization.
24 156 0.139155469404 Henry Cohn, 2026, needs more optimization.
24 157 0.141118834900 Henry Cohn, 2026, needs more optimization.
24 158 0.142857107111 Henry Cohn, 2026, needs more optimization.
24 159 0.142857110879 Henry Cohn, 2026, needs more optimization.
24 160 0.142857110902 Henry Cohn, 2026, needs more optimization.
24 162 0.142857110917 Henry Cohn, 2026, needs more optimization.
24 164 0.142857116293 Henry Cohn, 2026, needs more optimization.
24 166 0.142857121940 Henry Cohn, 2026, needs more optimization.
24 168 0.142857122001 Henry Cohn, 2026, needs more optimization.
24 171 0.142857138919 Henry Cohn, 2026, needs more optimization.
24 172 0.142857140416 Henry Cohn, 2026, needs more optimization.
24 173 0.142857171592 Henry Cohn, 2026, needs more optimization.
24 174 0.142857172713 Henry Cohn, 2026, needs more optimization.
24 175 0.143408867040 Henry Cohn, 2026, needs more optimization.
24 176 0.145880466458 Henry Cohn, 2026, needs more optimization.
24 177 0.145880466873 Henry Cohn, 2026, needs more optimization.
24 178 0.145883606552 Henry Cohn, 2026, needs more optimization.
24 179 0.146017716401 Henry Cohn, 2026, needs more optimization.
24 180 0.147283665957 Henry Cohn, 2026, needs more optimization.
24 181 0.147671629371 Henry Cohn, 2026, needs more optimization.
24 182 0.148037777843 Henry Cohn, 2026, needs more optimization.
24 183 0.148199578100 Henry Cohn, 2026, needs more optimization.
24 184 0.148268864796 Henry Cohn, 2026, needs more optimization.
24 186 0.148728163557 Henry Cohn, 2026, needs more optimization.
24 187 0.152036769384 Henry Cohn, 2026, needs more optimization.
24 188 0.152152499162 Henry Cohn, 2026, needs more optimization.
24 189 0.152169650228 Henry Cohn, 2026, needs more optimization.
24 190 0.153302835990 Henry Cohn, 2026, needs more optimization.
24 191 0.155105464259 Henry Cohn, 2026, needs more optimization.
24 192 0.155157909295 Henry Cohn, 2026, needs more optimization.
24 193 0.155183119903 Henry Cohn, 2026, needs more optimization.
24 194 0.157422032725 Henry Cohn, 2026, needs more optimization.
24 195 0.157763293576 Henry Cohn, 2026, needs more optimization.
24 196 0.159089477342 Henry Cohn, 2026, needs more optimization.
24 197 0.160025558691 Henry Cohn, 2026, needs more optimization.
24 198 0.160191095441 Henry Cohn, 2026, needs more optimization.
24 199 0.161379381689 Henry Cohn, 2026, needs more optimization.
24 200 0.161471603922 Henry Cohn, 2026, needs more optimization.
24 205 0.161904761905 Orthogonal union of 201 points in 22 dimensions and 4 points in 2 dimensions.
105⁢x−17
24 206 0.161904778792 Henry Cohn, 2026, needs more optimization.
24 207 0.161904778979 Henry Cohn, 2026, needs more optimization.
24 208 0.161904789200 Henry Cohn, 2026, needs more optimization.
24 209 0.161904789352 Henry Cohn, 2026, needs more optimization.
24 210 0.161904789382 Henry Cohn, 2026, needs more optimization.
24 212 0.161904799606 Henry Cohn, 2026, needs more optimization.
24 213 0.161905360980 Henry Cohn, 2026, needs more optimization.
24 214 0.161999049382 Henry Cohn, 2026, needs more optimization.
24 215 0.162166532206 Henry Cohn, 2026, needs more optimization.
24 216 0.163079459150 Henry Cohn, 2026, needs more optimization.
24 217 0.163168002279 Henry Cohn, 2026, needs more optimization.
24 218 0.164149339514 Henry Cohn, 2026, needs more optimization.
24 219 0.164900951016 Henry Cohn, 2026, needs more optimization.
24 220 0.165004593518 Henry Cohn, 2026, needs more optimization.
24 221 0.165523002653 Henry Cohn, 2026, needs more optimization.
24 222 0.165837118826 Henry Cohn, 2026, needs more optimization.
24 223 0.166148059932 Henry Cohn, 2026, needs more optimization.
24 224 0.166407996877 Henry Cohn, 2026, needs more optimization.
24 280 0.166666666667 Orthogonal union of 278 points in 23 dimensions and 2 points in 1 dimension.
6⁢x−1
24 281 0.166666872447 Henry Cohn, 2026, needs more optimization.
24 283 0.166666872448 Henry Cohn, 2026, needs more optimization.
24 284 0.166823803047 Henry Cohn, 2026, needs more optimization.
24 285 0.170017846308 Henry Cohn, 2026, needs more optimization.
24 286 0.171353778150 Henry Cohn, 2026, needs more optimization.
24 287 0.174955148837 Henry Cohn, 2026, needs more optimization.
24 288 0.177014115980 Henry Cohn, 2026, needs more optimization.
24 289 0.179237302311 Henry Cohn, 2026, needs more optimization.
24 290 0.181619521429 Henry Cohn, 2026, needs more optimization.
24 297 0.181818181819 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
11⁢x−2
24 313 0.181818181819 Henry Cohn, 2026, by enlarging a code from T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
11⁢x−2
24 314 0.182026301858 Henry Cohn, 2026, needs more optimization.
24 315 0.186792613971 Henry Cohn, 2026, needs more optimization.
24 316 0.189656736342 Henry Cohn, 2026, needs more optimization.
24 317 0.191040654359 Henry Cohn, 2026, needs more optimization.
24 318 0.192004275444 Henry Cohn, 2026, needs more optimization.
24 330 0.193548387097 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
31⁢x−6
24 555 0.2 Valentin Khrulkov, 2026, using the program of A. Kravatsky, V. Khrulkov, and I. Oseledets, ImprovEvolve: basin-hopping meets LLM-guided evolutionary search, ICML 2026 AI4Math Workshop Poster, https://openreview.net/forum?id=nE1q0gRDNr, arXiv:2602.10233.
5⁢x−1
24 556 0.200810414689 Henry Cohn, 2026, needs more optimization.
24 557 0.206708802860 Henry Cohn, 2026, needs more optimization.
24 558 0.213698067814 Henry Cohn, 2026, needs more optimization.
24 559 0.216965542235 Henry Cohn, 2026, needs more optimization.
24 560 0.219724280030 Henry Cohn, 2026, needs more optimization.
24 561 0.222335414621 Henry Cohn, 2026, needs more optimization.
24 562 0.222631863235 Henry Cohn, 2026, needs more optimization.
24 563 0.224103315248 Henry Cohn, 2026, needs more optimization.
24 564 0.225318836535 Henry Cohn, 2026, needs more optimization.
24 565 0.226555631528 Henry Cohn, 2026, needs more optimization.
24 566 0.228187912751 Henry Cohn, 2026, needs more optimization.
24 567 0.229101528942 Henry Cohn, 2026, needs more optimization.
24 568 0.230489745562 Henry Cohn, 2026, needs more optimization.
24 569 0.231641365896 Henry Cohn, 2026, needs more optimization.
24 570 0.231785663031 Henry Cohn, 2026, needs more optimization.
24 571 0.232153551205 Henry Cohn, 2026, needs more optimization.
24 572 0.232352084172 Henry Cohn, 2026, needs more optimization.
24 573 0.232834746329 Henry Cohn, 2026, needs more optimization.
24 574 0.233340929959 Henry Cohn, 2026, needs more optimization.
24 581 0.233711730709 Numaro AI Autoresearch, 11,000+ New Verified Spherical-Code Records from AI Autoresearch, Numaro Research Report NUMARO-2026-015 (2026), https://numaro.tech/research/spherical-codes-2026/.
160⁢x2−16⁢x−5
24 582 0.234149666387 Henry Cohn, 2026, needs more optimization.
24 583 0.234571789955 Henry Cohn, 2026, needs more optimization.
24 584 0.234981702152 Henry Cohn, 2026, needs more optimization.
24 585 0.235415802070 Henry Cohn, 2026, needs more optimization.
24 586 0.235875690644 Henry Cohn, 2026, needs more optimization.
24 587 0.238314422078 Henry Cohn, 2026, needs more optimization.
24 592 0.238436494868 Henry Cohn, 2026, needs more optimization.
24 593 0.238462973076 Henry Cohn, 2026, needs more optimization.
24 594 0.238730044931 Henry Cohn, 2026, needs more optimization.
24 596 0.239314562996 Henry Cohn, 2026, needs more optimization.
24 597 0.239538809932 Henry Cohn, 2026, needs more optimization.
24 598 0.240309043662 Henry Cohn, 2026, needs more optimization.
24 599 0.240489111823 Henry Cohn, 2026, needs more optimization.
24 600 0.241438389879 Henry Cohn, 2026, needs more optimization.
24 601 0.241663190770 Henry Cohn, 2026, needs more optimization.
24 602 0.241668771721 Henry Cohn, 2026, needs more optimization.
24 604 0.241725601978 Henry Cohn, 2026, needs more optimization.
24 605 0.241966281604 Henry Cohn, 2026, needs more optimization.
24 606 0.242210032982 Henry Cohn, 2026, needs more optimization.
24 607 0.242724471857 Henry Cohn, 2026, needs more optimization.
24 608 0.243233472636 Henry Cohn, 2026, needs more optimization.
24 609 0.243463956825 Henry Cohn, 2026, needs more optimization.
24 610 0.243644910903 Henry Cohn, 2026, needs more optimization.
24 611 0.244083429282 Henry Cohn, 2026, needs more optimization.
24 612 0.244436448166 Henry Cohn, 2026, needs more optimization.
24 613 0.244963673930 Henry Cohn, 2026, needs more optimization.
24 614 0.245511782169 Henry Cohn, 2026, needs more optimization.
24 615 0.245654661967 Henry Cohn, 2026, needs more optimization.
24 616 0.246256038291 Henry Cohn, 2026, needs more optimization.
24 617 0.246727784340 Henry Cohn, 2026, needs more optimization.
24 618 0.247121048181 Henry Cohn, 2026, needs more optimization.
24 619 0.247500117686 Henry Cohn, 2026, needs more optimization.
24 621 0.247608437587 Henry Cohn, 2026, needs more optimization.
24 622 0.248141596096 Henry Cohn, 2026, needs more optimization.
24 623 0.248433858809 Henry Cohn, 2026, needs more optimization.
24 624 0.248858019806 Henry Cohn, 2026, needs more optimization.
24 625 0.249071682481 Henry Cohn, 2026, needs more optimization.
24 626 0.249388870627 Henry Cohn, 2026, needs more optimization.
24 627 0.249552478427 Henry Cohn, 2026, needs more optimization.
24 628 0.249616504302 Henry Cohn, 2026, needs more optimization.
24 629 0.249778127524 Henry Cohn, 2026, needs more optimization.
24 896 0.25 Orthogonal union of 894 points in 23 dimensions and 2 points in 1 dimension.
4⁢x−1
24 897 0.250001006530 Numaro AI Autoresearch, 11,000+ New Verified Spherical-Code Records from AI Autoresearch, Numaro Research Report NUMARO-2026-015 (2026), https://numaro.tech/research/spherical-codes-2026/.
24 898 0.250016958024 Henry Cohn, 2026, needs more optimization.
24 899 0.250018177001 Henry Cohn, 2026, needs more optimization.
24 900 0.250026472759 Henry Cohn, 2026, needs more optimization.
24 901 0.250027457954 Henry Cohn, 2026, needs more optimization.
24 903 0.250119089043 Henry Cohn, 2026, needs more optimization.
24 904 0.250119280852 Henry Cohn, 2026, needs more optimization.
24 905 0.250125797676 Henry Cohn, 2026, needs more optimization.
24 906 0.250174852883 Henry Cohn, 2026, needs more optimization.
24 907 0.250242249782 Henry Cohn, 2026, needs more optimization.
24 908 0.251063567140 Henry Cohn, 2026, needs more optimization.
24 909 0.251280384381 Henry Cohn, 2026, needs more optimization.
24 910 0.251724414878 Henry Cohn, 2026, needs more optimization.
24 911 0.254872867055 Henry Cohn, 2026, needs more optimization.
24 912 0.255861526534 Henry Cohn, 2026, needs more optimization.
24 913 0.255943742170 Henry Cohn, 2026, needs more optimization.
24 914 0.256257237635 Henry Cohn, 2026, needs more optimization.
24 915 0.256454429782 Henry Cohn, 2026, needs more optimization.
24 916 0.256459979575 Henry Cohn, 2026, needs more optimization.
24 917 0.256470545673 Henry Cohn, 2026, needs more optimization.
24 918 0.256473310758 Henry Cohn, 2026, needs more optimization.
24 919 0.256751774803 Henry Cohn, 2026, needs more optimization.
24 920 0.257033815381 Henry Cohn, 2026, needs more optimization.
24 921 0.257594129794 Henry Cohn, 2026, needs more optimization.
24 922 0.258303285109 Henry Cohn, 2026, needs more optimization.
24 923 0.258827517918 Henry Cohn, 2026, needs more optimization.
24 924 0.259322021094 Henry Cohn, 2026, needs more optimization.
24 925 0.259347010466 Henry Cohn, 2026, needs more optimization.
24 926 0.261253107430 Henry Cohn, 2026, needs more optimization.
24 927 0.262252616760 Henry Cohn, 2026, needs more optimization.
24 928 0.262600057537 Henry Cohn, 2026, needs more optimization.
24 929 0.263666391414 Henry Cohn, 2026, needs more optimization.
24 930 0.264010371919 Henry Cohn, 2026, needs more optimization.
24 931 0.264463169760 Henry Cohn, 2026, needs more optimization.
24 932 0.265235994187 Henry Cohn, 2026, needs more optimization.
24 933 0.265461680478 Henry Cohn, 2026, needs more optimization.
24 934 0.266492717432 Henry Cohn, 2026, needs more optimization.
24 935 0.266799215842 Henry Cohn, 2026, needs more optimization.
24 936 0.267123590701 Henry Cohn, 2026, needs more optimization.
24 938 0.267445191478 Henry Cohn, 2026, needs more optimization.
24 939 0.267901771400 Henry Cohn, 2026, needs more optimization.
24 940 0.268407858679 Henry Cohn, 2026, needs more optimization.
24 941 0.268884692684 Henry Cohn, 2026, needs more optimization.
24 942 0.269124785948 Henry Cohn, 2026, needs more optimization.
24 943 0.270068645038 Henry Cohn, 2026, needs more optimization.
24 945 0.270857454413 Henry Cohn, 2026, needs more optimization.
24 946 0.271318631458 Henry Cohn, 2026, needs more optimization.
24 1024 0.272727272728 Code with 1024 points in 22 dimensions.
11⁢x−3
24 196560* 0.5 J. Leech, Notes on sphere packings, Canadian J. Math. 19 (1967), 251–267, doi:10.4153/CJM-1967-017-0; V. I. Levenšteĭn, On bounds for packings in n-dimensional Euclidean space (Russian), Dokl. Akad. Nauk SSSR 245 (1979), 1299–1303, English translation in Soviet Math. Dokl. 20 (1979), 417–421; A. M. Odlyzko and N. J. A. Sloane, New bounds on the number of unit spheres that can touch a unit sphere in n dimensions, J. Combin. Theory Ser. A 26 (1979), 210–214, doi:10.1016/0097-3165(79)90074-8.
2⁢x−1
25 51 0.031729360276 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
13225⁢x3−625⁢x2−25⁢x+1
25 52 0.037068271283 Henry Cohn, 2025.
25 55 0.04 Henry Cohn, 2026.
25⁢x−1
25 56 0.046433703861 Henry Cohn, 2025, needs more optimization.
25 57 0.046835501882 Henry Cohn, 2026, needs more optimization.
25 58 0.046863920964 Henry Cohn, 2025.
25 59 0.051394584232 Henry Cohn, 2024.
25 60 0.052966665528 Henry Cohn, 2026.
25 61 0.056064008005 Henry Cohn, 2026.
25 62 0.060613957797 Henry Cohn, 2026.
25 63 0.062392555280 Henry Cohn, 2026.
25 64 0.064223832775 Henry Cohn, 2026.
25 65 0.065021599204 Henry Cohn, 2026, needs more optimization.
25 66 0.065051276211 Henry Cohn, 2026, needs more optimization.
25 67 0.066210993305 Henry Cohn, 2026, needs more optimization.
25 68 0.066465899781 Henry Cohn, 2026, needs more optimization.
25 69 0.068627707329 Henry Cohn, 2026.
25 70 0.071055411990 Henry Cohn, 2026.
25 71 0.071772052828 Henry Cohn, 2026, needs more optimization.
25 72 0.073324160906 Henry Cohn, 2026, needs more optimization.
25 73 0.076166312463 Henry Cohn, 2026, needs more optimization.
25 74 0.076826408681 Henry Cohn, 2026, needs more optimization.
25 76 0.076922977355 Henry Cohn, 2026, needs more optimization.
25 77 0.077469182907 Henry Cohn, 2026, needs more optimization.
25 78 0.077915335021 Henry Cohn, 2026, needs more optimization.
25 79 0.078551129131 Henry Cohn, 2026, needs more optimization.
25 80 0.080764899090 Henry Cohn, 2026, needs more optimization.
25 81 0.082025428106 Henry Cohn, 2026, needs more optimization.
25 82 0.082586417485 Henry Cohn, 2026, needs more optimization.
25 83 0.082940817567 Henry Cohn, 2026, needs more optimization.
25 85 0.083095965795 Henry Cohn, 2026, needs more optimization.
25 86 0.083268256629 Henry Cohn, 2026, needs more optimization.
25 87 0.083303406091 Henry Cohn, 2026, needs more optimization.
25 88 0.083314404763 Henry Cohn, 2026, needs more optimization.
25 89 0.085157339103 Henry Cohn, 2026, needs more optimization.
25 90 0.087152564451 Henry Cohn, 2026, needs more optimization.
25 91 0.087278836679 Henry Cohn, 2026, needs more optimization.
25 92 0.088760121451 Henry Cohn, 2026, needs more optimization.
25 93 0.089631257932 Henry Cohn, 2026, needs more optimization.
25 94 0.089904495935 Henry Cohn, 2026, needs more optimization.
25 95 0.090423383619 Henry Cohn, 2026, needs more optimization.
25 96 0.090621489407 Henry Cohn, 2026, needs more optimization.
25 97 0.090825311562 Henry Cohn, 2026, needs more optimization.
25 98 0.090826489279 Henry Cohn, 2026, needs more optimization.
25 99 0.090890603871 Henry Cohn, 2026, needs more optimization.
25 100 0.090906142356 Henry Cohn, 2026, needs more optimization.
25 101 0.090908872477 Henry Cohn, 2026, needs more optimization.
25 106 0.090909090571 Henry Cohn, 2026, needs more optimization.
25 107 0.090909344634 Henry Cohn, 2026, needs more optimization.
25 108 0.090910559714 Henry Cohn, 2026, needs more optimization.
25 109 0.095542644965 Henry Cohn, 2026, needs more optimization.
25 110 0.099772185469 Henry Cohn, 2026, needs more optimization.
25 111 0.102626191747 Henry Cohn, 2026, needs more optimization.
25 117 0.105319726475 Henry Cohn, 2026.
375⁢x2−30⁢x−1
25 118 0.107225148391 Henry Cohn, 2026, needs more optimization.
25 119 0.108599687989 Henry Cohn, 2026, needs more optimization.
25 120 0.108643756678 Henry Cohn, 2026, needs more optimization.
25 121 0.109292354716 Henry Cohn, 2026, needs more optimization.
25 122 0.109483242771 Henry Cohn, 2026, needs more optimization.
25 123 0.109834549938 Henry Cohn, 2026, needs more optimization.
25 124 0.111025494939 Henry Cohn, 2026, needs more optimization.
25 125 0.111109577749 Henry Cohn, 2026, needs more optimization.
25 126 0.111115484597 Henry Cohn, 2026, needs more optimization.
25 127 0.111141878148 Henry Cohn, 2026, needs more optimization.
25 128 0.111329539236 Henry Cohn, 2026, needs more optimization.
25 129 0.117076939481 Henry Cohn, 2026, needs more optimization.
25 130 0.119943710439 Henry Cohn, 2026, needs more optimization.
25 131 0.121764571046 Henry Cohn, 2026, needs more optimization.
25 132 0.123580525731 Henry Cohn, 2026, needs more optimization.
25 133 0.124981451545 Henry Cohn, 2026, needs more optimization.
25 134 0.126241842542 Henry Cohn, 2026, needs more optimization.
25 135 0.128185811982 Henry Cohn, 2026, needs more optimization.
25 136 0.129707611770 Henry Cohn, 2026, needs more optimization.
25 137 0.131691146274 Henry Cohn, 2026, needs more optimization.
25 138 0.131739302507 Henry Cohn, 2026, needs more optimization.
25 139 0.131774235868 Henry Cohn, 2026, needs more optimization.
25 140 0.131778437848 Henry Cohn, 2026, needs more optimization.
25 141 0.131805872362 Henry Cohn, 2026, needs more optimization.
25 142 0.132199115126 Henry Cohn, 2026, needs more optimization.
25 143 0.132804913287 Henry Cohn, 2026, needs more optimization.
25 156 0.133333333334 Henry Cohn, 2023. In Ericson and Zinoviev's notation, this code is the union of a code constructed by CW2 from C : (26,6,8,130) and -S25 by CW2.
15⁢x−2
25 157 0.135170717187 Henry Cohn, 2026, needs more optimization.
25 158 0.136963466832 Henry Cohn, 2026, needs more optimization.
25 159 0.138087374340 Henry Cohn, 2026, needs more optimization.
25 160 0.139842764222 Henry Cohn, 2026, needs more optimization.
25 161 0.141378223189 Henry Cohn, 2026, needs more optimization.
25 162 0.142805144798 Henry Cohn, 2026, needs more optimization.
25 163 0.142822031850 Henry Cohn, 2026, needs more optimization.
25 164 0.142832912865 Henry Cohn, 2026, needs more optimization.
25 165 0.142837331432 Henry Cohn, 2026, needs more optimization.
25 166 0.142837332654 Henry Cohn, 2026, needs more optimization.
25 167 0.142838741787 Henry Cohn, 2026, needs more optimization.
25 168 0.142845443220 Henry Cohn, 2026, needs more optimization.
25 169 0.142849945272 Henry Cohn, 2026, needs more optimization.
25 170 0.142850087786 Henry Cohn, 2026, needs more optimization.
25 171 0.142850087847 Henry Cohn, 2026, needs more optimization.
25 172 0.142851004141 Henry Cohn, 2026, needs more optimization.
25 173 0.142855881206 Henry Cohn, 2026, needs more optimization.
25 174 0.142855881466 Henry Cohn, 2026, needs more optimization.
25 176 0.142855961673 Henry Cohn, 2026, needs more optimization.
25 177 0.142858216994 Henry Cohn, 2026, needs more optimization.
25 178 0.142877377792 Henry Cohn, 2026, needs more optimization.
25 179 0.142898546758 Henry Cohn, 2026, needs more optimization.
25 180 0.143251461141 Henry Cohn, 2026, needs more optimization.
25 181 0.144733179046 Henry Cohn, 2026, needs more optimization.
25 182 0.144739296180 Henry Cohn, 2026, needs more optimization.
25 183 0.145771493848 Henry Cohn, 2026, needs more optimization.
25 184 0.145771494804 Henry Cohn, 2026, needs more optimization.
25 185 0.146029580287 Henry Cohn, 2026, needs more optimization.
25 186 0.146181529172 Henry Cohn, 2026, needs more optimization.
25 187 0.146197144511 Henry Cohn, 2026, needs more optimization.
25 188 0.146793274481 Henry Cohn, 2026, needs more optimization.
25 189 0.147155582036 Henry Cohn, 2026, needs more optimization.
25 190 0.147234996772 Henry Cohn, 2026, needs more optimization.
25 191 0.147332696223 Henry Cohn, 2026, needs more optimization.
25 192 0.147676646742 Henry Cohn, 2026, needs more optimization.
25 193 0.150396957967 Henry Cohn, 2026, needs more optimization.
25 194 0.151345570611 Henry Cohn, 2026, needs more optimization.
25 195 0.152295231089 Henry Cohn, 2026, needs more optimization.
25 196 0.152634653469 Henry Cohn, 2026, needs more optimization.
25 197 0.152644495028 Henry Cohn, 2026, needs more optimization.
25 198 0.152707409888 Henry Cohn, 2026, needs more optimization.
25 199 0.152729848446 Henry Cohn, 2026, needs more optimization.
25 200 0.153212008046 Henry Cohn, 2026, needs more optimization.
25 201 0.153217083193 Henry Cohn, 2026, needs more optimization.
25 202 0.153708071823 Henry Cohn, 2026, needs more optimization.
25 203 0.153823448684 Henry Cohn, 2026, needs more optimization.
25 204 0.155228358478 Henry Cohn, 2026, needs more optimization.
25 205 0.155228432137 Henry Cohn, 2026, needs more optimization.
25 206 0.155399680765 Henry Cohn, 2026, needs more optimization.
25 207 0.155399682304 Henry Cohn, 2026, needs more optimization.
25 208 0.155399684564 Henry Cohn, 2026, needs more optimization.
25 209 0.156568031503 Henry Cohn, 2026, needs more optimization.
25 210 0.157315917557 Henry Cohn, 2026, needs more optimization.
25 211 0.158563866201 Henry Cohn, 2026, needs more optimization.
25 212 0.158675112660 Henry Cohn, 2026, needs more optimization.
25 214 0.159242479615 Henry Cohn, 2026, needs more optimization.
25 215 0.159264756116 Henry Cohn, 2026, needs more optimization.
25 216 0.159797714595 Henry Cohn, 2026, needs more optimization.
25 217 0.159868881459 Henry Cohn, 2026, needs more optimization.
25 218 0.160701200488 Henry Cohn, 2026, needs more optimization.
25 219 0.160855672272 Henry Cohn, 2026, needs more optimization.
25 220 0.161493983742 Henry Cohn, 2026, needs more optimization.
25 221 0.161923689939 Henry Cohn, 2026, needs more optimization.
25 222 0.161923695326 Henry Cohn, 2026, needs more optimization.
25 223 0.162163211000 Henry Cohn, 2026, needs more optimization.
25 224 0.162625236532 Henry Cohn, 2026, needs more optimization.
25 225 0.162858631543 Henry Cohn, 2026, needs more optimization.
25 226 0.163573464361 Henry Cohn, 2026, needs more optimization.
25 227 0.164285934650 Henry Cohn, 2026, needs more optimization.
25 228 0.164653882671 Henry Cohn, 2026, needs more optimization.
25 229 0.165082931006 Henry Cohn, 2026, needs more optimization.
25 230 0.165409424836 Henry Cohn, 2026, needs more optimization.
25 231 0.165848328200 Henry Cohn, 2026, needs more optimization.
25 232 0.165954619999 Henry Cohn, 2026, needs more optimization.
25 233 0.166177162253 Henry Cohn, 2026, needs more optimization.
25 234 0.166381770749 Henry Cohn, 2026, needs more optimization.
25 235 0.166444771986 Henry Cohn, 2026, needs more optimization.
25 236 0.166531500623 Henry Cohn, 2026, needs more optimization.
25 237 0.166569202044 Henry Cohn, 2026, needs more optimization.
25 238 0.166588558816 Henry Cohn, 2026, needs more optimization.
25 282 0.166666666667 Orthogonal union of 278 points in 23 dimensions and 4 points in 2 dimensions.
6⁢x−1
25 285 0.166666872445 Henry Cohn, 2026, needs more optimization.
25 287 0.166667610031 Henry Cohn, 2026, needs more optimization.
25 288 0.166667610225 Henry Cohn, 2026, needs more optimization.
25 289 0.166668396516 Henry Cohn, 2026, needs more optimization.
25 290 0.166693647764 Henry Cohn, 2026, needs more optimization.
25 291 0.167643892371 Henry Cohn, 2026, needs more optimization.
25 292 0.169481789260 Henry Cohn, 2026, needs more optimization.
25 293 0.169996156889 Henry Cohn, 2026, needs more optimization.
25 294 0.172043834150 Henry Cohn, 2026, needs more optimization.
25 295 0.173773087069 Henry Cohn, 2026, needs more optimization.
25 296 0.175881261133 Henry Cohn, 2026, needs more optimization.
25 297 0.177343315152 Henry Cohn, 2026, needs more optimization.
25 298 0.178927884277 Henry Cohn, 2026, needs more optimization.
25 299 0.180496405933 Henry Cohn, 2026, needs more optimization.
25 315 0.181818181819 Orthogonal union of 313 points in 24 dimensions and 2 points in 1 dimension.
11⁢x−2
25 318 0.181818678585 Henry Cohn, 2026, needs more optimization.
25 319 0.181819266673 Henry Cohn, 2026, needs more optimization.
25 320 0.181820282642 Henry Cohn, 2026, needs more optimization.
25 321 0.181824326734 Henry Cohn, 2026, needs more optimization.
25 322 0.183669539689 Henry Cohn, 2026, needs more optimization.
25 323 0.184797125679 Henry Cohn, 2026, needs more optimization.
25 324 0.185421055584 Henry Cohn, 2026, needs more optimization.
25 325 0.187069548254 Henry Cohn, 2026, needs more optimization.
25 326 0.187751127096 Henry Cohn, 2026, needs more optimization.
25 327 0.189795555530 Henry Cohn, 2026, needs more optimization.
25 328 0.191162946551 Henry Cohn, 2026, needs more optimization.
25 329 0.192095868404 Henry Cohn, 2026, needs more optimization.
25 332 0.193548387097 Orthogonal union of 330 points in 24 dimensions and 2 points in 1 dimension.
31⁢x−6
25 333 0.193548403014 Henry Cohn, 2026, needs more optimization.
25 334 0.193551665272 Henry Cohn, 2026, needs more optimization.
25 335 0.193891559982 Henry Cohn, 2026, needs more optimization.
25 340 0.194120819402 Henry Cohn, 2026, needs more optimization.
25 341 0.196567236582 Henry Cohn, 2026, needs more optimization.
25 342 0.198076126800 Henry Cohn, 2026, needs more optimization.
25 343 0.199509871327 Henry Cohn, 2026, needs more optimization.
25 557 0.2 Orthogonal union of 555 points in 24 dimensions and 2 points in 1 dimension.
5⁢x−1
25 560 0.200001495715 Henry Cohn, 2026, needs more optimization.
25 561 0.200001742850 Henry Cohn, 2026, needs more optimization.
25 562 0.200004107297 Henry Cohn, 2026, needs more optimization.
25 563 0.200189994661 Henry Cohn, 2026, needs more optimization.
25 564 0.201395436150 Henry Cohn, 2026, needs more optimization.
25 565 0.203326183247 Henry Cohn, 2026, needs more optimization.
25 566 0.206981620982 Henry Cohn, 2026, needs more optimization.
25 567 0.209904141592 Henry Cohn, 2026, needs more optimization.
25 568 0.211754446643 Henry Cohn, 2026, needs more optimization.
25 569 0.214498223145 Henry Cohn, 2026, needs more optimization.
25 570 0.216470534228 Henry Cohn, 2026, needs more optimization.
25 571 0.217980226545 Henry Cohn, 2026, needs more optimization.
25 572 0.219514101687 Henry Cohn, 2026, needs more optimization.
25 573 0.221344252695 Henry Cohn, 2026, needs more optimization.
25 574 0.222236027696 Henry Cohn, 2026, needs more optimization.
25 575 0.223718323910 Henry Cohn, 2026, needs more optimization.
25 576 0.224654128257 Henry Cohn, 2026, needs more optimization.
25 577 0.226221816105 Henry Cohn, 2026, needs more optimization.
25 578 0.226394101792 Henry Cohn, 2026, needs more optimization.
25 579 0.227363421795 Henry Cohn, 2026, needs more optimization.
25 580 0.228299692816 Henry Cohn, 2026, needs more optimization.
25 581 0.229074296247 Henry Cohn, 2026, needs more optimization.
25 582 0.229574635297 Henry Cohn, 2026, needs more optimization.
25 583 0.230788364001 Henry Cohn, 2026, needs more optimization.
25 584 0.231754087182 Henry Cohn, 2026, needs more optimization.
25 585 0.232042635699 Henry Cohn, 2026, needs more optimization.
25 586 0.232966997186 Henry Cohn, 2026, needs more optimization.
25 587 0.233520252234 Henry Cohn, 2026, needs more optimization.
25 588 0.234186570866 Henry Cohn, 2026, needs more optimization.
25 589 0.235014643679 Henry Cohn, 2026, needs more optimization.
25 590 0.235669602222 Henry Cohn, 2026, needs more optimization.
25 591 0.236457125262 Henry Cohn, 2026, needs more optimization.
25 592 0.237387946106 Henry Cohn, 2026, needs more optimization.
25 593 0.237481679874 Henry Cohn, 2026, needs more optimization.
25 594 0.237736352766 Henry Cohn, 2026, needs more optimization.
25 599 0.238096844782 Henry Cohn, 2026, needs more optimization.
25 603 0.238097666964 Henry Cohn, 2026, needs more optimization.
25 606 0.238098381260 Henry Cohn, 2026, needs more optimization.
25 607 0.238098468123 Henry Cohn, 2026, needs more optimization.
25 608 0.238101611563 Henry Cohn, 2026, needs more optimization.
25 609 0.238104305473 Henry Cohn, 2026, needs more optimization.
25 612 0.238109837376 Henry Cohn, 2026, needs more optimization.
25 613 0.238126840921 Henry Cohn, 2026, needs more optimization.
25 614 0.238363514394 Henry Cohn, 2026, needs more optimization.
25 615 0.238498238821 Henry Cohn, 2026, needs more optimization.
25 616 0.238626735644 Henry Cohn, 2026, needs more optimization.
25 617 0.238879178822 Henry Cohn, 2026, needs more optimization.
25 618 0.239091988867 Henry Cohn, 2026, needs more optimization.
25 620 0.239321214613 Henry Cohn, 2026, needs more optimization.
25 621 0.239790869112 Henry Cohn, 2026, needs more optimization.
25 622 0.240211183805 Henry Cohn, 2026, needs more optimization.
25 623 0.240851514504 Henry Cohn, 2026, needs more optimization.
25 624 0.241348715546 Henry Cohn, 2026, needs more optimization.
25 625 0.241730983689 Henry Cohn, 2026, needs more optimization.
25 626 0.241903154258 Henry Cohn, 2026, needs more optimization.
25 627 0.247248380009 Henry Cohn, 2026, needs more optimization.
25 630 0.247450209472 Henry Cohn, 2026, needs more optimization.
25 631 0.247846885305 Henry Cohn, 2026, needs more optimization.
25 634 0.248012405088 Henry Cohn, 2026, needs more optimization.
25 637 0.248219532039 Henry Cohn, 2026, needs more optimization.
25 638 0.248434515259 Henry Cohn, 2026, needs more optimization.
25 639 0.248483537932 Henry Cohn, 2026, needs more optimization.
25 642 0.248703897358 Henry Cohn, 2026, needs more optimization.
25 645 0.248727529936 Henry Cohn, 2026, needs more optimization.
25 646 0.248826417727 Henry Cohn, 2026, needs more optimization.
25 647 0.248861558306 Henry Cohn, 2026, needs more optimization.
25 648 0.249000709156 Henry Cohn, 2026, needs more optimization.
25 650 0.249059443438 Henry Cohn, 2026, needs more optimization.
25 651 0.249095717206 Henry Cohn, 2026, needs more optimization.
25 654 0.249109540285 Henry Cohn, 2026, needs more optimization.
25 655 0.249190852722 Henry Cohn, 2026, needs more optimization.
25 656 0.249247807580 Henry Cohn, 2026, needs more optimization.
25 657 0.249263548532 Henry Cohn, 2026, needs more optimization.
25 658 0.249292852609 Henry Cohn, 2026, needs more optimization.
25 659 0.249401756671 Henry Cohn, 2026, needs more optimization.
25 660 0.249436403126 Henry Cohn, 2026, needs more optimization.
25 661 0.249449604412 Henry Cohn, 2026, needs more optimization.
25 662 0.249486051344 Henry Cohn, 2026, needs more optimization.
25 663 0.249502200285 Henry Cohn, 2026, needs more optimization.
25 664 0.249561882427 Henry Cohn, 2026, needs more optimization.
25 665 0.249588672395 Henry Cohn, 2026, needs more optimization.
25 666 0.249625877454 Henry Cohn, 2026, needs more optimization.
25 667 0.249655526949 Henry Cohn, 2026, needs more optimization.
25 669 0.249710128997 Henry Cohn, 2026, needs more optimization.
25 670 0.249739998285 Henry Cohn, 2026, needs more optimization.
25 671 0.249759868123 Henry Cohn, 2026, needs more optimization.
25 672 0.249783729052 Henry Cohn, 2026, needs more optimization.
25 673 0.249833842297 Henry Cohn, 2026, needs more optimization.
25 674 0.249845527625 Henry Cohn, 2026, needs more optimization.
25 675 0.249865344951 Henry Cohn, 2026, needs more optimization.
25 676 0.249886558513 Henry Cohn, 2026, needs more optimization.
25 677 0.249897511865 Henry Cohn, 2026, needs more optimization.
25 900 0.25 Henry Cohn, 2025.
4⁢x−1
25 901 0.250002033400 Henry Cohn, 2026, needs more optimization.
25 908 0.250002221313 Henry Cohn, 2026, needs more optimization.
25 909 0.250002495371 Henry Cohn, 2026, needs more optimization.
25 911 0.250002504185 Henry Cohn, 2026, needs more optimization.
25 914 0.250002510823 Henry Cohn, 2026, needs more optimization.
25 915 0.250003226144 Henry Cohn, 2026, needs more optimization.
25 916 0.250004672574 Henry Cohn, 2026, needs more optimization.
25 917 0.250011837715 Henry Cohn, 2026, needs more optimization.
25 918 0.250030824217 Henry Cohn, 2026, needs more optimization.
25 919 0.250088017914 Henry Cohn, 2026, needs more optimization.
25 920 0.250244646429 Henry Cohn, 2026, needs more optimization.
25 921 0.250359018202 Henry Cohn, 2026, needs more optimization.
25 922 0.250759016271 Henry Cohn, 2026, needs more optimization.
25 923 0.250979287885 Henry Cohn, 2026, needs more optimization.
25 925 0.251226404366 Henry Cohn, 2026, needs more optimization.
25 926 0.251551627091 Henry Cohn, 2026, needs more optimization.
25 927 0.251780486003 Henry Cohn, 2026, needs more optimization.
25 928 0.252519336376 Henry Cohn, 2026, needs more optimization.
25 929 0.253476416972 Henry Cohn, 2026, needs more optimization.
25 930 0.253742231692 Henry Cohn, 2026, needs more optimization.
25 931 0.254320646414 Henry Cohn, 2026, needs more optimization.
25 932 0.254743196494 Henry Cohn, 2026, needs more optimization.
25 933 0.255069002632 Henry Cohn, 2026, needs more optimization.
25 934 0.255697154796 Henry Cohn, 2026, needs more optimization.
25 935 0.256102906140 Henry Cohn, 2026, needs more optimization.
25 936 0.256829423896 Henry Cohn, 2026, needs more optimization.
25 937 0.257382742853 Henry Cohn, 2026, needs more optimization.
25 938 0.257725543569 Henry Cohn, 2026, needs more optimization.
25 939 0.257998176040 Henry Cohn, 2026, needs more optimization.
25 940 0.258401488312 Henry Cohn, 2026, needs more optimization.
25 941 0.258998597971 Henry Cohn, 2026, needs more optimization.
25 942 0.259699012860 Henry Cohn, 2026, needs more optimization.
25 943 0.259933447494 Henry Cohn, 2026, needs more optimization.
25 944 0.260336558867 Henry Cohn, 2026, needs more optimization.
25 945 0.260804475203 Henry Cohn, 2026, needs more optimization.
25 946 0.261453799327 Henry Cohn, 2026, needs more optimization.
25 947 0.261714987329 Henry Cohn, 2026, needs more optimization.
25 948 0.262039669268 Henry Cohn, 2026, needs more optimization.
25 949 0.262784216748 Henry Cohn, 2026, needs more optimization.
25 950 0.263440613024 Henry Cohn, 2026, needs more optimization.
25 951 0.263587937197 Henry Cohn, 2026, needs more optimization.
25 952 0.263955317713 Henry Cohn, 2026, needs more optimization.
25 953 0.264303339159 Henry Cohn, 2026, needs more optimization.
25 954 0.264471056427 Henry Cohn, 2026, needs more optimization.
25 955 0.265013137770 Henry Cohn, 2026, needs more optimization.
25 956 0.265726774509 Henry Cohn, 2026, needs more optimization.
25 957 0.266135086249 Henry Cohn, 2026, needs more optimization.
25 958 0.266511493312 Henry Cohn, 2026, needs more optimization.
25 959 0.266937463982 Henry Cohn, 2026, needs more optimization.
25 960 0.267275389600 Henry Cohn, 2026, needs more optimization.
25 961 0.267515136250 Henry Cohn, 2026, needs more optimization.
25 962 0.267592573763 Henry Cohn, 2026, needs more optimization.
25 963 0.267822812180 Henry Cohn, 2026, needs more optimization.
25 964 0.268192290226 Henry Cohn, 2026, needs more optimization.
25 965 0.268574180915 Henry Cohn, 2026, needs more optimization.
25 966 0.268912929147 Henry Cohn, 2026, needs more optimization.
25 967 0.269283959150 Henry Cohn, 2026, needs more optimization.
25 968 0.269503648075 Henry Cohn, 2026, needs more optimization.
25 969 0.269811875990 Henry Cohn, 2026, needs more optimization.
25 970 0.269842036052 Henry Cohn, 2026, needs more optimization.
25 971 0.270354313220 Henry Cohn, 2026, needs more optimization.
25 973 0.270645752688 Henry Cohn, 2026, needs more optimization.
25 974 0.270838089706 Henry Cohn, 2026, needs more optimization.
25 975 0.271497686619 Henry Cohn, 2026, needs more optimization.
25 976 0.271759066379 Henry Cohn, 2026, needs more optimization.
25 1024 0.272727272728 Code with 1024 points in 22 dimensions.
11⁢x−3
26 53 0.030620650808 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
14976⁢x3−676⁢x2−26⁢x+1
26 54 0.035747861992 Henry Cohn, 2026.
26 55 0.039998970502 Henry Cohn, 2026, needs more optimization.
26 57 0.04 Orthogonal union of 55 points in 25 dimensions and 2 points in 1 dimension.
25⁢x−1
26 58 0.045550434603 Henry Cohn, 2024.
26 59 0.046163974402 Henry Cohn, 2025.
26 60 0.046455966295 Henry Cohn, 2026.
26 61 0.049243792036 Henry Cohn, 2026.
26 62 0.051908007699 Henry Cohn, 2026.
26 63 0.054427947454 Henry Cohn, 2026.
26 64 0.056899291385 Henry Cohn, 2026, needs more optimization.
26 65 0.060274304023 Henry Cohn, 2026, needs more optimization.
26 66 0.062099828320 Henry Cohn, 2026, needs more optimization.
26 67 0.063558078517 Henry Cohn, 2026, needs more optimization.
26 68 0.063599477821 Henry Cohn, 2026, needs more optimization.
26 69 0.064915242095 Henry Cohn, 2026, needs more optimization.
26 70 0.065398732375 Henry Cohn, 2026, needs more optimization.
26 71 0.067315604578 Henry Cohn, 2026.
26 72 0.068297564143 Henry Cohn, 2026, needs more optimization.
26 73 0.070930211069 Henry Cohn, 2026, needs more optimization.
26 74 0.073181772055 Henry Cohn, 2026, needs more optimization.
26 75 0.074026843961 Henry Cohn, 2026, needs more optimization.
26 76 0.075372291887 Henry Cohn, 2026, needs more optimization.
26 77 0.076353858442 Henry Cohn, 2026, needs more optimization.
26 78 0.076846445132 Henry Cohn, 2026, needs more optimization.
26 79 0.076914515146 Henry Cohn, 2026, needs more optimization.
26 80 0.076951826930 Henry Cohn, 2026, needs more optimization.
26 81 0.077575847529 Henry Cohn, 2026, needs more optimization.
26 82 0.077924828163 Henry Cohn, 2026, needs more optimization.
26 83 0.078204418450 Henry Cohn, 2026, needs more optimization.
26 84 0.078381128167 Henry Cohn, 2026, needs more optimization.
26 85 0.078751875862 Henry Cohn, 2026, needs more optimization.
26 86 0.079365739511 Henry Cohn, 2026, needs more optimization.
26 94 0.080685003328 Henry Cohn, 2026.
575⁢x2−34⁢x−1
26 95 0.082980205437 Henry Cohn, 2026, needs more optimization.
26 96 0.085913008595 Henry Cohn, 2026, needs more optimization.
26 97 0.089146474487 Henry Cohn, 2026, needs more optimization.
26 98 0.089647565245 Henry Cohn, 2026, needs more optimization.
26 99 0.090045422778 Henry Cohn, 2026, needs more optimization.
26 100 0.090257603504 Henry Cohn, 2026, needs more optimization.
26 101 0.090489578027 Henry Cohn, 2026, needs more optimization.
26 102 0.090675651749 Henry Cohn, 2026, needs more optimization.
26 103 0.090757060140 Henry Cohn, 2026, needs more optimization.
26 104 0.090837057229 Henry Cohn, 2026, needs more optimization.
26 105 0.090855852244 Henry Cohn, 2026, needs more optimization.
26 106 0.090896206224 Henry Cohn, 2026, needs more optimization.
26 108 0.090897053645 Henry Cohn, 2026, needs more optimization.
26 109 0.090902499338 Henry Cohn, 2026, needs more optimization.
26 110 0.090908500577 Henry Cohn, 2026, needs more optimization.
26 111 0.091744798796 Henry Cohn, 2026, needs more optimization.
26 112 0.094490098389 Henry Cohn, 2026, needs more optimization.
26 113 0.097426671093 Henry Cohn, 2026, needs more optimization.
26 114 0.100692911134 Henry Cohn, 2026, needs more optimization.
26 120 0.103125332235 Henry Cohn, 2026.
191⁢x2−10⁢x−1
26 121 0.103746590262 Henry Cohn, 2026, needs more optimization.
26 122 0.105407245496 Henry Cohn, 2026, needs more optimization.
26 123 0.106258413834 Henry Cohn, 2026, needs more optimization.
26 124 0.107109897771 Henry Cohn, 2026, needs more optimization.
26 125 0.107664866687 Henry Cohn, 2026, needs more optimization.
26 126 0.108555049356 Henry Cohn, 2026, needs more optimization.
26 127 0.109071031328 Henry Cohn, 2026, needs more optimization.
26 128 0.111056719541 Henry Cohn, 2026, needs more optimization.
26 129 0.111060364641 Henry Cohn, 2026, needs more optimization.
26 130 0.111079882631 Henry Cohn, 2026, needs more optimization.
26 131 0.111105297376 Henry Cohn, 2026, needs more optimization.
26 132 0.112888750678 Henry Cohn, 2026, needs more optimization.
26 133 0.114520698381 Henry Cohn, 2026, needs more optimization.
26 134 0.115288474861 Henry Cohn, 2026, needs more optimization.
26 135 0.116296121560 Henry Cohn, 2026, needs more optimization.
26 136 0.116447587829 Henry Cohn, 2026, needs more optimization.
26 137 0.117070042553 Henry Cohn, 2026, needs more optimization.
26 138 0.118625425485 Henry Cohn, 2026, needs more optimization.
26 139 0.122342188726 Henry Cohn, 2026, needs more optimization.
26 140 0.125308138393 Henry Cohn, 2026, needs more optimization.
26 141 0.127923713740 Henry Cohn, 2026, needs more optimization.
26 142 0.130225473345 Henry Cohn, 2026, needs more optimization.
26 143 0.131429157647 Henry Cohn, 2026, needs more optimization.
26 144 0.131609710593 Henry Cohn, 2026, needs more optimization.
26 145 0.131716482474 Henry Cohn, 2026, needs more optimization.
26 146 0.131773272285 Henry Cohn, 2026, needs more optimization.
26 147 0.131900106515 Henry Cohn, 2026, needs more optimization.
26 148 0.132068105508 Henry Cohn, 2026, needs more optimization.
26 149 0.132340769859 Henry Cohn, 2026, needs more optimization.
26 150 0.132996032312 Henry Cohn, 2026, needs more optimization.
26 158 0.133333333334 Orthogonal union of 156 points in 25 dimensions and 2 points in 1 dimension.
15⁢x−2
26 159 0.133334797041 Henry Cohn, 2026, needs more optimization.
26 160 0.134520569674 Henry Cohn, 2026, needs more optimization.
26 161 0.135127305352 Henry Cohn, 2026, needs more optimization.
26 162 0.135323044627 Henry Cohn, 2026, needs more optimization.
26 163 0.136045769151 Henry Cohn, 2026, needs more optimization.
26 164 0.136696338474 Henry Cohn, 2026, needs more optimization.
26 165 0.137898845583 Henry Cohn, 2026, needs more optimization.
26 166 0.138939481825 Henry Cohn, 2026, needs more optimization.
26 167 0.139937937886 Henry Cohn, 2026, needs more optimization.
26 168 0.141029262416 Henry Cohn, 2026, needs more optimization.
26 169 0.142690563226 Henry Cohn, 2026, needs more optimization.
26 170 0.142703782589 Henry Cohn, 2026, needs more optimization.
26 171 0.142711813653 Henry Cohn, 2026, needs more optimization.
26 172 0.142734182542 Henry Cohn, 2026, needs more optimization.
26 173 0.142744771955 Henry Cohn, 2026, needs more optimization.
26 174 0.142776068074 Henry Cohn, 2026, needs more optimization.
26 175 0.142790180617 Henry Cohn, 2026, needs more optimization.
26 176 0.142796313955 Henry Cohn, 2026, needs more optimization.
26 177 0.142799781977 Henry Cohn, 2026, needs more optimization.
26 178 0.142806210576 Henry Cohn, 2026, needs more optimization.
26 179 0.142809098947 Henry Cohn, 2026, needs more optimization.
26 180 0.142810454486 Henry Cohn, 2026, needs more optimization.
26 181 0.142827167437 Henry Cohn, 2026, needs more optimization.
26 182 0.142846017804 Henry Cohn, 2026, needs more optimization.
26 183 0.142852059980 Henry Cohn, 2026, needs more optimization.
26 184 0.142855877211 Henry Cohn, 2026, needs more optimization.
26 185 0.142893545856 Henry Cohn, 2026, needs more optimization.
26 186 0.143123227436 Henry Cohn, 2026, needs more optimization.
26 187 0.143815490400 Henry Cohn, 2026, needs more optimization.
26 188 0.145213925087 Henry Cohn, 2026, needs more optimization.
26 189 0.145474277341 Henry Cohn, 2026, needs more optimization.
26 190 0.145474584673 Henry Cohn, 2026, needs more optimization.
26 191 0.146049394662 Henry Cohn, 2026, needs more optimization.
26 192 0.146206950424 Henry Cohn, 2026, needs more optimization.
26 193 0.146606564369 Henry Cohn, 2026, needs more optimization.
26 194 0.146820076022 Henry Cohn, 2026, needs more optimization.
26 195 0.146894002976 Henry Cohn, 2026, needs more optimization.
26 196 0.147005891471 Henry Cohn, 2026, needs more optimization.
26 197 0.147007738378 Henry Cohn, 2026, needs more optimization.
26 198 0.147007738457 Henry Cohn, 2026, needs more optimization.
26 199 0.147107314549 Henry Cohn, 2026, needs more optimization.
26 200 0.147149915320 Henry Cohn, 2026, needs more optimization.
26 201 0.147483024097 Henry Cohn, 2026, needs more optimization.
26 202 0.147489700944 Henry Cohn, 2026, needs more optimization.
26 203 0.148133620197 Henry Cohn, 2026, needs more optimization.
26 204 0.148897079983 Henry Cohn, 2026, needs more optimization.
26 205 0.149234992693 Henry Cohn, 2026, needs more optimization.
26 206 0.149249067318 Henry Cohn, 2026, needs more optimization.
26 207 0.149973510730 Henry Cohn, 2026, needs more optimization.
26 208 0.150254652347 Henry Cohn, 2026, needs more optimization.
26 209 0.150309109669 Henry Cohn, 2026, needs more optimization.
26 211 0.150466308644 Henry Cohn, 2026, needs more optimization.
26 212 0.150998106294 Henry Cohn, 2026, needs more optimization.
26 213 0.151225645592 Henry Cohn, 2026, needs more optimization.
26 214 0.151282748165 Henry Cohn, 2026, needs more optimization.
26 215 0.151282813710 Henry Cohn, 2026, needs more optimization.
26 216 0.151825494905 Henry Cohn, 2026, needs more optimization.
26 217 0.151831386678 Henry Cohn, 2026, needs more optimization.
26 218 0.151923696406 Henry Cohn, 2026, needs more optimization.
26 219 0.151933921322 Henry Cohn, 2026, needs more optimization.
26 220 0.152487301649 Henry Cohn, 2026, needs more optimization.
26 221 0.154073528808 Henry Cohn, 2026, needs more optimization.
26 222 0.154405318762 Henry Cohn, 2026, needs more optimization.
26 223 0.154609709127 Henry Cohn, 2026, needs more optimization.
26 224 0.155109750213 Henry Cohn, 2026, needs more optimization.
26 225 0.156461561459 Henry Cohn, 2026, needs more optimization.
26 226 0.156910135252 Henry Cohn, 2026, needs more optimization.
26 227 0.157287308984 Henry Cohn, 2026, needs more optimization.
26 228 0.158667618708 Henry Cohn, 2026, needs more optimization.
26 229 0.158690917686 Henry Cohn, 2026, needs more optimization.
26 230 0.159329682120 Henry Cohn, 2026, needs more optimization.
26 231 0.160244464871 Henry Cohn, 2026, needs more optimization.
26 232 0.161964033014 Henry Cohn, 2026, needs more optimization.
26 233 0.162060190128 Henry Cohn, 2026, needs more optimization.
26 234 0.162548952169 Henry Cohn, 2026, needs more optimization.
26 235 0.162918730128 Henry Cohn, 2026, needs more optimization.
26 236 0.163196819352 Henry Cohn, 2026, needs more optimization.
26 237 0.163320937312 Henry Cohn, 2026, needs more optimization.
26 238 0.163919716754 Henry Cohn, 2026, needs more optimization.
26 239 0.164438224822 Henry Cohn, 2026, needs more optimization.
26 240 0.164539037927 Henry Cohn, 2026, needs more optimization.
26 241 0.165089061910 Henry Cohn, 2026, needs more optimization.
26 242 0.165311855495 Henry Cohn, 2026, needs more optimization.
26 243 0.165632634337 Henry Cohn, 2026, needs more optimization.
26 244 0.165867661649 Henry Cohn, 2026, needs more optimization.
26 245 0.165984134393 Henry Cohn, 2026, needs more optimization.
26 246 0.166217998789 Henry Cohn, 2026, needs more optimization.
26 247 0.166332353693 Henry Cohn, 2026, needs more optimization.
26 248 0.166407215990 Henry Cohn, 2026, needs more optimization.
26 249 0.166422216877 Henry Cohn, 2026, needs more optimization.
26 250 0.166422353501 Henry Cohn, 2026, needs more optimization.
26 251 0.166466116075 Henry Cohn, 2026, needs more optimization.
26 252 0.166500390365 Henry Cohn, 2026, needs more optimization.
26 253 0.166599821926 Henry Cohn, 2026, needs more optimization.
26 285 0.166666666667 Orthogonal union of 275 points in 22 dimensions and 10 points in 4 dimensions.
6⁢x−1
26 287 0.166666872444 Henry Cohn, 2026, needs more optimization.
26 290 0.166667610225 Orthogonal union of 288 points in 25 dimensions and 2 points in 1 dimension.
26 291 0.166668244277 Henry Cohn, 2026, needs more optimization.
26 292 0.166668244289 Henry Cohn, 2026, needs more optimization.
26 294 0.166669119938 Henry Cohn, 2026, needs more optimization.
26 295 0.166674813389 Henry Cohn, 2026, needs more optimization.
26 296 0.166693231236 Henry Cohn, 2026, needs more optimization.
26 297 0.166878244560 Henry Cohn, 2026, needs more optimization.
26 298 0.167303774491 Henry Cohn, 2026, needs more optimization.
26 299 0.168423943984 Henry Cohn, 2026, needs more optimization.
26 300 0.169915092444 Henry Cohn, 2026, needs more optimization.
26 301 0.170968845417 Henry Cohn, 2026, needs more optimization.
26 302 0.172059473855 Henry Cohn, 2026, needs more optimization.
26 303 0.173843174757 Henry Cohn, 2026, needs more optimization.
26 304 0.175635071872 Henry Cohn, 2026, needs more optimization.
26 305 0.176542831089 Henry Cohn, 2026, needs more optimization.
26 306 0.178292673718 Henry Cohn, 2026, needs more optimization.
26 307 0.179598662812 Henry Cohn, 2026, needs more optimization.
26 308 0.180436409480 Henry Cohn, 2026, needs more optimization.
26 317 0.181818181819 Orthogonal union of 313 points in 24 dimensions and 4 points in 2 dimensions.
11⁢x−2
26 318 0.181818678585 Orthogonal union of 316 points in 25 dimensions and 2 points in 1 dimension.
26 323 0.181818875487 Henry Cohn, 2026, needs more optimization.
26 325 0.181819027653 Henry Cohn, 2026, needs more optimization.
26 326 0.181819213815 Henry Cohn, 2026, needs more optimization.
26 327 0.181819278045 Henry Cohn, 2026, needs more optimization.
26 328 0.181820171862 Henry Cohn, 2026, needs more optimization.
26 329 0.181820679091 Henry Cohn, 2026, needs more optimization.
26 330 0.181822651156 Henry Cohn, 2026, needs more optimization.
26 331 0.182091887517 Henry Cohn, 2026, needs more optimization.
26 332 0.182702277919 Henry Cohn, 2026, needs more optimization.
26 333 0.184006376631 Henry Cohn, 2026, needs more optimization.
26 334 0.185140009883 Henry Cohn, 2026, needs more optimization.
26 335 0.185776920032 Henry Cohn, 2026, needs more optimization.
26 336 0.187116712734 Henry Cohn, 2026, needs more optimization.
26 337 0.187946319556 Henry Cohn, 2026, needs more optimization.
26 338 0.188837510468 Henry Cohn, 2026, needs more optimization.
26 339 0.189989912016 Henry Cohn, 2026, needs more optimization.
26 340 0.190310773064 Henry Cohn, 2026, needs more optimization.
26 341 0.192155493947 Henry Cohn, 2026, needs more optimization.
26 342 0.192561193913 Henry Cohn, 2026, needs more optimization.
26 343 0.193206828595 Henry Cohn, 2026, needs more optimization.
26 344 0.194463481964 Henry Cohn, 2026, needs more optimization.
26 345 0.195171822308 Henry Cohn, 2026, needs more optimization.
26 346 0.196294150993 Henry Cohn, 2026, needs more optimization.
26 347 0.196433297390 Henry Cohn, 2026, needs more optimization.
26 348 0.196573571974 Henry Cohn, 2026, needs more optimization.
26 349 0.196657862278 Henry Cohn, 2026, needs more optimization.
26 350 0.196894885682 Henry Cohn, 2026, needs more optimization.
26 351 0.196979585488 Henry Cohn, 2026, needs more optimization.
26 352 0.197113339988 Henry Cohn, 2026, needs more optimization.
26 353 0.197248661812 Henry Cohn, 2026, needs more optimization.
26 354 0.197321566972 Henry Cohn, 2026, needs more optimization.
26 355 0.197409252160 Henry Cohn, 2026, needs more optimization.
26 356 0.197669548056 Henry Cohn, 2026, needs more optimization.
26 357 0.197757145949 Henry Cohn, 2026, needs more optimization.
26 358 0.197848624884 Henry Cohn, 2026, needs more optimization.
26 359 0.198030078912 Henry Cohn, 2026, needs more optimization.
26 360 0.198122501785 Henry Cohn, 2026, needs more optimization.
26 361 0.198216489304 Henry Cohn, 2026, needs more optimization.
26 362 0.198267959987 Henry Cohn, 2026, needs more optimization.
26 363 0.198311908680 Henry Cohn, 2026, needs more optimization.
26 364 0.198396800842 Henry Cohn, 2026, needs more optimization.
26 365 0.198493881690 Henry Cohn, 2026, needs more optimization.
26 366 0.198541588007 Henry Cohn, 2026, needs more optimization.
26 367 0.198627875716 Henry Cohn, 2026, needs more optimization.
26 368 0.198686992987 Henry Cohn, 2026, needs more optimization.
26 369 0.198800353821 Henry Cohn, 2026, needs more optimization.
26 370 0.198866480934 Henry Cohn, 2026, needs more optimization.
26 371 0.199006536844 Henry Cohn, 2026, needs more optimization.
26 372 0.199070347430 Henry Cohn, 2026, needs more optimization.
26 373 0.199079492328 Henry Cohn, 2026, needs more optimization.
26 374 0.199181450416 Henry Cohn, 2026, needs more optimization.
26 375 0.199244089968 Henry Cohn, 2026, needs more optimization.
26 376 0.199297325804 Henry Cohn, 2026, needs more optimization.
26 377 0.199332411656 Henry Cohn, 2026, needs more optimization.
26 378 0.199409849169 Henry Cohn, 2026, needs more optimization.
26 379 0.199454395222 Henry Cohn, 2026, needs more optimization.
26 380 0.199492818770 Henry Cohn, 2026, needs more optimization.
26 381 0.199501483949 Henry Cohn, 2026, needs more optimization.
26 382 0.199518637491 Henry Cohn, 2026, needs more optimization.
26 383 0.199528992302 Henry Cohn, 2026, needs more optimization.
26 384 0.199558929658 Henry Cohn, 2026, needs more optimization.
26 385 0.199598368318 Henry Cohn, 2026, needs more optimization.
26 386 0.199651831758 Henry Cohn, 2026, needs more optimization.
26 387 0.199687163933 Henry Cohn, 2026, needs more optimization.
26 388 0.199710352760 Henry Cohn, 2026, needs more optimization.
26 389 0.199750700957 Henry Cohn, 2026, needs more optimization.
26 390 0.199808935352 Henry Cohn, 2026, needs more optimization.
26 391 0.199820279442 Henry Cohn, 2026, needs more optimization.
26 392 0.199827833474 Henry Cohn, 2026, needs more optimization.
26 393 0.199843806628 Henry Cohn, 2026, needs more optimization.
26 394 0.199859778573 Henry Cohn, 2026, needs more optimization.
26 395 0.199879711560 Henry Cohn, 2026, needs more optimization.
26 396 0.199906892342 Henry Cohn, 2026, needs more optimization.
26 397 0.199936228573 Henry Cohn, 2026, needs more optimization.
26 398 0.199951964267 Henry Cohn, 2026, needs more optimization.
26 399 0.199959039327 Henry Cohn, 2026, needs more optimization.
26 400 0.199966120209 Henry Cohn, 2026, needs more optimization.
26 559 0.2 Orthogonal union of 555 points in 24 dimensions and 4 points in 2 dimensions.
5⁢x−1
26 568 0.200000846014 Henry Cohn, 2026, needs more optimization.
26 569 0.200009787536 Henry Cohn, 2026, needs more optimization.
26 570 0.200042804527 Henry Cohn, 2026, needs more optimization.
26 571 0.200478888284 Henry Cohn, 2026, needs more optimization.
26 572 0.200566880117 Henry Cohn, 2026, needs more optimization.
26 573 0.200959647534 Henry Cohn, 2026, needs more optimization.
26 574 0.202303745210 Henry Cohn, 2026, needs more optimization.
26 575 0.204393550710 Henry Cohn, 2026, needs more optimization.
26 576 0.205509562979 Henry Cohn, 2026, needs more optimization.
26 577 0.208754985359 Henry Cohn, 2026, needs more optimization.
26 578 0.210040076295 Henry Cohn, 2026, needs more optimization.
26 579 0.211455146964 Henry Cohn, 2026, needs more optimization.
26 580 0.212526180856 Henry Cohn, 2026, needs more optimization.
26 581 0.214547030466 Henry Cohn, 2026, needs more optimization.
26 582 0.215937674542 Henry Cohn, 2026, needs more optimization.
26 583 0.216866452489 Henry Cohn, 2026, needs more optimization.
26 584 0.217492933399 Henry Cohn, 2026, needs more optimization.
26 585 0.218831686925 Henry Cohn, 2026, needs more optimization.
26 586 0.219381312290 Henry Cohn, 2026, needs more optimization.
26 587 0.220716328214 Henry Cohn, 2026, needs more optimization.
26 588 0.221594928808 Henry Cohn, 2026, needs more optimization.
26 589 0.222090362380 Henry Cohn, 2026, needs more optimization.
26 590 0.222862480429 Henry Cohn, 2026, needs more optimization.
26 591 0.223959700675 Henry Cohn, 2026, needs more optimization.
26 592 0.224527264125 Henry Cohn, 2026, needs more optimization.
26 593 0.224983140019 Henry Cohn, 2026, needs more optimization.
26 594 0.225937976960 Henry Cohn, 2026, needs more optimization.
26 595 0.226174151403 Henry Cohn, 2026, needs more optimization.
26 596 0.226469185502 Henry Cohn, 2026, needs more optimization.
26 602 0.238096469173 Henry Cohn, 2026, needs more optimization.
26 614 0.238096570683 Henry Cohn, 2026, needs more optimization.
26 619 0.238096808824 Henry Cohn, 2026, needs more optimization.
26 620 0.238097442216 Henry Cohn, 2026, needs more optimization.
26 622 0.238097987804 Henry Cohn, 2026, needs more optimization.
26 623 0.238098603510 Henry Cohn, 2026, needs more optimization.
26 627 0.238104787751 Henry Cohn, 2026, needs more optimization.
26 628 0.238117439877 Henry Cohn, 2026, needs more optimization.
26 629 0.238226672539 Henry Cohn, 2026, needs more optimization.
26 630 0.238350163847 Henry Cohn, 2026, needs more optimization.
26 631 0.238510705754 Henry Cohn, 2026, needs more optimization.
26 633 0.238842584849 Henry Cohn, 2026, needs more optimization.
26 634 0.239387647896 Henry Cohn, 2026, needs more optimization.
26 635 0.240203012238 Henry Cohn, 2026, needs more optimization.
26 636 0.240740811512 Henry Cohn, 2026, needs more optimization.
26 637 0.240908127002 Henry Cohn, 2026, needs more optimization.
26 638 0.241335040907 Henry Cohn, 2026, needs more optimization.
26 640 0.242292268784 Henry Cohn, 2026, needs more optimization.
26 641 0.243201053977 Henry Cohn, 2026, needs more optimization.
26 642 0.243345984456 Henry Cohn, 2026, needs more optimization.
26 643 0.243745251796 Henry Cohn, 2026, needs more optimization.
26 644 0.244193733048 Henry Cohn, 2026, needs more optimization.
26 647 0.245130498515 Henry Cohn, 2026, needs more optimization.
26 648 0.245500374839 Henry Cohn, 2026, needs more optimization.
26 649 0.245758420674 Henry Cohn, 2026, needs more optimization.
26 650 0.245806318676 Henry Cohn, 2026, needs more optimization.
26 651 0.246109527820 Henry Cohn, 2026, needs more optimization.
26 652 0.246412167647 Henry Cohn, 2026, needs more optimization.
26 653 0.246612767605 Henry Cohn, 2026, needs more optimization.
26 654 0.246714252332 Henry Cohn, 2026, needs more optimization.
26 655 0.247051773249 Henry Cohn, 2026, needs more optimization.
26 656 0.247122292910 Henry Cohn, 2026, needs more optimization.
26 658 0.247201759515 Henry Cohn, 2026, needs more optimization.
26 659 0.247576180010 Henry Cohn, 2026, needs more optimization.
26 660 0.247623369130 Henry Cohn, 2026, needs more optimization.
26 661 0.247780976538 Henry Cohn, 2026, needs more optimization.
26 662 0.247832607278 Henry Cohn, 2026, needs more optimization.
26 664 0.247854223566 Henry Cohn, 2026, needs more optimization.
26 665 0.248118362234 Henry Cohn, 2026, needs more optimization.
26 667 0.248155657661 Henry Cohn, 2026, needs more optimization.
26 668 0.248171867971 Henry Cohn, 2026, needs more optimization.
26 672 0.248365308442 Henry Cohn, 2026, needs more optimization.
26 673 0.248385012782 Henry Cohn, 2026, needs more optimization.
26 674 0.248405577092 Henry Cohn, 2026, needs more optimization.
26 675 0.248519561724 Henry Cohn, 2026, needs more optimization.
26 676 0.248535491026 Henry Cohn, 2026, needs more optimization.
26 677 0.248661476056 Henry Cohn, 2026, needs more optimization.
26 678 0.248714076662 Henry Cohn, 2026, needs more optimization.
26 679 0.248740984451 Henry Cohn, 2026, needs more optimization.
26 681 0.248785173231 Henry Cohn, 2026, needs more optimization.
26 682 0.248853351081 Henry Cohn, 2026, needs more optimization.
26 683 0.248925113274 Henry Cohn, 2026, needs more optimization.
26 685 0.248929781310 Henry Cohn, 2026, needs more optimization.
26 686 0.249023342059 Henry Cohn, 2026, needs more optimization.
26 687 0.249097095300 Henry Cohn, 2026, needs more optimization.
26 688 0.249111009834 Henry Cohn, 2026, needs more optimization.
26 689 0.249168570993 Henry Cohn, 2026, needs more optimization.
26 690 0.249195238770 Henry Cohn, 2026, needs more optimization.
26 691 0.249202350103 Henry Cohn, 2026, needs more optimization.
26 692 0.249234479386 Henry Cohn, 2026, needs more optimization.
26 693 0.249354569467 Henry Cohn, 2026, needs more optimization.
26 694 0.249384439100 Henry Cohn, 2026, needs more optimization.
26 695 0.249401459293 Henry Cohn, 2026, needs more optimization.
26 698 0.249414412898 Henry Cohn, 2026, needs more optimization.
26 699 0.249427182208 Henry Cohn, 2026, needs more optimization.
26 700 0.249430249075 Henry Cohn, 2026, needs more optimization.
26 701 0.249459684740 Henry Cohn, 2026, needs more optimization.
26 702 0.249482100466 Henry Cohn, 2026, needs more optimization.
26 703 0.249517574253 Henry Cohn, 2026, needs more optimization.
26 704 0.249535221998 Henry Cohn, 2026, needs more optimization.
26 705 0.249541375810 Henry Cohn, 2026, needs more optimization.
26 706 0.249588324257 Henry Cohn, 2026, needs more optimization.
26 707 0.249649673353 Henry Cohn, 2026, needs more optimization.
26 708 0.249658581277 Henry Cohn, 2026, needs more optimization.
26 709 0.249673170311 Henry Cohn, 2026, needs more optimization.
26 710 0.249690714172 Henry Cohn, 2026, needs more optimization.
26 712 0.249716532393 Henry Cohn, 2026, needs more optimization.
26 713 0.249728389950 Henry Cohn, 2026, needs more optimization.
26 714 0.249735363083 Henry Cohn, 2026, needs more optimization.
26 715 0.249752185178 Henry Cohn, 2026, needs more optimization.
26 716 0.249785658902 Henry Cohn, 2026, needs more optimization.
26 717 0.249789644880 Henry Cohn, 2026, needs more optimization.
26 718 0.249809459845 Henry Cohn, 2026, needs more optimization.
26 719 0.249830630122 Henry Cohn, 2026, needs more optimization.
26 720 0.249838748682 Henry Cohn, 2026, needs more optimization.
26 721 0.249850994958 Henry Cohn, 2026, needs more optimization.
26 722 0.249868203520 Henry Cohn, 2026, needs more optimization.
26 723 0.249892932099 Henry Cohn, 2026, needs more optimization.
26 903 0.25 Orthogonal union of 891 points in 22 dimensions and 12 points in 4 dimensions.
4⁢x−1
26 907 0.250001699450 Henry Cohn, 2026, needs more optimization.
26 913 0.250001701750 Henry Cohn, 2026, needs more optimization.
26 924 0.250001988336 Henry Cohn, 2026, needs more optimization.
26 926 0.250002345485 Henry Cohn, 2026, needs more optimization.
26 927 0.250003144766 Henry Cohn, 2026, needs more optimization.
26 930 0.250004562939 Henry Cohn, 2026, needs more optimization.
26 932 0.250004917380 Henry Cohn, 2026, needs more optimization.
26 933 0.250007274219 Henry Cohn, 2026, needs more optimization.
26 934 0.250010063759 Henry Cohn, 2026, needs more optimization.
26 935 0.250031350092 Henry Cohn, 2026, needs more optimization.
26 936 0.250055132804 Henry Cohn, 2026, needs more optimization.
26 937 0.250111597476 Henry Cohn, 2026, needs more optimization.
26 938 0.250153142396 Henry Cohn, 2026, needs more optimization.
26 939 0.250280394359 Henry Cohn, 2026, needs more optimization.
26 940 0.250291534538 Henry Cohn, 2026, needs more optimization.
26 941 0.250509607746 Henry Cohn, 2026, needs more optimization.
26 942 0.250810678075 Henry Cohn, 2026, needs more optimization.
26 943 0.250938099582 Henry Cohn, 2026, needs more optimization.
26 944 0.251194367750 Henry Cohn, 2026, needs more optimization.
26 945 0.251587467078 Henry Cohn, 2026, needs more optimization.
26 946 0.251969774062 Henry Cohn, 2026, needs more optimization.
26 947 0.252216344176 Henry Cohn, 2026, needs more optimization.
26 948 0.252557532294 Henry Cohn, 2026, needs more optimization.
26 949 0.253090047026 Henry Cohn, 2026, needs more optimization.
26 950 0.253248252679 Henry Cohn, 2026, needs more optimization.
26 951 0.253508759299 Henry Cohn, 2026, needs more optimization.
26 952 0.254011712610 Henry Cohn, 2026, needs more optimization.
26 953 0.254268283581 Henry Cohn, 2026, needs more optimization.
26 954 0.254807144963 Henry Cohn, 2026, needs more optimization.
26 955 0.255170443796 Henry Cohn, 2026, needs more optimization.
26 956 0.255653373334 Henry Cohn, 2026, needs more optimization.
26 957 0.255985584633 Henry Cohn, 2026, needs more optimization.
26 958 0.256159088504 Henry Cohn, 2026, needs more optimization.
26 959 0.256572420597 Henry Cohn, 2026, needs more optimization.
26 960 0.257124945018 Henry Cohn, 2026, needs more optimization.
26 961 0.257203961915 Henry Cohn, 2026, needs more optimization.
26 962 0.257611297979 Henry Cohn, 2026, needs more optimization.
26 963 0.258220706019 Henry Cohn, 2026, needs more optimization.
26 964 0.258521783642 Henry Cohn, 2026, needs more optimization.
26 965 0.258616388585 Henry Cohn, 2026, needs more optimization.
26 966 0.258962343601 Henry Cohn, 2026, needs more optimization.
26 967 0.259413692120 Henry Cohn, 2026, needs more optimization.
26 968 0.259614615277 Henry Cohn, 2026, needs more optimization.
26 969 0.259875665258 Henry Cohn, 2026, needs more optimization.
26 970 0.260085911897 Henry Cohn, 2026, needs more optimization.
26 971 0.260691164260 Henry Cohn, 2026, needs more optimization.
26 972 0.261043692325 Henry Cohn, 2026, needs more optimization.
26 973 0.261252271751 Henry Cohn, 2026, needs more optimization.
26 974 0.261790659183 Henry Cohn, 2026, needs more optimization.
26 975 0.262179507652 Henry Cohn, 2026, needs more optimization.
26 976 0.262785274372 Henry Cohn, 2026, needs more optimization.
26 977 0.263033143043 Henry Cohn, 2026, needs more optimization.
26 978 0.263496941836 Henry Cohn, 2026, needs more optimization.
26 979 0.263613941503 Henry Cohn, 2026, needs more optimization.
26 980 0.263736837192 Henry Cohn, 2026, needs more optimization.
26 981 0.264434586883 Henry Cohn, 2026, needs more optimization.
26 982 0.265000324510 Henry Cohn, 2026, needs more optimization.
26 983 0.265427474866 Henry Cohn, 2026, needs more optimization.
26 984 0.265695914335 Henry Cohn, 2026, needs more optimization.
26 985 0.265957780482 Henry Cohn, 2026, needs more optimization.
26 986 0.266259393929 Henry Cohn, 2026, needs more optimization.
26 987 0.266322480804 Henry Cohn, 2026, needs more optimization.
26 988 0.266584962078 Henry Cohn, 2026, needs more optimization.
26 989 0.266795585810 Henry Cohn, 2026, needs more optimization.
26 990 0.267203325613 Henry Cohn, 2026, needs more optimization.
26 991 0.267262449761 Henry Cohn, 2026, needs more optimization.
26 992 0.267475798052 Henry Cohn, 2026, needs more optimization.
26 993 0.267710623239 Henry Cohn, 2026, needs more optimization.
26 994 0.267941121597 Henry Cohn, 2026, needs more optimization.
26 995 0.268070765356 Henry Cohn, 2026, needs more optimization.
26 996 0.268260549954 Henry Cohn, 2026, needs more optimization.
26 997 0.268563286887 Henry Cohn, 2026, needs more optimization.
26 998 0.268824330388 Henry Cohn, 2026, needs more optimization.
26 999 0.269249843484 Henry Cohn, 2026, needs more optimization.
26 1000 0.269472359598 Henry Cohn, 2026, needs more optimization.
26 1001 0.269823875994 Henry Cohn, 2026, needs more optimization.
26 1002 0.269963746635 Henry Cohn, 2026, needs more optimization.
26 1003 0.270395471522 Henry Cohn, 2026, needs more optimization.
26 1004 0.270492589668 Henry Cohn, 2026, needs more optimization.
26 1005 0.270691347978 Henry Cohn, 2026, needs more optimization.
26 1007 0.271113826945 Henry Cohn, 2026, needs more optimization.
26 1008 0.271267085675 Henry Cohn, 2026, needs more optimization.
26 1009 0.271453717666 Henry Cohn, 2026, needs more optimization.
26 1010 0.271769909737 Henry Cohn, 2026, needs more optimization.
26 1011 0.271921930821 Henry Cohn, 2026, needs more optimization.
26 1024 0.272727272728 Code with 1024 points in 22 dimensions.
11⁢x−3
27 55 0.029589200879 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
16875⁢x3−729⁢x2−27⁢x+1
27 56 0.034511432831 Henry Cohn, 2024.
27 58 0.039896885932 Henry Cohn, 2026, needs more optimization.
27 59 0.039967796543 Henry Cohn, 2026.
27 60 0.044786634957 Henry Cohn, 2026, needs more optimization.
27 61 0.045484192884 Henry Cohn, 2026.
27 62 0.046198040189 Henry Cohn, 2025.
27 63 0.047652441689 Henry Cohn, 2026.
27 64 0.050067815256 Henry Cohn, 2026.
27 65 0.054259436682 Henry Cohn, 2026, needs more optimization.
27 66 0.056203231214 Henry Cohn, 2026, needs more optimization.
27 67 0.058358030299 Henry Cohn, 2026, needs more optimization.
27 68 0.060150459250 Henry Cohn, 2026.
27 69 0.061646691897 Henry Cohn, 2026.
27 70 0.062921570445 Henry Cohn, 2026, needs more optimization.
27 71 0.064107007001 Henry Cohn, 2026, needs more optimization.
27 72 0.064938030767 Henry Cohn, 2026, needs more optimization.
27 73 0.065796346088 Henry Cohn, 2026, needs more optimization.
27 74 0.066304724979 Henry Cohn, 2026, needs more optimization.
27 75 0.067944284023 Henry Cohn, 2026, needs more optimization.
27 76 0.069937587917 Henry Cohn, 2026, needs more optimization.
27 77 0.072325859984 Henry Cohn, 2026, needs more optimization.
27 78 0.074623461422 Henry Cohn, 2026, needs more optimization.
27 79 0.075323685853 Henry Cohn, 2026, needs more optimization.
27 80 0.076112448134 Henry Cohn, 2026, needs more optimization.
27 81 0.076614767951 Henry Cohn, 2026, needs more optimization.
27 82 0.076871551931 Henry Cohn, 2026, needs more optimization.
27 83 0.076905079671 Henry Cohn, 2026, needs more optimization.
27 84 0.077004662899 Henry Cohn, 2026, needs more optimization.
27 85 0.077371169025 Henry Cohn, 2026, needs more optimization.
27 86 0.077582866310 Henry Cohn, 2026, needs more optimization.
27 87 0.078368588940 Henry Cohn, 2026, needs more optimization.
27 88 0.078627436454 Henry Cohn, 2026, needs more optimization.
27 89 0.079086005363 Henry Cohn, 2026, needs more optimization.
27 90 0.079547686799 Henry Cohn, 2026, needs more optimization.
27 91 0.080269734194 Henry Cohn, 2026, needs more optimization.
27 92 0.080397348706 Henry Cohn, 2026, needs more optimization.
27 93 0.080670831555 Henry Cohn, 2026, needs more optimization.
27 94 0.080682780934 Henry Cohn, 2026, needs more optimization.
27 95 0.080684833766 Henry Cohn, 2026, needs more optimization.
27 96 0.080685003328 Orthogonal union of 94 points in 26 dimensions and 2 points in 1 dimension.
575⁢x2−34⁢x−1
27 97 0.080685560950 Henry Cohn, 2026, needs more optimization.
27 98 0.080685608415 Henry Cohn, 2026, needs more optimization.
27 99 0.084156894092 Henry Cohn, 2026, needs more optimization.
27 100 0.086566249461 Henry Cohn, 2026, needs more optimization.
27 101 0.088590539850 Henry Cohn, 2026, needs more optimization.
27 102 0.089445524538 Henry Cohn, 2026, needs more optimization.
27 103 0.089766479140 Henry Cohn, 2026, needs more optimization.
27 104 0.089958863274 Henry Cohn, 2026, needs more optimization.
27 105 0.090188792878 Henry Cohn, 2026, needs more optimization.
27 106 0.090273268125 Henry Cohn, 2026, needs more optimization.
27 107 0.090517728616 Henry Cohn, 2026, needs more optimization.
27 108 0.090582138024 Henry Cohn, 2026, needs more optimization.
27 109 0.090630770509 Henry Cohn, 2026, needs more optimization.
27 110 0.090630770827 Henry Cohn, 2026, needs more optimization.
27 111 0.090766771281 Henry Cohn, 2026, needs more optimization.
27 112 0.090858043768 Henry Cohn, 2026, needs more optimization.
27 113 0.090888932858 Henry Cohn, 2026, needs more optimization.
27 114 0.091261777963 Henry Cohn, 2026, needs more optimization.
27 115 0.092923916242 Henry Cohn, 2026, needs more optimization.
27 116 0.095573310182 Henry Cohn, 2026, needs more optimization.
27 117 0.098515838666 Henry Cohn, 2026, needs more optimization.
27 118 0.100950538449 Henry Cohn, 2026, needs more optimization.
27 119 0.102960009058 Henry Cohn, 2026, needs more optimization.
27 120 0.103031483200 Henry Cohn, 2026, needs more optimization.
27 121 0.103031484107 Henry Cohn, 2026, needs more optimization.
27 122 0.103111833370 Henry Cohn, 2026, needs more optimization.
27 125 0.103125332566 Henry Cohn, 2026, needs more optimization.
27 126 0.104301940420 Henry Cohn, 2026, needs more optimization.
27 127 0.105168361025 Henry Cohn, 2026, needs more optimization.
27 128 0.105899010868 Henry Cohn, 2026, needs more optimization.
27 129 0.107226937540 Henry Cohn, 2026, needs more optimization.
27 130 0.107683470584 Henry Cohn, 2026, needs more optimization.
27 131 0.108485258698 Henry Cohn, 2026, needs more optimization.
27 132 0.109597777432 Henry Cohn, 2026, needs more optimization.
27 133 0.110548360525 Henry Cohn, 2026, needs more optimization.
27 134 0.111003554513 Henry Cohn, 2026, needs more optimization.
27 135 0.111009488212 Henry Cohn, 2026, needs more optimization.
27 136 0.111391902487 Henry Cohn, 2026, needs more optimization.
27 137 0.112893701175 Henry Cohn, 2026, needs more optimization.
27 138 0.114326029970 Henry Cohn, 2026, needs more optimization.
27 139 0.114830608712 Henry Cohn, 2026, needs more optimization.
27 140 0.115260411411 Henry Cohn, 2026, needs more optimization.
27 141 0.116308472685 Henry Cohn, 2026, needs more optimization.
27 142 0.117412225685 Henry Cohn, 2026, needs more optimization.
27 143 0.119136300592 Henry Cohn, 2026, needs more optimization.
27 144 0.120994251755 Henry Cohn, 2026, needs more optimization.
27 145 0.123133563098 Henry Cohn, 2026, needs more optimization.
27 146 0.125354279892 Henry Cohn, 2026, needs more optimization.
27 147 0.127230977997 Henry Cohn, 2026, needs more optimization.
27 148 0.128556753093 Henry Cohn, 2026, needs more optimization.
27 149 0.129948130863 Henry Cohn, 2026, needs more optimization.
27 150 0.131242616621 Henry Cohn, 2026, needs more optimization.
27 151 0.131378496240 Henry Cohn, 2026, needs more optimization.
27 152 0.131596530633 Henry Cohn, 2026, needs more optimization.
27 153 0.131753223462 Henry Cohn, 2026, needs more optimization.
27 154 0.132000665088 Henry Cohn, 2026, needs more optimization.
27 155 0.132013977217 Henry Cohn, 2026, needs more optimization.
27 156 0.132208001066 Henry Cohn, 2026, needs more optimization.
27 157 0.132527438109 Henry Cohn, 2026, needs more optimization.
27 158 0.132743405420 Henry Cohn, 2026, needs more optimization.
27 159 0.132998177051 Henry Cohn, 2026, needs more optimization.
27 160 0.133268784549 Henry Cohn, 2026, needs more optimization.
27 161 0.133301308358 Henry Cohn, 2026, needs more optimization.
27 162 0.133316675319 Henry Cohn, 2026, needs more optimization.
27 163 0.133329300090 Henry Cohn, 2026, needs more optimization.
27 164 0.133482387060 Henry Cohn, 2026, needs more optimization.
27 165 0.135017332116 Henry Cohn, 2026, needs more optimization.
27 166 0.135025473920 Henry Cohn, 2026, needs more optimization.
27 167 0.135106303519 Henry Cohn, 2026, needs more optimization.
27 168 0.135124216625 Henry Cohn, 2026, needs more optimization.
27 169 0.135254176819 Henry Cohn, 2026, needs more optimization.
27 170 0.135783815515 Henry Cohn, 2026, needs more optimization.
27 171 0.136291682633 Henry Cohn, 2026, needs more optimization.
27 172 0.137278206283 Henry Cohn, 2026, needs more optimization.
27 173 0.138901423597 Henry Cohn, 2026, needs more optimization.
27 174 0.139554118786 Henry Cohn, 2026, needs more optimization.
27 175 0.140948398011 Henry Cohn, 2026, needs more optimization.
27 176 0.142247705085 Henry Cohn, 2026, needs more optimization.
27 177 0.142295942804 Henry Cohn, 2026, needs more optimization.
27 178 0.142402011463 Henry Cohn, 2026, needs more optimization.
27 179 0.142415781802 Henry Cohn, 2026, needs more optimization.
27 180 0.142492716187 Henry Cohn, 2026, needs more optimization.
27 181 0.142532875503 Henry Cohn, 2026, needs more optimization.
27 182 0.142551650594 Henry Cohn, 2026, needs more optimization.
27 183 0.142568621727 Henry Cohn, 2026, needs more optimization.
27 184 0.142671511536 Henry Cohn, 2026, needs more optimization.
27 185 0.142695876783 Henry Cohn, 2026, needs more optimization.
27 186 0.142745942530 Henry Cohn, 2026, needs more optimization.
27 187 0.142747458400 Henry Cohn, 2026, needs more optimization.
27 188 0.142757556492 Henry Cohn, 2026, needs more optimization.
27 190 0.142758827358 Henry Cohn, 2026, needs more optimization.
27 191 0.142829525454 Henry Cohn, 2026, needs more optimization.
27 192 0.142968406377 Henry Cohn, 2026, needs more optimization.
27 193 0.142976497319 Henry Cohn, 2026, needs more optimization.
27 194 0.143905862499 Henry Cohn, 2026, needs more optimization.
27 195 0.144424724008 Henry Cohn, 2026, needs more optimization.
27 196 0.145381753785 Henry Cohn, 2026, needs more optimization.
27 197 0.145383230565 Henry Cohn, 2026, needs more optimization.
27 198 0.145413689191 Henry Cohn, 2026, needs more optimization.
27 199 0.145492561872 Henry Cohn, 2026, needs more optimization.
27 200 0.145775089046 Henry Cohn, 2026, needs more optimization.
27 201 0.146083702262 Henry Cohn, 2026, needs more optimization.
27 202 0.146348760223 Henry Cohn, 2026, needs more optimization.
27 203 0.146521214472 Henry Cohn, 2026, needs more optimization.
27 204 0.146942852921 Henry Cohn, 2026, needs more optimization.
27 205 0.147166176305 Henry Cohn, 2026, needs more optimization.
27 206 0.147193435327 Henry Cohn, 2026, needs more optimization.
27 207 0.147328515081 Henry Cohn, 2026, needs more optimization.
27 208 0.147416791829 Henry Cohn, 2026, needs more optimization.
27 209 0.147416908502 Henry Cohn, 2026, needs more optimization.
27 210 0.147418475083 Henry Cohn, 2026, needs more optimization.
27 211 0.147419762854 Henry Cohn, 2026, needs more optimization.
27 212 0.147451744616 Henry Cohn, 2026, needs more optimization.
27 215 0.147651517511 Henry Cohn, 2026.
1655⁢x2−136⁢x−16
27 216 0.147963766538 Henry Cohn, 2026, needs more optimization.
27 217 0.148993501758 Henry Cohn, 2026, needs more optimization.
27 218 0.149003109432 Henry Cohn, 2026, needs more optimization.
27 219 0.149321917460 Henry Cohn, 2026, needs more optimization.
27 220 0.149321952206 Henry Cohn, 2026, needs more optimization.
27 221 0.149323859713 Henry Cohn, 2026, needs more optimization.
27 222 0.149331315540 Henry Cohn, 2026, needs more optimization.
27 223 0.149331315549 Henry Cohn, 2026, needs more optimization.
27 224 0.149331315553 Henry Cohn, 2026, needs more optimization.
27 225 0.149405815524 Henry Cohn, 2026, needs more optimization.
27 226 0.149711243003 Henry Cohn, 2026, needs more optimization.
27 227 0.149742686938 Henry Cohn, 2026, needs more optimization.
27 228 0.150035568948 Henry Cohn, 2026, needs more optimization.
27 229 0.150041532829 Henry Cohn, 2026, needs more optimization.
27 230 0.150314684872 Henry Cohn, 2026, needs more optimization.
27 231 0.150366696224 Henry Cohn, 2026, needs more optimization.
27 232 0.150898839611 Henry Cohn, 2026, needs more optimization.
27 233 0.151548190735 Henry Cohn, 2026, needs more optimization.
27 234 0.152313304765 Henry Cohn, 2026, needs more optimization.
27 235 0.152393427511 Henry Cohn, 2026, needs more optimization.
27 236 0.153632415530 Henry Cohn, 2026, needs more optimization.
27 237 0.155588711629 Henry Cohn, 2026, needs more optimization.
27 238 0.157681450511 Henry Cohn, 2026, needs more optimization.
27 239 0.157707004355 Henry Cohn, 2026, needs more optimization.
27 240 0.158836014255 Henry Cohn, 2026, needs more optimization.
27 241 0.159827406127 Henry Cohn, 2026, needs more optimization.
27 242 0.160381423411 Henry Cohn, 2026, needs more optimization.
27 243 0.161433311875 Henry Cohn, 2026, needs more optimization.
27 244 0.162258874685 Henry Cohn, 2026, needs more optimization.
27 245 0.162284584561 Henry Cohn, 2026, needs more optimization.
27 246 0.162534145319 Henry Cohn, 2026, needs more optimization.
27 247 0.162671349381 Henry Cohn, 2026, needs more optimization.
27 248 0.162721492572 Henry Cohn, 2026, needs more optimization.
27 249 0.162902860556 Henry Cohn, 2026, needs more optimization.
27 250 0.163015097332 Henry Cohn, 2026, needs more optimization.
27 251 0.163638300231 Henry Cohn, 2026, needs more optimization.
27 252 0.163904931649 Henry Cohn, 2026, needs more optimization.
27 253 0.164117187213 Henry Cohn, 2026, needs more optimization.
27 254 0.164161243133 Henry Cohn, 2026, needs more optimization.
27 255 0.164502469748 Henry Cohn, 2026, needs more optimization.
27 256 0.164633169564 Henry Cohn, 2026, needs more optimization.
27 257 0.164806040638 Henry Cohn, 2026, needs more optimization.
27 258 0.165013299229 Henry Cohn, 2026, needs more optimization.
27 259 0.165103301721 Henry Cohn, 2026, needs more optimization.
27 260 0.165244469852 Henry Cohn, 2026, needs more optimization.
27 261 0.165399553955 Henry Cohn, 2026, needs more optimization.
27 262 0.165508483834 Henry Cohn, 2026, needs more optimization.
27 263 0.165596335802 Henry Cohn, 2026, needs more optimization.
27 264 0.165705789097 Henry Cohn, 2026, needs more optimization.
27 265 0.165792321929 Henry Cohn, 2026, needs more optimization.
27 266 0.165856948506 Henry Cohn, 2026, needs more optimization.
27 267 0.165904205368 Henry Cohn, 2026, needs more optimization.
27 268 0.165983470904 Henry Cohn, 2026, needs more optimization.
27 269 0.166049729318 Henry Cohn, 2026, needs more optimization.
27 270 0.166166553943 Henry Cohn, 2026, needs more optimization.
27 271 0.166260606612 Henry Cohn, 2026, needs more optimization.
27 272 0.166309230425 Henry Cohn, 2026, needs more optimization.
27 273 0.166353336715 Henry Cohn, 2026, needs more optimization.
27 274 0.166403877006 Henry Cohn, 2026, needs more optimization.
27 275 0.166440470000 Henry Cohn, 2026, needs more optimization.
27 276 0.166479522477 Henry Cohn, 2026, needs more optimization.
27 277 0.166496246864 Henry Cohn, 2026, needs more optimization.
27 278 0.166545594283 Henry Cohn, 2026, needs more optimization.
27 279 0.166579220633 Henry Cohn, 2026, needs more optimization.
27 280 0.166579223059 Henry Cohn, 2026, needs more optimization.
27 281 0.166608240836 Henry Cohn, 2026, needs more optimization.
27 288 0.166666666667 Orthogonal union of 278 points in 23 dimensions and 10 points in 4 dimensions.
6⁢x−1
27 293 0.166666864290 Henry Cohn, 2026, needs more optimization.
27 294 0.166667326904 Henry Cohn, 2026, needs more optimization.
27 295 0.166667326907 Henry Cohn, 2026, needs more optimization.
27 296 0.166667326911 Henry Cohn, 2026, needs more optimization.
27 297 0.166668078751 Henry Cohn, 2026, needs more optimization.
27 298 0.166668078942 Henry Cohn, 2026, needs more optimization.
27 302 0.166668154586 Henry Cohn, 2026, needs more optimization.
27 303 0.166668637380 Henry Cohn, 2026, needs more optimization.
27 304 0.166686482236 Henry Cohn, 2026, needs more optimization.
27 305 0.166737497896 Henry Cohn, 2026, needs more optimization.
27 306 0.166927909366 Henry Cohn, 2026, needs more optimization.
27 307 0.167298912019 Henry Cohn, 2026, needs more optimization.
27 308 0.168124960968 Henry Cohn, 2026, needs more optimization.
27 309 0.169392556964 Henry Cohn, 2026, needs more optimization.
27 310 0.170450805345 Henry Cohn, 2026, needs more optimization.
27 311 0.171686344501 Henry Cohn, 2026, needs more optimization.
27 312 0.172836710697 Henry Cohn, 2026, needs more optimization.
27 313 0.173872885978 Henry Cohn, 2026, needs more optimization.
27 314 0.174681051170 Henry Cohn, 2026, needs more optimization.
27 315 0.176005212409 Henry Cohn, 2026, needs more optimization.
27 316 0.177382133809 Henry Cohn, 2026, needs more optimization.
27 317 0.178088884649 Henry Cohn, 2026, needs more optimization.
27 318 0.179066387575 Henry Cohn, 2026, needs more optimization.
27 319 0.179745037550 Henry Cohn, 2026, needs more optimization.
27 320 0.180599075065 Henry Cohn, 2026, needs more optimization.
27 321 0.180959904932 Henry Cohn, 2026, needs more optimization.
27 322 0.181002751573 Henry Cohn, 2026, needs more optimization.
27 323 0.181181726906 Henry Cohn, 2026, needs more optimization.
27 324 0.181274317673 Henry Cohn, 2026, needs more optimization.
27 325 0.181377692227 Henry Cohn, 2026, needs more optimization.
27 326 0.181442819309 Henry Cohn, 2026, needs more optimization.
27 327 0.181480474408 Henry Cohn, 2026, needs more optimization.
27 328 0.181483800624 Henry Cohn, 2026, needs more optimization.
27 329 0.181653222895 Henry Cohn, 2026, needs more optimization.
27 330 0.181701471446 Henry Cohn, 2026, needs more optimization.
27 331 0.181711499380 Henry Cohn, 2026, needs more optimization.
27 332 0.181737127335 Henry Cohn, 2026, needs more optimization.
27 333 0.181762154729 Henry Cohn, 2026, needs more optimization.
27 334 0.181815488193 Henry Cohn, 2026, needs more optimization.
27 335 0.181816581427 Henry Cohn, 2026, needs more optimization.
27 336 0.181821004398 Henry Cohn, 2026, needs more optimization.
27 337 0.181830292260 Henry Cohn, 2026, needs more optimization.
27 338 0.181845087566 Henry Cohn, 2026, needs more optimization.
27 339 0.181970100636 Henry Cohn, 2026, needs more optimization.
27 340 0.182286219707 Henry Cohn, 2026, needs more optimization.
27 341 0.182694759802 Henry Cohn, 2026, needs more optimization.
27 342 0.183560656462 Henry Cohn, 2026, needs more optimization.
27 343 0.184170277186 Henry Cohn, 2026, needs more optimization.
27 344 0.184549924828 Henry Cohn, 2026, needs more optimization.
27 345 0.185603640696 Henry Cohn, 2026, needs more optimization.
27 346 0.186389447204 Henry Cohn, 2026, needs more optimization.
27 347 0.186706055139 Henry Cohn, 2026, needs more optimization.
27 348 0.187544265469 Henry Cohn, 2026, needs more optimization.
27 349 0.188104859101 Henry Cohn, 2026, needs more optimization.
27 350 0.188593800875 Henry Cohn, 2026, needs more optimization.
27 351 0.189327140009 Henry Cohn, 2026, needs more optimization.
27 352 0.190307997022 Henry Cohn, 2026, needs more optimization.
27 353 0.191009624211 Henry Cohn, 2026, needs more optimization.
27 354 0.191879999633 Henry Cohn, 2026, needs more optimization.
27 355 0.192677525495 Henry Cohn, 2026, needs more optimization.
27 356 0.193339062064 Henry Cohn, 2026, needs more optimization.
27 357 0.193842135088 Henry Cohn, 2026, needs more optimization.
27 358 0.193886367741 Henry Cohn, 2026, needs more optimization.
27 359 0.194009434960 Henry Cohn, 2026, needs more optimization.
27 360 0.194529400485 Henry Cohn, 2026, needs more optimization.
27 361 0.195806925222 Henry Cohn, 2026, needs more optimization.
27 362 0.195917189814 Henry Cohn, 2026, needs more optimization.
27 363 0.196032159754 Henry Cohn, 2026, needs more optimization.
27 364 0.196209109707 Henry Cohn, 2026, needs more optimization.
27 365 0.196304275578 Henry Cohn, 2026, needs more optimization.
27 366 0.196461049099 Henry Cohn, 2026, needs more optimization.
27 367 0.196499893838 Henry Cohn, 2026, needs more optimization.
27 368 0.196530364519 Henry Cohn, 2026, needs more optimization.
27 369 0.196569832064 Henry Cohn, 2026, needs more optimization.
27 370 0.196646421502 Henry Cohn, 2026, needs more optimization.
27 371 0.196720910826 Henry Cohn, 2026, needs more optimization.
27 372 0.196828472549 Henry Cohn, 2026, needs more optimization.
27 373 0.196971828001 Henry Cohn, 2026, needs more optimization.
27 374 0.197098075062 Henry Cohn, 2026, needs more optimization.
27 375 0.197140244609 Henry Cohn, 2026, needs more optimization.
27 376 0.197252404454 Henry Cohn, 2026, needs more optimization.
27 377 0.197490608766 Henry Cohn, 2026, needs more optimization.
27 378 0.197612450508 Henry Cohn, 2026, needs more optimization.
27 379 0.197718768234 Henry Cohn, 2026, needs more optimization.
27 380 0.197816295046 Henry Cohn, 2026, needs more optimization.
27 381 0.197952193725 Henry Cohn, 2026, needs more optimization.
27 382 0.198017850195 Henry Cohn, 2026, needs more optimization.
27 383 0.198105386175 Henry Cohn, 2026, needs more optimization.
27 384 0.198142881393 Henry Cohn, 2026, needs more optimization.
27 385 0.198262490549 Henry Cohn, 2026, needs more optimization.
27 386 0.198374713784 Henry Cohn, 2026, needs more optimization.
27 387 0.198478590651 Henry Cohn, 2026, needs more optimization.
27 388 0.198538696363 Henry Cohn, 2026, needs more optimization.
27 389 0.198681576383 Henry Cohn, 2026, needs more optimization.
27 390 0.198733626576 Henry Cohn, 2026, needs more optimization.
27 391 0.198777958847 Henry Cohn, 2026, needs more optimization.
27 392 0.198842707227 Henry Cohn, 2026, needs more optimization.
27 393 0.198892185498 Henry Cohn, 2026, needs more optimization.
27 394 0.198995124213 Henry Cohn, 2026, needs more optimization.
27 396 0.199077763707 Henry Cohn, 2026, needs more optimization.
27 397 0.199150007337 Henry Cohn, 2026, needs more optimization.
27 398 0.199187991669 Henry Cohn, 2026, needs more optimization.
27 399 0.199210569501 Henry Cohn, 2026, needs more optimization.
27 401 0.199273770628 Henry Cohn, 2026, needs more optimization.
27 402 0.199304861515 Henry Cohn, 2026, needs more optimization.
27 403 0.199339546839 Henry Cohn, 2026, needs more optimization.
27 404 0.199385480689 Henry Cohn, 2026, needs more optimization.
27 405 0.199401121038 Henry Cohn, 2026, needs more optimization.
27 406 0.199425377923 Henry Cohn, 2026, needs more optimization.
27 407 0.199487727728 Henry Cohn, 2026, needs more optimization.
27 408 0.199525944395 Henry Cohn, 2026, needs more optimization.
27 410 0.199590644219 Henry Cohn, 2026, needs more optimization.
27 411 0.199620732337 Henry Cohn, 2026, needs more optimization.
27 412 0.199672129665 Henry Cohn, 2026, needs more optimization.
27 413 0.199708289630 Henry Cohn, 2026, needs more optimization.
27 414 0.199734767654 Henry Cohn, 2026, needs more optimization.
27 415 0.199752617470 Henry Cohn, 2026, needs more optimization.
27 416 0.199756911026 Henry Cohn, 2026, needs more optimization.
27 417 0.199784262406 Henry Cohn, 2026, needs more optimization.
27 418 0.199800562101 Henry Cohn, 2026, needs more optimization.
27 419 0.199834774073 Henry Cohn, 2026, needs more optimization.
27 420 0.199857801860 Henry Cohn, 2026, needs more optimization.
27 421 0.199890193271 Henry Cohn, 2026, needs more optimization.
27 422 0.199895856336 Henry Cohn, 2026, needs more optimization.
27 423 0.199921324435 Henry Cohn, 2026, needs more optimization.
27 424 0.199942972394 Henry Cohn, 2026, needs more optimization.
27 425 0.199945679732 Henry Cohn, 2026, needs more optimization.
27 562 0.2 Orthogonal union of 552 points in 23 dimensions and 10 points in 4 dimensions.
5⁢x−1
27 570 0.200000846014 Orthogonal union of 568 points in 26 dimensions and 2 points in 1 dimension.
27 571 0.200001194153 Henry Cohn, 2026, needs more optimization.
27 574 0.200001701654 Henry Cohn, 2026, needs more optimization.
27 575 0.200001951776 Henry Cohn, 2026, needs more optimization.
27 576 0.200013026342 Henry Cohn, 2026, needs more optimization.
27 577 0.200027326210 Henry Cohn, 2026, needs more optimization.
27 578 0.200051463446 Henry Cohn, 2026, needs more optimization.
27 579 0.200060154954 Henry Cohn, 2026, needs more optimization.
27 580 0.200168918613 Henry Cohn, 2026, needs more optimization.
27 581 0.200213884993 Henry Cohn, 2026, needs more optimization.
27 582 0.200795338694 Henry Cohn, 2026, needs more optimization.
27 583 0.201190001384 Henry Cohn, 2026, needs more optimization.
27 584 0.202587101689 Henry Cohn, 2026, needs more optimization.
27 585 0.203159150986 Henry Cohn, 2026, needs more optimization.
27 586 0.203755208525 Henry Cohn, 2026, needs more optimization.
27 587 0.205326478632 Henry Cohn, 2026, needs more optimization.
27 588 0.206488433201 Henry Cohn, 2026, needs more optimization.
27 589 0.207352569664 Henry Cohn, 2026, needs more optimization.
27 590 0.208835691735 Henry Cohn, 2026, needs more optimization.
27 591 0.209625542942 Henry Cohn, 2026, needs more optimization.
27 592 0.210628446907 Henry Cohn, 2026, needs more optimization.
27 593 0.212043716162 Henry Cohn, 2026, needs more optimization.
27 594 0.212348182788 Henry Cohn, 2026, needs more optimization.
27 595 0.213420641504 Henry Cohn, 2026, needs more optimization.
27 596 0.213972512742 Henry Cohn, 2026, needs more optimization.
27 597 0.214504288854 Henry Cohn, 2026, needs more optimization.
27 598 0.215120328872 Henry Cohn, 2026, needs more optimization.
27 616 0.238095214846 Henry Cohn, 2026, needs more optimization.
27 622 0.238095529464 Henry Cohn, 2026, needs more optimization.
27 632 0.238095849791 Henry Cohn, 2026, needs more optimization.
27 634 0.238096575876 Henry Cohn, 2026, needs more optimization.
27 636 0.238098704206 Henry Cohn, 2026, needs more optimization.
27 637 0.238098930264 Henry Cohn, 2026, needs more optimization.
27 639 0.238099075547 Henry Cohn, 2026, needs more optimization.
27 640 0.238099746738 Henry Cohn, 2026, needs more optimization.
27 641 0.238124459887 Henry Cohn, 2026, needs more optimization.
27 642 0.238134091377 Henry Cohn, 2026, needs more optimization.
27 643 0.238140785077 Henry Cohn, 2026, needs more optimization.
27 644 0.238142529537 Henry Cohn, 2026, needs more optimization.
27 649 0.238144211898 Henry Cohn, 2026, needs more optimization.
27 651 0.238207323323 Henry Cohn, 2026, needs more optimization.
27 653 0.238315416486 Henry Cohn, 2026, needs more optimization.
27 655 0.238514201390 Henry Cohn, 2026, needs more optimization.
27 658 0.238659458560 Henry Cohn, 2026, needs more optimization.
27 659 0.238995436058 Henry Cohn, 2026, needs more optimization.
27 660 0.239324729848 Henry Cohn, 2026, needs more optimization.
27 661 0.239668969550 Henry Cohn, 2026, needs more optimization.
27 662 0.239896680022 Henry Cohn, 2026, needs more optimization.
27 663 0.240062650109 Henry Cohn, 2026, needs more optimization.
27 664 0.240604456675 Henry Cohn, 2026, needs more optimization.
27 665 0.240951235508 Henry Cohn, 2026, needs more optimization.
27 666 0.240992422400 Henry Cohn, 2026, needs more optimization.
27 667 0.240995033550 Henry Cohn, 2026, needs more optimization.
27 669 0.241173719613 Henry Cohn, 2026, needs more optimization.
27 670 0.241357496716 Henry Cohn, 2026, needs more optimization.
27 671 0.241968810052 Henry Cohn, 2026, needs more optimization.
27 674 0.242188364742 Henry Cohn, 2026, needs more optimization.
27 676 0.242845455230 Henry Cohn, 2026, needs more optimization.
27 677 0.242909141204 Henry Cohn, 2026, needs more optimization.
27 678 0.243119212348 Henry Cohn, 2026, needs more optimization.
27 679 0.243307358041 Henry Cohn, 2026, needs more optimization.
27 680 0.243390058139 Henry Cohn, 2026, needs more optimization.
27 681 0.244237449678 Henry Cohn, 2026, needs more optimization.
27 683 0.244495800344 Henry Cohn, 2026, needs more optimization.
27 684 0.244675590975 Henry Cohn, 2026, needs more optimization.
27 685 0.244952571060 Henry Cohn, 2026, needs more optimization.
27 686 0.245016184343 Henry Cohn, 2026, needs more optimization.
27 687 0.245198581876 Henry Cohn, 2026, needs more optimization.
27 692 0.245270955413 Henry Cohn, 2026, needs more optimization.
27 693 0.245375940528 Henry Cohn, 2026, needs more optimization.
27 695 0.245644209003 Henry Cohn, 2026, needs more optimization.
27 696 0.245829871842 Henry Cohn, 2026, needs more optimization.
27 697 0.245897576316 Henry Cohn, 2026, needs more optimization.
27 698 0.245986995759 Henry Cohn, 2026, needs more optimization.
27 699 0.246193373201 Henry Cohn, 2026, needs more optimization.
27 700 0.246400982298 Henry Cohn, 2026, needs more optimization.
27 701 0.246555828480 Henry Cohn, 2026, needs more optimization.
27 702 0.246671332615 Henry Cohn, 2026, needs more optimization.
27 703 0.246730062173 Henry Cohn, 2026, needs more optimization.
27 704 0.246900013777 Henry Cohn, 2026, needs more optimization.
27 705 0.246945469557 Henry Cohn, 2026, needs more optimization.
27 706 0.247040953371 Henry Cohn, 2026, needs more optimization.
27 707 0.247133007081 Henry Cohn, 2026, needs more optimization.
27 708 0.247338850573 Henry Cohn, 2026, needs more optimization.
27 709 0.247405551659 Henry Cohn, 2026, needs more optimization.
27 712 0.247555038620 Henry Cohn, 2026, needs more optimization.
27 714 0.247792710304 Henry Cohn, 2026, needs more optimization.
27 715 0.247932440916 Henry Cohn, 2026, needs more optimization.
27 716 0.248009274408 Henry Cohn, 2026, needs more optimization.
27 718 0.248095495963 Henry Cohn, 2026, needs more optimization.
27 721 0.248164530508 Henry Cohn, 2026, needs more optimization.
27 723 0.248287545891 Henry Cohn, 2026, needs more optimization.
27 724 0.248372693283 Henry Cohn, 2026, needs more optimization.
27 725 0.248433924551 Henry Cohn, 2026, needs more optimization.
27 726 0.248551890925 Henry Cohn, 2026, needs more optimization.
27 727 0.248604051781 Henry Cohn, 2026, needs more optimization.
27 728 0.248616708611 Henry Cohn, 2026, needs more optimization.
27 729 0.248674816100 Henry Cohn, 2026, needs more optimization.
27 730 0.248760437568 Henry Cohn, 2026, needs more optimization.
27 732 0.248838227689 Henry Cohn, 2026, needs more optimization.
27 733 0.248907321734 Henry Cohn, 2026, needs more optimization.
27 735 0.249011234180 Henry Cohn, 2026, needs more optimization.
27 736 0.249105738687 Henry Cohn, 2026, needs more optimization.
27 737 0.249132445166 Henry Cohn, 2026, needs more optimization.
27 738 0.249202659154 Henry Cohn, 2026, needs more optimization.
27 739 0.249221668141 Henry Cohn, 2026, needs more optimization.
27 740 0.249293178857 Henry Cohn, 2026, needs more optimization.
27 741 0.249335995779 Henry Cohn, 2026, needs more optimization.
27 742 0.249373679373 Henry Cohn, 2026, needs more optimization.
27 744 0.249407831272 Henry Cohn, 2026, needs more optimization.
27 745 0.249457441570 Henry Cohn, 2026, needs more optimization.
27 747 0.249467911853 Henry Cohn, 2026, needs more optimization.
27 750 0.249469810399 Henry Cohn, 2026, needs more optimization.
27 751 0.249523465455 Henry Cohn, 2026, needs more optimization.
27 752 0.249556901882 Henry Cohn, 2026, needs more optimization.
27 753 0.249557563352 Henry Cohn, 2026, needs more optimization.
27 754 0.249611094888 Henry Cohn, 2026, needs more optimization.
27 755 0.249644295179 Henry Cohn, 2026, needs more optimization.
27 756 0.249685642032 Henry Cohn, 2026, needs more optimization.
27 758 0.249705053635 Henry Cohn, 2026, needs more optimization.
27 759 0.249747564171 Henry Cohn, 2026, needs more optimization.
27 760 0.249753688153 Henry Cohn, 2026, needs more optimization.
27 761 0.249772711656 Henry Cohn, 2026, needs more optimization.
27 762 0.249794810609 Henry Cohn, 2026, needs more optimization.
27 763 0.249804243368 Henry Cohn, 2026, needs more optimization.
27 764 0.249834427143 Henry Cohn, 2026, needs more optimization.
27 907 0.25 Orthogonal union of 891 points in 22 dimensions and 16 points in 5 dimensions.
4⁢x−1
27 909 0.250000470818 Numaro AI Autoresearch, 11,000+ New Verified Spherical-Code Records from AI Autoresearch, Numaro Research Report NUMARO-2026-015 (2026), https://numaro.tech/research/spherical-codes-2026/.
27 916 0.250001195341 Henry Cohn, 2026, needs more optimization.
27 919 0.250001286482 Henry Cohn, 2026, needs more optimization.
27 924 0.250001347628 Henry Cohn, 2026, needs more optimization.
27 934 0.250001764049 Henry Cohn, 2026, needs more optimization.
27 935 0.250002245028 Henry Cohn, 2026, needs more optimization.
27 936 0.250002373448 Henry Cohn, 2026, needs more optimization.
27 939 0.250002604798 Henry Cohn, 2026, needs more optimization.
27 940 0.250003271295 Henry Cohn, 2026, needs more optimization.
27 943 0.250003747149 Henry Cohn, 2026, needs more optimization.
27 945 0.250006026070 Henry Cohn, 2026, needs more optimization.
27 946 0.250045027394 Henry Cohn, 2026, needs more optimization.
27 947 0.250078939130 Henry Cohn, 2026, needs more optimization.
27 948 0.250085199160 Henry Cohn, 2026, needs more optimization.
27 949 0.250103088816 Henry Cohn, 2026, needs more optimization.
27 950 0.250114231628 Henry Cohn, 2026, needs more optimization.
27 951 0.250154131604 Henry Cohn, 2026, needs more optimization.
27 952 0.250200773810 Henry Cohn, 2026, needs more optimization.
27 954 0.250287573647 Henry Cohn, 2026, needs more optimization.
27 959 0.250296932681 Henry Cohn, 2026, needs more optimization.
27 961 0.250403398792 Henry Cohn, 2026, needs more optimization.
27 962 0.250510358485 Henry Cohn, 2026, needs more optimization.
27 964 0.250550396492 Henry Cohn, 2026, needs more optimization.
27 965 0.250645516991 Henry Cohn, 2026, needs more optimization.
27 966 0.250930278619 Henry Cohn, 2026, needs more optimization.
27 967 0.250973152877 Henry Cohn, 2026, needs more optimization.
27 968 0.251456660298 Henry Cohn, 2026, needs more optimization.
27 969 0.251782975233 Henry Cohn, 2026, needs more optimization.
27 970 0.251879027597 Henry Cohn, 2026, needs more optimization.
27 971 0.252168693576 Henry Cohn, 2026, needs more optimization.
27 972 0.252476632565 Henry Cohn, 2026, needs more optimization.
27 973 0.252489501968 Henry Cohn, 2026, needs more optimization.
27 974 0.252645033750 Henry Cohn, 2026, needs more optimization.
27 975 0.252908628697 Henry Cohn, 2026, needs more optimization.
27 976 0.253259100387 Henry Cohn, 2026, needs more optimization.
27 977 0.253933017507 Henry Cohn, 2026, needs more optimization.
27 978 0.254120857312 Henry Cohn, 2026, needs more optimization.
27 979 0.254618482341 Henry Cohn, 2026, needs more optimization.
27 980 0.254790335922 Henry Cohn, 2026, needs more optimization.
27 981 0.254972110284 Henry Cohn, 2026, needs more optimization.
27 982 0.255152799275 Henry Cohn, 2026, needs more optimization.
27 983 0.255365047017 Henry Cohn, 2026, needs more optimization.
27 984 0.255509174715 Henry Cohn, 2026, needs more optimization.
27 985 0.257137513853 Henry Cohn, 2026, needs more optimization.
27 986 0.257263392475 Henry Cohn, 2026, needs more optimization.
27 987 0.257452625704 Henry Cohn, 2026, needs more optimization.
27 988 0.257739411533 Henry Cohn, 2026, needs more optimization.
27 989 0.257898369893 Henry Cohn, 2026, needs more optimization.
27 990 0.258036725884 Henry Cohn, 2026, needs more optimization.
27 991 0.258971783664 Henry Cohn, 2026, needs more optimization.
27 992 0.259280383014 Henry Cohn, 2026, needs more optimization.
27 993 0.259651094152 Henry Cohn, 2026, needs more optimization.
27 994 0.260351786487 Henry Cohn, 2026, needs more optimization.
27 996 0.260412311239 Henry Cohn, 2026, needs more optimization.
27 997 0.260602739813 Henry Cohn, 2026, needs more optimization.
27 998 0.260803502790 Henry Cohn, 2026, needs more optimization.
27 999 0.260957774208 Henry Cohn, 2026, needs more optimization.
27 1000 0.261099134615 Henry Cohn, 2026, needs more optimization.
27 1001 0.262221828838 Henry Cohn, 2026, needs more optimization.
27 1002 0.262656603139 Henry Cohn, 2026, needs more optimization.
27 1003 0.263012776470 Henry Cohn, 2026, needs more optimization.
27 1004 0.263209941631 Henry Cohn, 2026, needs more optimization.
27 1005 0.263389081602 Henry Cohn, 2026, needs more optimization.
27 1006 0.263650969078 Henry Cohn, 2026, needs more optimization.
27 1007 0.263872291183 Henry Cohn, 2026, needs more optimization.
27 1008 0.264092197877 Henry Cohn, 2026, needs more optimization.
27 1009 0.264456280473 Henry Cohn, 2026, needs more optimization.
27 1010 0.264523688923 Henry Cohn, 2026, needs more optimization.
27 1011 0.264722632280 Henry Cohn, 2026, needs more optimization.
27 1012 0.264804385452 Henry Cohn, 2026, needs more optimization.
27 1013 0.265010504505 Henry Cohn, 2026, needs more optimization.
27 1014 0.265197196484 Henry Cohn, 2026, needs more optimization.
27 1015 0.265585187729 Henry Cohn, 2026, needs more optimization.
27 1016 0.265880126495 Henry Cohn, 2026, needs more optimization.
27 1017 0.266195604076 Henry Cohn, 2026, needs more optimization.
27 1018 0.266301793625 Henry Cohn, 2026, needs more optimization.
27 1019 0.266534639883 Henry Cohn, 2026, needs more optimization.
27 1020 0.266815407393 Henry Cohn, 2026, needs more optimization.
27 1021 0.267011716031 Henry Cohn, 2026, needs more optimization.
27 1022 0.267218793973 Henry Cohn, 2026, needs more optimization.
27 1023 0.267531641200 Henry Cohn, 2026, needs more optimization.
27 1024 0.267881465930 Henry Cohn, 2026, needs more optimization.
28 57 0.028627089329 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
18928⁢x3−784⁢x2−28⁢x+1
28 58 0.033333333334 H. Cohn, D. de Laat, and N. Leijenhorst, Optimality of spherical codes via exact semidefinite programming bounds, preprint, 2024, arXiv:2403.16874.
30⁢x−1
28 59 0.039693085758 Henry Cohn, 2026, needs more optimization.
28 60 0.039721697123 Henry Cohn, 2026.
28 61 0.039748128111 Henry Cohn, 2026.
28 62 0.044113391839 Henry Cohn, 2026, needs more optimization.
28 63 0.045182094797 Henry Cohn, 2026.
28 64 0.045901657151 Henry Cohn, 2024, needs more optimization.
28 65 0.046144411319 Henry Cohn, 2026.
28 66 0.047459655815 Henry Cohn, 2026.
28 67 0.052249912377 Henry Cohn, 2026.
28 68 0.054257387201 Henry Cohn, 2026.
28 69 0.055901485675 Henry Cohn, 2026, needs more optimization.
28 70 0.058160699163 Henry Cohn, 2026, needs more optimization.
28 71 0.059586716587 Henry Cohn, 2026.
28 72 0.061336054837 Henry Cohn, 2026.
28 73 0.063218203873 Henry Cohn, 2026, needs more optimization.
28 74 0.063890997132 Henry Cohn, 2026, needs more optimization.
28 75 0.064434742778 Henry Cohn, 2026, needs more optimization.
28 76 0.064717246550 Henry Cohn, 2026, needs more optimization.
28 77 0.065922164600 Henry Cohn, 2026, needs more optimization.
28 78 0.067448950547 Henry Cohn, 2026, needs more optimization.
28 79 0.069479913814 Henry Cohn, 2026, needs more optimization.
28 80 0.070910361346 Henry Cohn, 2026, needs more optimization.
28 81 0.072768932730 Henry Cohn, 2026, needs more optimization.
28 82 0.074527160880 Henry Cohn, 2026, needs more optimization.
28 83 0.074837431449 Henry Cohn, 2026, needs more optimization.
28 84 0.075982738095 Henry Cohn, 2026, needs more optimization.
28 85 0.076676451117 Henry Cohn, 2026, needs more optimization.
28 86 0.076860480296 Henry Cohn, 2026, needs more optimization.
28 87 0.076905025239 Henry Cohn, 2026, needs more optimization.
28 88 0.076923523265 Henry Cohn, 2026, needs more optimization.
28 89 0.077231167153 Henry Cohn, 2026, needs more optimization.
28 90 0.077490902559 Henry Cohn, 2026, needs more optimization.
28 91 0.078290622906 Henry Cohn, 2026, needs more optimization.
28 92 0.078673310150 Henry Cohn, 2026, needs more optimization.
28 93 0.079213328765 Henry Cohn, 2026, needs more optimization.
28 94 0.079375595124 Henry Cohn, 2026, needs more optimization.
28 95 0.079798734737 Henry Cohn, 2026, needs more optimization.
28 96 0.080118153231 Henry Cohn, 2026, needs more optimization.
28 97 0.080241546072 Henry Cohn, 2026, needs more optimization.
28 98 0.080465072965 Henry Cohn, 2026, needs more optimization.
28 99 0.080634601073 Henry Cohn, 2026, needs more optimization.
28 100 0.080685071015 Henry Cohn, 2026, needs more optimization.
28 101 0.080685483983 Henry Cohn, 2026, needs more optimization.
28 102 0.080896647377 Henry Cohn, 2026, needs more optimization.
28 103 0.083869990082 Henry Cohn, 2026, needs more optimization.
28 104 0.085671211384 Henry Cohn, 2026, needs more optimization.
28 105 0.086914864601 Henry Cohn, 2026, needs more optimization.
28 106 0.088256960913 Henry Cohn, 2026, needs more optimization.
28 107 0.088683066625 Henry Cohn, 2026, needs more optimization.
28 108 0.089272765939 Henry Cohn, 2026, needs more optimization.
28 109 0.089566495355 Henry Cohn, 2026, needs more optimization.
28 110 0.089694208604 Henry Cohn, 2026, needs more optimization.
28 111 0.089783503541 Henry Cohn, 2026, needs more optimization.
28 112 0.090075963123 Henry Cohn, 2026, needs more optimization.
28 113 0.090252043255 Henry Cohn, 2026, needs more optimization.
28 114 0.090520305102 Henry Cohn, 2026, needs more optimization.
28 115 0.090761771980 Henry Cohn, 2026, needs more optimization.
28 116 0.090836283906 Henry Cohn, 2026, needs more optimization.
28 117 0.090872950145 Henry Cohn, 2026, needs more optimization.
28 118 0.091674123086 Henry Cohn, 2026, needs more optimization.
28 119 0.093902195725 Henry Cohn, 2026, needs more optimization.
28 120 0.096028126221 Henry Cohn, 2026, needs more optimization.
28 121 0.098093429376 Henry Cohn, 2026, needs more optimization.
28 122 0.099649899680 Henry Cohn, 2026, needs more optimization.
28 123 0.101610350568 Henry Cohn, 2026, needs more optimization.
28 124 0.102422528072 Henry Cohn, 2026, needs more optimization.
28 125 0.102478287302 Henry Cohn, 2026, needs more optimization.
28 126 0.102882702251 Henry Cohn, 2026, needs more optimization.
28 127 0.102892415675 Henry Cohn, 2026, needs more optimization.
28 128 0.103048201987 Henry Cohn, 2026, needs more optimization.
28 129 0.103102421109 Henry Cohn, 2026, needs more optimization.
28 130 0.103120603774 Henry Cohn, 2026, needs more optimization.
28 131 0.104307860539 Henry Cohn, 2026, needs more optimization.
28 132 0.105404226627 Henry Cohn, 2026, needs more optimization.
28 133 0.106248446822 Henry Cohn, 2026, needs more optimization.
28 134 0.107850775608 Henry Cohn, 2026, needs more optimization.
28 135 0.108597892846 Henry Cohn, 2026, needs more optimization.
28 136 0.109042528183 Henry Cohn, 2026, needs more optimization.
28 137 0.109744749102 Henry Cohn, 2026, needs more optimization.
28 138 0.110880682636 Henry Cohn, 2026, needs more optimization.
28 139 0.110913418329 Henry Cohn, 2026, needs more optimization.
28 140 0.110988698107 Henry Cohn, 2026, needs more optimization.
28 150 0.111111111112 Henry Cohn, 2026.
9⁢x−1
28 151 0.111556075883 Henry Cohn, 2026.
73⁢x2−44⁢x+4
28 152 0.116948610781 Henry Cohn, 2026.
28 153 0.119770666825 Henry Cohn, 2026, needs more optimization.
28 154 0.122975008722 Henry Cohn, 2026, needs more optimization.
28 155 0.125261838113 Henry Cohn, 2026, needs more optimization.
28 156 0.126321828678 Henry Cohn, 2026, needs more optimization.
28 157 0.127118914492 Henry Cohn, 2026, needs more optimization.
28 158 0.127740447125 Henry Cohn, 2026, needs more optimization.
28 159 0.128111924495 Henry Cohn, 2026, needs more optimization.
28 182 0.128238684469 Henry Cohn, 2026.
92⁢x2−4⁢x−1
28 183 0.130665724291 Henry Cohn, 2026.
28 184 0.141612907758 Henry Cohn, 2026, needs more optimization.
28 185 0.142134537441 Henry Cohn, 2026, needs more optimization.
28 186 0.142160300417 Henry Cohn, 2026, needs more optimization.
28 187 0.142165777958 Henry Cohn, 2026, needs more optimization.
28 188 0.142186239557 Henry Cohn, 2026, needs more optimization.
28 189 0.142222207428 Henry Cohn, 2026, needs more optimization.
28 190 0.142238602470 Henry Cohn, 2026, needs more optimization.
28 191 0.142253081385 Henry Cohn, 2026, needs more optimization.
28 192 0.142393053269 Henry Cohn, 2026, needs more optimization.
28 193 0.142482288606 Henry Cohn, 2026, needs more optimization.
28 194 0.142529317105 Henry Cohn, 2026, needs more optimization.
28 195 0.142599783787 Henry Cohn, 2026, needs more optimization.
28 196 0.142694693630 Henry Cohn, 2026, needs more optimization.
28 197 0.142754918547 Henry Cohn, 2026, needs more optimization.
28 198 0.142783065611 Henry Cohn, 2026, needs more optimization.
28 199 0.142878383882 Henry Cohn, 2026, needs more optimization.
28 200 0.143368710274 Henry Cohn, 2026, needs more optimization.
28 201 0.143695963028 Henry Cohn, 2026, needs more optimization.
28 202 0.144186927106 Henry Cohn, 2026, needs more optimization.
28 203 0.145065828044 Henry Cohn, 2026, needs more optimization.
28 204 0.145910827661 Henry Cohn, 2026, needs more optimization.
28 205 0.145967734632 Henry Cohn, 2026, needs more optimization.
28 206 0.145967762819 Henry Cohn, 2026, needs more optimization.
28 207 0.145967792762 Henry Cohn, 2026, needs more optimization.
28 208 0.146064111966 Henry Cohn, 2026, needs more optimization.
28 209 0.146200636669 Henry Cohn, 2026, needs more optimization.
28 210 0.146202041176 Henry Cohn, 2026, needs more optimization.
28 211 0.146290571582 Henry Cohn, 2026, needs more optimization.
28 212 0.146444913568 Henry Cohn, 2026, needs more optimization.
28 213 0.146890417504 Henry Cohn, 2026, needs more optimization.
28 214 0.147041538525 Henry Cohn, 2026, needs more optimization.
28 215 0.147122272184 Henry Cohn, 2026, needs more optimization.
28 216 0.147126967275 Henry Cohn, 2026, needs more optimization.
28 217 0.147212224526 Henry Cohn, 2026, needs more optimization.
28 218 0.147330631231 Henry Cohn, 2026, needs more optimization.
28 219 0.147390845345 Henry Cohn, 2026, needs more optimization.
28 220 0.147494289866 Henry Cohn, 2026, needs more optimization.
28 221 0.147570500739 Henry Cohn, 2026, needs more optimization.
28 222 0.147654285752 Henry Cohn, 2026, needs more optimization.
28 224 0.147655356096 Henry Cohn, 2026, needs more optimization.
28 225 0.147664586412 Henry Cohn, 2026, needs more optimization.
28 226 0.147673589655 Henry Cohn, 2026, needs more optimization.
28 227 0.147747040683 Henry Cohn, 2026, needs more optimization.
28 228 0.147894789288 Henry Cohn, 2026, needs more optimization.
28 229 0.148221536311 Henry Cohn, 2026, needs more optimization.
28 230 0.148960792540 Henry Cohn, 2026, needs more optimization.
28 231 0.149101618571 Henry Cohn, 2026, needs more optimization.
28 232 0.149210290026 Henry Cohn, 2026, needs more optimization.
28 233 0.149282991821 Henry Cohn, 2026, needs more optimization.
28 234 0.149287517627 Henry Cohn, 2026, needs more optimization.
28 235 0.149313500539 Henry Cohn, 2026, needs more optimization.
28 236 0.149321973650 Henry Cohn, 2026, needs more optimization.
28 237 0.149321973864 Henry Cohn, 2026, needs more optimization.
28 238 0.149323892304 Henry Cohn, 2026, needs more optimization.
28 239 0.149422637246 Henry Cohn, 2026, needs more optimization.
28 240 0.150164164131 Henry Cohn, 2026, needs more optimization.
28 241 0.150635161664 Henry Cohn, 2026, needs more optimization.
28 242 0.151813774910 Henry Cohn, 2026, needs more optimization.
28 243 0.152630076010 Henry Cohn, 2026, needs more optimization.
28 244 0.154126393975 Henry Cohn, 2026, needs more optimization.
28 245 0.155239042749 Henry Cohn, 2026, needs more optimization.
28 246 0.156941063863 Henry Cohn, 2026, needs more optimization.
28 247 0.157034935339 Henry Cohn, 2026, needs more optimization.
28 248 0.157636036709 Henry Cohn, 2026, needs more optimization.
28 249 0.158610062466 Henry Cohn, 2026, needs more optimization.
28 250 0.160096626445 Henry Cohn, 2026, needs more optimization.
28 251 0.161289121759 Henry Cohn, 2026, needs more optimization.
28 252 0.162023968701 Henry Cohn, 2026, needs more optimization.
28 253 0.162048304048 Henry Cohn, 2026, needs more optimization.
28 254 0.162087895795 Henry Cohn, 2026, needs more optimization.
28 255 0.162159451447 Henry Cohn, 2026, needs more optimization.
28 256 0.162395264023 Henry Cohn, 2026, needs more optimization.
28 257 0.162657806430 Henry Cohn, 2026, needs more optimization.
28 258 0.162868775961 Henry Cohn, 2026, needs more optimization.
28 259 0.163030888409 Henry Cohn, 2026, needs more optimization.
28 260 0.163399112088 Henry Cohn, 2026, needs more optimization.
28 261 0.163581237060 Henry Cohn, 2026, needs more optimization.
28 262 0.163784050500 Henry Cohn, 2026, needs more optimization.
28 263 0.163903066200 Henry Cohn, 2026, needs more optimization.
28 264 0.164106472106 Henry Cohn, 2026, needs more optimization.
28 265 0.164309902704 Henry Cohn, 2026, needs more optimization.
28 266 0.164635950273 Henry Cohn, 2026, needs more optimization.
28 267 0.164742839869 Henry Cohn, 2026, needs more optimization.
28 268 0.164799603624 Henry Cohn, 2026, needs more optimization.
28 269 0.164799647978 Henry Cohn, 2026, needs more optimization.
28 270 0.164892390854 Henry Cohn, 2026, needs more optimization.
28 271 0.164945459552 Henry Cohn, 2026, needs more optimization.
28 272 0.165059726376 Henry Cohn, 2026, needs more optimization.
28 273 0.165217971963 Henry Cohn, 2026, needs more optimization.
28 274 0.165332510132 Henry Cohn, 2026, needs more optimization.
28 275 0.165345950285 Henry Cohn, 2026, needs more optimization.
28 276 0.165429940997 Henry Cohn, 2026, needs more optimization.
28 277 0.165459048256 Henry Cohn, 2026, needs more optimization.
28 278 0.165571548803 Henry Cohn, 2026, needs more optimization.
28 279 0.165623485217 Henry Cohn, 2026, needs more optimization.
28 280 0.165653509848 Henry Cohn, 2026, needs more optimization.
28 281 0.165680161772 Henry Cohn, 2026, needs more optimization.
28 282 0.165744881098 Henry Cohn, 2026, needs more optimization.
28 283 0.165839616360 Henry Cohn, 2026, needs more optimization.
28 284 0.165871960134 Henry Cohn, 2026, needs more optimization.
28 285 0.165912912849 Henry Cohn, 2026, needs more optimization.
28 286 0.166030766294 Henry Cohn, 2026, needs more optimization.
28 287 0.166106289301 Henry Cohn, 2026, needs more optimization.
28 288 0.166165580258 Henry Cohn, 2026, needs more optimization.
28 289 0.166282641041 Henry Cohn, 2026, needs more optimization.
28 290 0.166327184103 Henry Cohn, 2026, needs more optimization.
28 291 0.166351700675 Henry Cohn, 2026, needs more optimization.
28 292 0.166365391723 Henry Cohn, 2026, needs more optimization.
28 293 0.166408606854 Henry Cohn, 2026, needs more optimization.
28 294 0.166454323513 Henry Cohn, 2026, needs more optimization.
28 295 0.166461656290 Henry Cohn, 2026, needs more optimization.
28 296 0.166472424199 Henry Cohn, 2026, needs more optimization.
28 297 0.166488082392 Henry Cohn, 2026, needs more optimization.
28 298 0.166507055857 Henry Cohn, 2026, needs more optimization.
28 299 0.166524204768 Henry Cohn, 2026, needs more optimization.
28 300 0.166555720888 Henry Cohn, 2026, needs more optimization.
28 301 0.166578498571 Henry Cohn, 2026, needs more optimization.
28 302 0.166594403052 Henry Cohn, 2026, needs more optimization.
28 305 0.166664601532 Henry Cohn, 2026, needs more optimization.
28 306 0.166664853656 Henry Cohn, 2026, needs more optimization.
28 307 0.166665061912 Henry Cohn, 2026, needs more optimization.
28 309 0.166667684933 Henry Cohn, 2026, needs more optimization.
28 311 0.166675263896 Henry Cohn, 2026, needs more optimization.
28 312 0.166678670896 Henry Cohn, 2026, needs more optimization.
28 313 0.166710367107 Henry Cohn, 2026, needs more optimization.
28 314 0.167083014087 Henry Cohn, 2026, needs more optimization.
28 315 0.167156886828 Henry Cohn, 2026, needs more optimization.
28 316 0.167668405579 Henry Cohn, 2026, needs more optimization.
28 317 0.168016481861 Henry Cohn, 2026, needs more optimization.
28 318 0.168664679821 Henry Cohn, 2026, needs more optimization.
28 319 0.169467863373 Henry Cohn, 2026, needs more optimization.
28 320 0.170175271796 Henry Cohn, 2026, needs more optimization.
28 321 0.171459699247 Henry Cohn, 2026, needs more optimization.
28 322 0.171962510728 Henry Cohn, 2026, needs more optimization.
28 323 0.172993681824 Henry Cohn, 2026, needs more optimization.
28 324 0.173490189655 Henry Cohn, 2026, needs more optimization.
28 325 0.174925622893 Henry Cohn, 2026, needs more optimization.
28 326 0.175613097170 Henry Cohn, 2026, needs more optimization.
28 327 0.176198749505 Henry Cohn, 2026, needs more optimization.
28 328 0.177114761462 Henry Cohn, 2026, needs more optimization.
28 329 0.178572130574 Henry Cohn, 2026, needs more optimization.
28 330 0.178572529269 Henry Cohn, 2026, needs more optimization.
28 331 0.178574790785 Henry Cohn, 2026, needs more optimization.
28 332 0.178626349962 Henry Cohn, 2026, needs more optimization.
28 333 0.178879419467 Henry Cohn, 2026, needs more optimization.
28 334 0.178890611591 Henry Cohn, 2026, needs more optimization.
28 335 0.179502185510 Henry Cohn, 2026, needs more optimization.
28 336 0.180152541440 Henry Cohn, 2026, needs more optimization.
28 337 0.180154451498 Henry Cohn, 2026, needs more optimization.
28 338 0.180528943429 Henry Cohn, 2026, needs more optimization.
28 339 0.181434983572 Henry Cohn, 2026, needs more optimization.
28 340 0.181478349918 Henry Cohn, 2026, needs more optimization.
28 341 0.181558621537 Henry Cohn, 2026, needs more optimization.
28 342 0.181625774034 Henry Cohn, 2026, needs more optimization.
28 343 0.181657039724 Henry Cohn, 2026, needs more optimization.
28 344 0.181736943140 Henry Cohn, 2026, needs more optimization.
28 345 0.181778943187 Henry Cohn, 2026, needs more optimization.
28 346 0.181804786234 Henry Cohn, 2026, needs more optimization.
28 347 0.181821081974 Henry Cohn, 2026, needs more optimization.
28 348 0.181827373674 Henry Cohn, 2026, needs more optimization.
28 349 0.181838848178 Henry Cohn, 2026, needs more optimization.
28 350 0.181871377898 Henry Cohn, 2026, needs more optimization.
28 351 0.182081045108 Henry Cohn, 2026, needs more optimization.
28 352 0.182373425246 Henry Cohn, 2026, needs more optimization.
28 353 0.182641933695 Henry Cohn, 2026, needs more optimization.
28 354 0.183646465383 Henry Cohn, 2026, needs more optimization.
28 355 0.184384543959 Henry Cohn, 2026, needs more optimization.
28 356 0.184954483762 Henry Cohn, 2026, needs more optimization.
28 357 0.185207190386 Henry Cohn, 2026, needs more optimization.
28 358 0.185760621601 Henry Cohn, 2026, needs more optimization.
28 359 0.186352225993 Henry Cohn, 2026, needs more optimization.
28 360 0.186521045250 Henry Cohn, 2026, needs more optimization.
28 361 0.191559270389 Henry Cohn, 2026, needs more optimization.
28 362 0.191806250951 Henry Cohn, 2026, needs more optimization.
28 363 0.192269130099 Henry Cohn, 2026, needs more optimization.
28 364 0.192378316359 Henry Cohn, 2026, needs more optimization.
28 365 0.192450824779 Henry Cohn, 2026, needs more optimization.
28 366 0.192548051540 Henry Cohn, 2026, needs more optimization.
28 367 0.192831871255 Henry Cohn, 2026, needs more optimization.
28 368 0.192977705975 Henry Cohn, 2026, needs more optimization.
28 369 0.193181456251 Henry Cohn, 2026, needs more optimization.
28 370 0.193377452998 Henry Cohn, 2026, needs more optimization.
28 371 0.193718412876 Henry Cohn, 2026, needs more optimization.
28 372 0.193815493299 Henry Cohn, 2026, needs more optimization.
28 373 0.193986316452 Henry Cohn, 2026, needs more optimization.
28 374 0.194190904616 Henry Cohn, 2026, needs more optimization.
28 375 0.194392525657 Henry Cohn, 2026, needs more optimization.
28 376 0.194594616192 Henry Cohn, 2026, needs more optimization.
28 377 0.194704398385 Henry Cohn, 2026, needs more optimization.
28 378 0.194949370950 Henry Cohn, 2026, needs more optimization.
28 379 0.195078460951 Henry Cohn, 2026, needs more optimization.
28 380 0.195360983339 Henry Cohn, 2026, needs more optimization.
28 381 0.195575679113 Henry Cohn, 2026, needs more optimization.
28 382 0.195677088974 Henry Cohn, 2026, needs more optimization.
28 383 0.195873606950 Henry Cohn, 2026, needs more optimization.
28 384 0.195998945633 Henry Cohn, 2026, needs more optimization.
28 385 0.196171898822 Henry Cohn, 2026, needs more optimization.
28 386 0.196195748490 Henry Cohn, 2026, needs more optimization.
28 387 0.196364420611 Henry Cohn, 2026, needs more optimization.
28 388 0.196487868042 Henry Cohn, 2026, needs more optimization.
28 389 0.196674644647 Henry Cohn, 2026, needs more optimization.
28 390 0.196819305174 Henry Cohn, 2026, needs more optimization.
28 391 0.196851276357 Henry Cohn, 2026, needs more optimization.
28 392 0.196985210655 Henry Cohn, 2026, needs more optimization.
28 393 0.197067697745 Henry Cohn, 2026, needs more optimization.
28 394 0.197171194291 Henry Cohn, 2026, needs more optimization.
28 395 0.197348467643 Henry Cohn, 2026, needs more optimization.
28 396 0.197414067741 Henry Cohn, 2026, needs more optimization.
28 397 0.197439053835 Henry Cohn, 2026, needs more optimization.
28 398 0.197529936427 Henry Cohn, 2026, needs more optimization.
28 399 0.197603310768 Henry Cohn, 2026, needs more optimization.
28 400 0.197756103545 Henry Cohn, 2026, needs more optimization.
28 401 0.197846176821 Henry Cohn, 2026, needs more optimization.
28 402 0.197894608876 Henry Cohn, 2026, needs more optimization.
28 403 0.198081137386 Henry Cohn, 2026, needs more optimization.
28 404 0.198148368017 Henry Cohn, 2026, needs more optimization.
28 405 0.198153741065 Henry Cohn, 2026, needs more optimization.
28 406 0.198246163766 Henry Cohn, 2026, needs more optimization.
28 407 0.198250982327 Henry Cohn, 2026, needs more optimization.
28 408 0.198460492272 Henry Cohn, 2026, needs more optimization.
28 409 0.198527860535 Henry Cohn, 2026, needs more optimization.
28 410 0.198550887130 Henry Cohn, 2026, needs more optimization.
28 411 0.198616696170 Henry Cohn, 2026, needs more optimization.
28 412 0.198629682941 Henry Cohn, 2026, needs more optimization.
28 413 0.198672015339 Henry Cohn, 2026, needs more optimization.
28 414 0.198757314373 Henry Cohn, 2026, needs more optimization.
28 415 0.198792608467 Henry Cohn, 2026, needs more optimization.
28 416 0.198886161708 Henry Cohn, 2026, needs more optimization.
28 417 0.198920838928 Henry Cohn, 2026, needs more optimization.
28 418 0.199021706424 Henry Cohn, 2026, needs more optimization.
28 419 0.199041732066 Henry Cohn, 2026, needs more optimization.
28 420 0.199049115252 Henry Cohn, 2026, needs more optimization.
28 421 0.199121950358 Henry Cohn, 2026, needs more optimization.
28 422 0.199137813725 Henry Cohn, 2026, needs more optimization.
28 423 0.199202229571 Henry Cohn, 2026, needs more optimization.
28 424 0.199223681482 Henry Cohn, 2026, needs more optimization.
28 425 0.199255848398 Henry Cohn, 2026, needs more optimization.
28 426 0.199345140095 Henry Cohn, 2026, needs more optimization.
28 427 0.199363023774 Henry Cohn, 2026, needs more optimization.
28 428 0.199382349622 Henry Cohn, 2026, needs more optimization.
28 429 0.199424928906 Henry Cohn, 2026, needs more optimization.
28 430 0.199468080142 Henry Cohn, 2026, needs more optimization.
28 431 0.199485525772 Henry Cohn, 2026, needs more optimization.
28 432 0.199502762692 Henry Cohn, 2026, needs more optimization.
28 433 0.199503700864 Henry Cohn, 2026, needs more optimization.
28 434 0.199536598184 Henry Cohn, 2026, needs more optimization.
28 435 0.199556771986 Henry Cohn, 2026, needs more optimization.
28 436 0.199599099976 Henry Cohn, 2026, needs more optimization.
28 437 0.199615157347 Henry Cohn, 2026, needs more optimization.
28 438 0.199660914097 Henry Cohn, 2026, needs more optimization.
28 439 0.199671918588 Henry Cohn, 2026, needs more optimization.
28 440 0.199678704219 Henry Cohn, 2026, needs more optimization.
28 441 0.199685366074 Henry Cohn, 2026, needs more optimization.
28 442 0.199699724647 Henry Cohn, 2026, needs more optimization.
28 443 0.199710086817 Henry Cohn, 2026, needs more optimization.
28 444 0.199736131114 Henry Cohn, 2026, needs more optimization.
28 445 0.199751566184 Henry Cohn, 2026, needs more optimization.
28 446 0.199798466109 Henry Cohn, 2026, needs more optimization.
28 447 0.199816596262 Henry Cohn, 2026, needs more optimization.
28 448 0.199840647429 Henry Cohn, 2026, needs more optimization.
28 449 0.199841358804 Henry Cohn, 2026, needs more optimization.
28 450 0.199852446793 Henry Cohn, 2026, needs more optimization.
28 451 0.199860753095 Henry Cohn, 2026, needs more optimization.
28 452 0.199869501777 Henry Cohn, 2026, needs more optimization.
28 453 0.199877908391 Henry Cohn, 2026, needs more optimization.
28 455 0.199900919098 Henry Cohn, 2026, needs more optimization.
28 456 0.199909449419 Henry Cohn, 2026, needs more optimization.
28 457 0.199914652831 Henry Cohn, 2026, needs more optimization.
28 458 0.199921835995 Henry Cohn, 2026, needs more optimization.
28 459 0.199926452134 Henry Cohn, 2026, needs more optimization.
28 460 0.199950308219 Henry Cohn, 2026, needs more optimization.
28 568 0.2 Orthogonal union of 552 points in 23 dimensions and 16 points in 5 dimensions.
5⁢x−1
28 572 0.200000846011 Henry Cohn, 2026, needs more optimization.
28 573 0.200001189008 Henry Cohn, 2026, needs more optimization.
28 577 0.200001485942 Henry Cohn, 2026, needs more optimization.
28 580 0.200001949653 Henry Cohn, 2026, needs more optimization.
28 582 0.200003603766 Henry Cohn, 2026, needs more optimization.
28 583 0.200004241438 Henry Cohn, 2026, needs more optimization.
28 584 0.200005318830 Henry Cohn, 2026, needs more optimization.
28 585 0.200006674863 Henry Cohn, 2026, needs more optimization.
28 586 0.200011265434 Henry Cohn, 2026, needs more optimization.
28 587 0.200033985961 Henry Cohn, 2026, needs more optimization.
28 588 0.200064207352 Henry Cohn, 2026, needs more optimization.
28 589 0.200073428224 Henry Cohn, 2026, needs more optimization.
28 590 0.200214224021 Henry Cohn, 2026, needs more optimization.
28 591 0.200332316610 Henry Cohn, 2026, needs more optimization.
28 592 0.200471023180 Henry Cohn, 2026, needs more optimization.
28 593 0.200830117510 Henry Cohn, 2026, needs more optimization.
28 594 0.200944450792 Henry Cohn, 2026, needs more optimization.
28 595 0.201675152100 Henry Cohn, 2026, needs more optimization.
28 596 0.202223988177 Henry Cohn, 2026, needs more optimization.
28 597 0.202945893572 Henry Cohn, 2026, needs more optimization.
28 598 0.203369903952 Henry Cohn, 2026, needs more optimization.
28 599 0.203957527033 Henry Cohn, 2026, needs more optimization.
28 600 0.204521399507 Henry Cohn, 2026, needs more optimization.
28 601 0.237154357989 Henry Cohn, 2026, needs more optimization.
28 602 0.237188104652 Henry Cohn, 2026, needs more optimization.
28 604 0.237205503816 Henry Cohn, 2026, needs more optimization.
28 606 0.237217193753 Henry Cohn, 2026, needs more optimization.
28 608 0.237467362579 Henry Cohn, 2026, needs more optimization.
28 610 0.237515120908 Henry Cohn, 2026, needs more optimization.
28 612 0.237541849396 Henry Cohn, 2026, needs more optimization.
28 613 0.237662581404 Henry Cohn, 2026, needs more optimization.
28 614 0.237689543669 Henry Cohn, 2026, needs more optimization.
28 619 0.238007395004 Henry Cohn, 2026, needs more optimization.
28 632 0.238024777968 Henry Cohn, 2026, needs more optimization.
28 637 0.238027873184 Henry Cohn, 2026, needs more optimization.
28 660 0.238090160858 Henry Cohn, 2026, needs more optimization.
28 661 0.238092771913 Henry Cohn, 2026, needs more optimization.
28 662 0.238098259641 Henry Cohn, 2026, needs more optimization.
28 666 0.238114315332 Henry Cohn, 2026, needs more optimization.
28 667 0.238118008650 Henry Cohn, 2026, needs more optimization.
28 671 0.238132980445 Henry Cohn, 2026, needs more optimization.
28 673 0.238149966112 Henry Cohn, 2026, needs more optimization.
28 677 0.238153585541 Henry Cohn, 2026, needs more optimization.
28 678 0.238181647104 Henry Cohn, 2026, needs more optimization.
28 680 0.238217293806 Henry Cohn, 2026, needs more optimization.
28 685 0.238325378420 Henry Cohn, 2026, needs more optimization.
28 686 0.238337431626 Henry Cohn, 2026, needs more optimization.
28 687 0.238615690812 Henry Cohn, 2026, needs more optimization.
28 688 0.238706442131 Henry Cohn, 2026, needs more optimization.
28 689 0.238925871640 Henry Cohn, 2026, needs more optimization.
28 690 0.238955551333 Henry Cohn, 2026, needs more optimization.
28 692 0.239042141509 Henry Cohn, 2026, needs more optimization.
28 694 0.239611182225 Henry Cohn, 2026, needs more optimization.
28 695 0.239865047753 Henry Cohn, 2026, needs more optimization.
28 696 0.240286589463 Henry Cohn, 2026, needs more optimization.
28 697 0.240303239225 Henry Cohn, 2026, needs more optimization.
28 698 0.240626007142 Henry Cohn, 2026, needs more optimization.
28 699 0.240713875201 Henry Cohn, 2026, needs more optimization.
28 700 0.241109070125 Henry Cohn, 2026, needs more optimization.
28 701 0.241216988162 Henry Cohn, 2026, needs more optimization.
28 703 0.241345060258 Henry Cohn, 2026, needs more optimization.
28 704 0.241424248531 Henry Cohn, 2026, needs more optimization.
28 705 0.241518574489 Henry Cohn, 2026, needs more optimization.
28 707 0.241641383365 Henry Cohn, 2026, needs more optimization.
28 708 0.241894946031 Henry Cohn, 2026, needs more optimization.
28 710 0.242093750126 Henry Cohn, 2026, needs more optimization.
28 711 0.242608696676 Henry Cohn, 2026, needs more optimization.
28 712 0.242810643711 Henry Cohn, 2026, needs more optimization.
28 713 0.242876242002 Henry Cohn, 2026, needs more optimization.
28 714 0.243031881106 Henry Cohn, 2026, needs more optimization.
28 716 0.243239666432 Henry Cohn, 2026, needs more optimization.
28 717 0.243806004181 Henry Cohn, 2026, needs more optimization.
28 718 0.247479874062 Henry Cohn, 2026, needs more optimization.
28 720 0.247515542216 Henry Cohn, 2026, needs more optimization.
28 721 0.247572702049 Henry Cohn, 2026, needs more optimization.
28 722 0.247610991792 Henry Cohn, 2026, needs more optimization.
28 723 0.247628283551 Henry Cohn, 2026, needs more optimization.
28 724 0.247633248545 Henry Cohn, 2026, needs more optimization.
28 725 0.247638993717 Henry Cohn, 2026, needs more optimization.
28 726 0.247689930683 Henry Cohn, 2026, needs more optimization.
28 727 0.247711369901 Henry Cohn, 2026, needs more optimization.
28 731 0.247845831745 Henry Cohn, 2026, needs more optimization.
28 732 0.247875650532 Henry Cohn, 2026, needs more optimization.
28 735 0.247952943095 Henry Cohn, 2026, needs more optimization.
28 736 0.248038518637 Henry Cohn, 2026, needs more optimization.
28 737 0.248091084843 Henry Cohn, 2026, needs more optimization.
28 738 0.248126908084 Henry Cohn, 2026, needs more optimization.
28 739 0.248161064435 Henry Cohn, 2026, needs more optimization.
28 740 0.248183620209 Henry Cohn, 2026, needs more optimization.
28 741 0.248214594810 Henry Cohn, 2026, needs more optimization.
28 742 0.248295463406 Henry Cohn, 2026, needs more optimization.
28 744 0.248303067387 Henry Cohn, 2026, needs more optimization.
28 746 0.248374566960 Henry Cohn, 2026, needs more optimization.
28 747 0.248438621310 Henry Cohn, 2026, needs more optimization.
28 748 0.248461466332 Henry Cohn, 2026, needs more optimization.
28 749 0.248492659899 Henry Cohn, 2026, needs more optimization.
28 750 0.248565360724 Henry Cohn, 2026, needs more optimization.
28 751 0.248606789925 Henry Cohn, 2026, needs more optimization.
28 752 0.248650132927 Henry Cohn, 2026, needs more optimization.
28 753 0.248686429254 Henry Cohn, 2026, needs more optimization.
28 754 0.248738534321 Henry Cohn, 2026, needs more optimization.
28 755 0.248779185516 Henry Cohn, 2026, needs more optimization.
28 756 0.248819935669 Henry Cohn, 2026, needs more optimization.
28 757 0.248865337906 Henry Cohn, 2026, needs more optimization.
28 759 0.248910052504 Henry Cohn, 2026, needs more optimization.
28 760 0.248918220136 Henry Cohn, 2026, needs more optimization.
28 761 0.248971101405 Henry Cohn, 2026, needs more optimization.
28 762 0.249000781960 Henry Cohn, 2026, needs more optimization.
28 763 0.249005765124 Henry Cohn, 2026, needs more optimization.
28 764 0.249044456391 Henry Cohn, 2026, needs more optimization.
28 765 0.249059996713 Henry Cohn, 2026, needs more optimization.
28 766 0.249099527800 Henry Cohn, 2026, needs more optimization.
28 767 0.249126893218 Henry Cohn, 2026, needs more optimization.
28 768 0.249158246522 Henry Cohn, 2026, needs more optimization.
28 769 0.249184533710 Henry Cohn, 2026, needs more optimization.
28 770 0.249204794525 Henry Cohn, 2026, needs more optimization.
28 771 0.249234793670 Henry Cohn, 2026, needs more optimization.
28 772 0.249250359374 Henry Cohn, 2026, needs more optimization.
28 773 0.249270353288 Henry Cohn, 2026, needs more optimization.
28 774 0.249302387198 Henry Cohn, 2026, needs more optimization.
28 775 0.249318248507 Henry Cohn, 2026, needs more optimization.
28 776 0.249351552471 Henry Cohn, 2026, needs more optimization.
28 777 0.249378491287 Henry Cohn, 2026, needs more optimization.
28 778 0.249396137617 Henry Cohn, 2026, needs more optimization.
28 779 0.249401698894 Henry Cohn, 2026, needs more optimization.
28 780 0.249404888354 Henry Cohn, 2026, needs more optimization.
28 781 0.249419937587 Henry Cohn, 2026, needs more optimization.
28 782 0.249442086254 Henry Cohn, 2026, needs more optimization.
28 783 0.249458473140 Henry Cohn, 2026, needs more optimization.
28 784 0.249482098399 Henry Cohn, 2026, needs more optimization.
28 785 0.249516523179 Henry Cohn, 2026, needs more optimization.
28 786 0.249533905997 Henry Cohn, 2026, needs more optimization.
28 788 0.249534235596 Henry Cohn, 2026, needs more optimization.
28 789 0.249543903161 Henry Cohn, 2026, needs more optimization.
28 790 0.249547164819 Henry Cohn, 2026, needs more optimization.
28 791 0.249557128049 Henry Cohn, 2026, needs more optimization.
28 792 0.249564007235 Henry Cohn, 2026, needs more optimization.
28 793 0.249588547322 Henry Cohn, 2026, needs more optimization.
28 794 0.249596410224 Henry Cohn, 2026, needs more optimization.
28 795 0.249614644876 Henry Cohn, 2026, needs more optimization.
28 796 0.249616948496 Henry Cohn, 2026, needs more optimization.
28 797 0.249628170060 Henry Cohn, 2026, needs more optimization.
28 798 0.249644890198 Henry Cohn, 2026, needs more optimization.
28 799 0.249645686007 Henry Cohn, 2026, needs more optimization.
28 801 0.249674273209 Henry Cohn, 2026, needs more optimization.
28 804 0.249683016882 Henry Cohn, 2026, needs more optimization.
28 805 0.249699019282 Henry Cohn, 2026, needs more optimization.
28 806 0.249711097779 Henry Cohn, 2026, needs more optimization.
28 808 0.249726991389 Henry Cohn, 2026, needs more optimization.
28 809 0.249741776659 Henry Cohn, 2026, needs more optimization.
28 810 0.249746653844 Henry Cohn, 2026, needs more optimization.
28 811 0.249759557077 Henry Cohn, 2026, needs more optimization.
28 814 0.249790861269 Henry Cohn, 2026, needs more optimization.
28 815 0.249804459318 Henry Cohn, 2026, needs more optimization.
28 816 0.249813888930 Henry Cohn, 2026, needs more optimization.
28 817 0.249832719157 Henry Cohn, 2026, needs more optimization.
28 818 0.249852736942 Henry Cohn, 2026, needs more optimization.
28 819 0.249863399774 Henry Cohn, 2026, needs more optimization.
28 820 0.249867530351 Henry Cohn, 2026, needs more optimization.
28 821 0.249869404903 Henry Cohn, 2026, needs more optimization.
28 822 0.249878578013 Henry Cohn, 2026, needs more optimization.
28 823 0.249885209856 Henry Cohn, 2026, needs more optimization.
28 825 0.249899984622 Henry Cohn, 2026, needs more optimization.
28 976 0.25 Henry Cohn, 2026.
4⁢x−1
28 977 0.250002255718 Henry Cohn, 2026, needs more optimization.
28 986 0.250003379890 Henry Cohn, 2026, needs more optimization.
28 987 0.250004833652 Henry Cohn, 2026, needs more optimization.
28 989 0.250005886985 Henry Cohn, 2026, needs more optimization.
28 993 0.250009871202 Henry Cohn, 2026, needs more optimization.
28 994 0.250012647860 Henry Cohn, 2026, needs more optimization.
28 997 0.250012917653 Henry Cohn, 2026, needs more optimization.
28 998 0.250015064449 Henry Cohn, 2026, needs more optimization.
28 1002 0.250027292085 Henry Cohn, 2026, needs more optimization.
28 1004 0.250048822564 Henry Cohn, 2026, needs more optimization.
28 1005 0.250077095987 Henry Cohn, 2026, needs more optimization.
28 1006 0.250095458800 Henry Cohn, 2026, needs more optimization.
28 1009 0.250237923405 Henry Cohn, 2026, needs more optimization.
28 1010 0.250481953932 Henry Cohn, 2026, needs more optimization.
28 1011 0.250597719161 Henry Cohn, 2026, needs more optimization.
28 1012 0.250700850324 Henry Cohn, 2026, needs more optimization.
28 1013 0.250988421010 Henry Cohn, 2026, needs more optimization.
28 1014 0.251281565544 Henry Cohn, 2026, needs more optimization.
28 1015 0.251347047917 Henry Cohn, 2026, needs more optimization.
28 1016 0.251682016189 Henry Cohn, 2026, needs more optimization.
28 1017 0.251999212202 Henry Cohn, 2026, needs more optimization.
28 1018 0.252290014868 Henry Cohn, 2026, needs more optimization.
28 1019 0.252562566862 Henry Cohn, 2026, needs more optimization.
28 1020 0.252836381888 Henry Cohn, 2026, needs more optimization.
28 1021 0.252984050118 Henry Cohn, 2026, needs more optimization.
28 1022 0.253121263504 Henry Cohn, 2026, needs more optimization.
28 1023 0.253441331511 Henry Cohn, 2026, needs more optimization.
28 1024 0.253782904906 Henry Cohn, 2026, needs more optimization.
29 59 0.027727451354 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
21141⁢x3−841⁢x2−29⁢x+1
29 60 0.032283994156 Henry Cohn, 2024.
29 61 0.038074677873 Henry Cohn, 2026, needs more optimization.
29 62 0.039037971400 Henry Cohn, 2026.
29 63 0.039552183365 Henry Cohn, 2026.
29 64 0.043272075045 Henry Cohn, 2026.
29 65 0.044603988536 Henry Cohn, 2026.
29 66 0.044603988567 Henry Cohn, 2026, needs more optimization.
29 67 0.044634924676 Henry Cohn, 2026, needs more optimization.
29 68 0.046023717623 Henry Cohn, 2026.
29 69 0.050837623819 Henry Cohn, 2026.
29 70 0.052553724164 Henry Cohn, 2026, needs more optimization.
29 71 0.054294429930 Henry Cohn, 2026, needs more optimization.
29 72 0.056102523445 Henry Cohn, 2026, needs more optimization.
29 73 0.057718815198 Henry Cohn, 2026, needs more optimization.
29 74 0.059424876151 Henry Cohn, 2026, needs more optimization.
29 75 0.060942469759 Henry Cohn, 2026, needs more optimization.
29 76 0.062589517928 Henry Cohn, 2026, needs more optimization.
29 77 0.063095786166 Henry Cohn, 2026, needs more optimization.
29 78 0.063573776379 Henry Cohn, 2026, needs more optimization.
29 79 0.064129364736 Henry Cohn, 2026, needs more optimization.
29 80 0.065728964641 Henry Cohn, 2026, needs more optimization.
29 81 0.066915472195 Henry Cohn, 2026, needs more optimization.
29 82 0.068550020171 Henry Cohn, 2026, needs more optimization.
29 83 0.070356707229 Henry Cohn, 2026, needs more optimization.
29 84 0.072177323531 Henry Cohn, 2026, needs more optimization.
29 85 0.073569994869 Henry Cohn, 2026, needs more optimization.
29 86 0.074833545719 Henry Cohn, 2026, needs more optimization.
29 87 0.075739731908 Henry Cohn, 2026, needs more optimization.
29 88 0.075918576762 Henry Cohn, 2026, needs more optimization.
29 89 0.076439769781 Henry Cohn, 2026, needs more optimization.
29 90 0.076764560938 Henry Cohn, 2026, needs more optimization.
29 91 0.076968467452 Henry Cohn, 2026, needs more optimization.
29 92 0.077166104164 Henry Cohn, 2026, needs more optimization.
29 93 0.077365642998 Henry Cohn, 2026, needs more optimization.
29 94 0.077814568362 Henry Cohn, 2026, needs more optimization.
29 95 0.078076693495 Henry Cohn, 2026, needs more optimization.
29 96 0.078170510775 Henry Cohn, 2026, needs more optimization.
29 97 0.078815334819 Henry Cohn, 2026, needs more optimization.
29 98 0.078869686233 Henry Cohn, 2026, needs more optimization.
29 99 0.079107935180 Henry Cohn, 2026, needs more optimization.
29 100 0.079418976765 Henry Cohn, 2026, needs more optimization.
29 101 0.080105806017 Henry Cohn, 2026, needs more optimization.
29 102 0.080261661364 Henry Cohn, 2026, needs more optimization.
29 103 0.080656473305 Henry Cohn, 2026, needs more optimization.
29 104 0.080670491114 Henry Cohn, 2026, needs more optimization.
29 105 0.080715142488 Henry Cohn, 2026, needs more optimization.
29 106 0.081955713357 Henry Cohn, 2026, needs more optimization.
29 107 0.082789538286 Henry Cohn, 2026, needs more optimization.
29 108 0.084736292620 Henry Cohn, 2026, needs more optimization.
29 112 0.086333380579 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001, Example 5.10.1.
111⁢x2+2⁢x−1
29 113 0.089539207077 Henry Cohn, 2026, needs more optimization.
29 114 0.089789915539 Henry Cohn, 2026, needs more optimization.
29 115 0.089892504168 Henry Cohn, 2026, needs more optimization.
29 116 0.090009279393 Henry Cohn, 2026, needs more optimization.
29 117 0.090278429900 Henry Cohn, 2026, needs more optimization.
29 118 0.090535440490 Henry Cohn, 2026, needs more optimization.
29 119 0.090606916314 Henry Cohn, 2026, needs more optimization.
29 120 0.090737933529 Henry Cohn, 2026, needs more optimization.
29 121 0.091120663816 Henry Cohn, 2026, needs more optimization.
29 122 0.091808217788 Henry Cohn, 2026, needs more optimization.
29 123 0.093248983397 Henry Cohn, 2026, needs more optimization.
29 124 0.094247403920 Henry Cohn, 2026, needs more optimization.
29 125 0.096609334477 Henry Cohn, 2026, needs more optimization.
29 126 0.098256838980 Henry Cohn, 2026, needs more optimization.
29 127 0.099852824604 Henry Cohn, 2026, needs more optimization.
29 128 0.101502374903 Henry Cohn, 2026, needs more optimization.
29 129 0.102412999978 Henry Cohn, 2026, needs more optimization.
29 130 0.102428812541 Henry Cohn, 2026, needs more optimization.
29 131 0.102515272198 Henry Cohn, 2026, needs more optimization.
29 132 0.102549510757 Henry Cohn, 2026, needs more optimization.
29 133 0.102589091369 Henry Cohn, 2026, needs more optimization.
29 134 0.102712388914 Henry Cohn, 2026, needs more optimization.
29 135 0.103126796099 Henry Cohn, 2026, needs more optimization.
29 136 0.103823445421 Henry Cohn, 2026, needs more optimization.
29 137 0.105087340468 Henry Cohn, 2026, needs more optimization.
29 138 0.106289229390 Henry Cohn, 2026, needs more optimization.
29 139 0.107430915889 Henry Cohn, 2026, needs more optimization.
29 140 0.108105107626 Henry Cohn, 2026, needs more optimization.
29 141 0.108720011782 Henry Cohn, 2026, needs more optimization.
29 142 0.109452223843 Henry Cohn, 2026, needs more optimization.
29 143 0.110245268615 Henry Cohn, 2026, needs more optimization.
29 144 0.110691892505 Henry Cohn, 2026, needs more optimization.
29 145 0.110900537692 Henry Cohn, 2026, needs more optimization.
29 146 0.111108989109 Henry Cohn, 2026, needs more optimization.
29 147 0.111109114582 Henry Cohn, 2026, needs more optimization.
29 149 0.111110832778 Henry Cohn, 2026, needs more optimization.
29 152 0.111111111112 Orthogonal union of 150 points in 28 dimensions and 2 points in 1 dimension.
9⁢x−1
29 154 0.111111608081 Henry Cohn, 2026, needs more optimization.
29 155 0.112103342436 Henry Cohn, 2026, needs more optimization.
29 156 0.113936479386 Henry Cohn, 2026, needs more optimization.
29 157 0.117883178600 Henry Cohn, 2026, needs more optimization.
29 158 0.119120559861 Henry Cohn, 2026, needs more optimization.
29 159 0.121143557027 Henry Cohn, 2026, needs more optimization.
29 160 0.121313581527 Henry Cohn, 2026, needs more optimization.
29 161 0.122573263458 Henry Cohn, 2026, needs more optimization.
29 162 0.124337217517 Henry Cohn, 2026, needs more optimization.
29 163 0.125681518320 Henry Cohn, 2026, needs more optimization.
29 164 0.126053973049 Henry Cohn, 2026, needs more optimization.
29 165 0.126265398783 Henry Cohn, 2026, needs more optimization.
29 166 0.128052859892 Henry Cohn, 2026, needs more optimization.
29 184 0.128238684469 Orthogonal union of 182 points in 28 dimensions and 2 points in 1 dimension.
92⁢x2−4⁢x−1
29 185 0.128239416803 Henry Cohn, 2026, needs more optimization.
29 186 0.129288755611 Henry Cohn, 2026, needs more optimization.
29 187 0.131022624577 Henry Cohn, 2026, needs more optimization.
29 188 0.131505465154 Henry Cohn, 2026, needs more optimization.
29 189 0.131505465663 Henry Cohn, 2026, needs more optimization.
29 190 0.138788778011 Henry Cohn, 2026, needs more optimization.
29 191 0.139943484652 Henry Cohn, 2026, needs more optimization.
29 192 0.140857716569 Henry Cohn, 2026, needs more optimization.
29 193 0.141711955671 Henry Cohn, 2026, needs more optimization.
29 194 0.141834590828 Henry Cohn, 2026, needs more optimization.
29 195 0.141861709599 Henry Cohn, 2026, needs more optimization.
29 196 0.142025293811 Henry Cohn, 2026, needs more optimization.
29 197 0.142070049954 Henry Cohn, 2026, needs more optimization.
29 198 0.142134302554 Henry Cohn, 2026, needs more optimization.
29 199 0.142183126325 Henry Cohn, 2026, needs more optimization.
29 200 0.142256307029 Henry Cohn, 2026, needs more optimization.
29 201 0.142312681128 Henry Cohn, 2026, needs more optimization.
29 202 0.142361559409 Henry Cohn, 2026, needs more optimization.
29 203 0.142392349021 Henry Cohn, 2026, needs more optimization.
29 204 0.142430123086 Henry Cohn, 2026, needs more optimization.
29 205 0.142532467002 Henry Cohn, 2026, needs more optimization.
29 206 0.142683555936 Henry Cohn, 2026, needs more optimization.
29 207 0.142856047406 Henry Cohn, 2026, needs more optimization.
29 208 0.142989353244 Henry Cohn, 2026, needs more optimization.
29 209 0.143544726715 Henry Cohn, 2026, needs more optimization.
29 210 0.143761526148 Henry Cohn, 2026, needs more optimization.
29 211 0.144242298137 Henry Cohn, 2026, needs more optimization.
29 212 0.144975790127 Henry Cohn, 2026, needs more optimization.
29 213 0.145546804335 Henry Cohn, 2026, needs more optimization.
29 214 0.145769609647 Henry Cohn, 2026, needs more optimization.
29 215 0.145788189313 Henry Cohn, 2026, needs more optimization.
29 216 0.145792658419 Henry Cohn, 2026, needs more optimization.
29 217 0.145798460052 Henry Cohn, 2026, needs more optimization.
29 218 0.145977266161 Henry Cohn, 2026, needs more optimization.
29 219 0.146190344874 Henry Cohn, 2026, needs more optimization.
29 220 0.146331683408 Henry Cohn, 2026, needs more optimization.
29 221 0.146473498355 Henry Cohn, 2026, needs more optimization.
29 222 0.146589264380 Henry Cohn, 2026, needs more optimization.
29 223 0.146691451902 Henry Cohn, 2026, needs more optimization.
29 224 0.146838633259 Henry Cohn, 2026, needs more optimization.
29 225 0.146903653448 Henry Cohn, 2026, needs more optimization.
29 235 0.147102976680 Henry Cohn, 2026.
87⁢x2−6⁢x−1
29 236 0.147877026331 Henry Cohn, 2026, needs more optimization.
29 237 0.147913491605 Henry Cohn, 2026, needs more optimization.
29 238 0.147915826827 Henry Cohn, 2026, needs more optimization.
29 239 0.147982610080 Henry Cohn, 2026.
29 240 0.147998131190 Henry Cohn, 2026, needs more optimization.
29 241 0.148132532601 Henry Cohn, 2026, needs more optimization.
29 242 0.148370703652 Henry Cohn, 2026, needs more optimization.
29 243 0.148710748608 Henry Cohn, 2026, needs more optimization.
29 244 0.148924100674 Henry Cohn, 2026, needs more optimization.
29 245 0.149384821708 Henry Cohn, 2026, needs more optimization.
29 246 0.149964647624 Henry Cohn, 2026, needs more optimization.
29 247 0.150235338119 Henry Cohn, 2026, needs more optimization.
29 248 0.150623778244 Henry Cohn, 2026, needs more optimization.
29 249 0.151075977671 Henry Cohn, 2026, needs more optimization.
29 250 0.151758313647 Henry Cohn, 2026, needs more optimization.
29 251 0.152194778250 Henry Cohn, 2026, needs more optimization.
29 252 0.153232376438 Henry Cohn, 2026, needs more optimization.
29 253 0.153815143215 Henry Cohn, 2026, needs more optimization.
29 254 0.155245006221 Henry Cohn, 2026, needs more optimization.
29 255 0.156025166165 Henry Cohn, 2026, needs more optimization.
29 256 0.156620751367 Henry Cohn, 2026, needs more optimization.
29 257 0.157577210672 Henry Cohn, 2026, needs more optimization.
29 258 0.158307795962 Henry Cohn, 2026, needs more optimization.
29 259 0.159040269090 Henry Cohn, 2026, needs more optimization.
29 260 0.159327211570 Henry Cohn, 2026, needs more optimization.
29 261 0.159977338957 Henry Cohn, 2026, needs more optimization.
29 262 0.160794529893 Henry Cohn, 2026, needs more optimization.
29 263 0.161860757472 Henry Cohn, 2026, needs more optimization.
29 264 0.162281406126 Henry Cohn, 2026, needs more optimization.
29 265 0.162289971068 Henry Cohn, 2026, needs more optimization.
29 266 0.162358038515 Henry Cohn, 2026, needs more optimization.
29 267 0.162360902610 Henry Cohn, 2026, needs more optimization.
29 268 0.162405860009 Henry Cohn, 2026, needs more optimization.
29 269 0.162802416050 Henry Cohn, 2026, needs more optimization.
29 270 0.162802442602 Henry Cohn, 2026, needs more optimization.
29 271 0.162829726490 Henry Cohn, 2026, needs more optimization.
29 272 0.162940086846 Henry Cohn, 2026, needs more optimization.
29 273 0.163363837990 Henry Cohn, 2026, needs more optimization.
29 274 0.163425403916 Henry Cohn, 2026, needs more optimization.
29 275 0.163506446433 Henry Cohn, 2026, needs more optimization.
29 276 0.163574905403 Henry Cohn, 2026, needs more optimization.
29 277 0.163657635659 Henry Cohn, 2026, needs more optimization.
29 278 0.163799073404 Henry Cohn, 2026, needs more optimization.
29 279 0.163876456571 Henry Cohn, 2026, needs more optimization.
29 280 0.163963886880 Henry Cohn, 2026, needs more optimization.
29 281 0.164117079124 Henry Cohn, 2026, needs more optimization.
29 282 0.164306420673 Henry Cohn, 2026, needs more optimization.
29 283 0.164455002225 Henry Cohn, 2026, needs more optimization.
29 284 0.164565545628 Henry Cohn, 2026, needs more optimization.
29 285 0.164647375136 Henry Cohn, 2026, needs more optimization.
29 286 0.164687692242 Henry Cohn, 2026, needs more optimization.
29 287 0.164790104938 Henry Cohn, 2026, needs more optimization.
29 288 0.164943799370 Henry Cohn, 2026, needs more optimization.
29 289 0.165031944062 Henry Cohn, 2026, needs more optimization.
29 290 0.165057085842 Henry Cohn, 2026, needs more optimization.
29 291 0.165109309882 Henry Cohn, 2026, needs more optimization.
29 292 0.165131855432 Henry Cohn, 2026, needs more optimization.
29 293 0.165171701373 Henry Cohn, 2026, needs more optimization.
29 294 0.165219953869 Henry Cohn, 2026, needs more optimization.
29 295 0.165239968876 Henry Cohn, 2026, needs more optimization.
29 296 0.165273780395 Henry Cohn, 2026, needs more optimization.
29 297 0.165327080951 Henry Cohn, 2026, needs more optimization.
29 298 0.165363625980 Henry Cohn, 2026, needs more optimization.
29 299 0.165458002423 Henry Cohn, 2026, needs more optimization.
29 300 0.165541771534 Henry Cohn, 2026, needs more optimization.
29 301 0.165583822211 Henry Cohn, 2026, needs more optimization.
29 302 0.165659386797 Henry Cohn, 2026, needs more optimization.
29 303 0.165738876365 Henry Cohn, 2026, needs more optimization.
29 304 0.165801439554 Henry Cohn, 2026, needs more optimization.
29 305 0.165849217686 Henry Cohn, 2026, needs more optimization.
29 306 0.165943973101 Henry Cohn, 2026, needs more optimization.
29 307 0.165997683033 Henry Cohn, 2026, needs more optimization.
29 308 0.166129131989 Henry Cohn, 2026, needs more optimization.
29 309 0.166155495113 Henry Cohn, 2026, needs more optimization.
29 310 0.166308374369 Henry Cohn, 2026, needs more optimization.
29 311 0.166340499342 Henry Cohn, 2026, needs more optimization.
29 312 0.166459874297 Henry Cohn, 2026, needs more optimization.
29 314 0.166516534126 Henry Cohn, 2026, needs more optimization.
29 315 0.166601124841 Henry Cohn, 2026, needs more optimization.
29 316 0.166658742587 Henry Cohn, 2026, needs more optimization.
29 317 0.166660068150 Henry Cohn, 2026, needs more optimization.
29 319 0.166662932661 Henry Cohn, 2026, needs more optimization.
29 320 0.166666909115 Henry Cohn, 2026, needs more optimization.
29 321 0.166681481455 Henry Cohn, 2026, needs more optimization.
29 322 0.166687616025 Henry Cohn, 2026, needs more optimization.
29 323 0.166880394291 Henry Cohn, 2026, needs more optimization.
29 324 0.166941921085 Henry Cohn, 2026, needs more optimization.
29 325 0.167098796348 Henry Cohn, 2026, needs more optimization.
29 326 0.167183400003 Henry Cohn, 2026, needs more optimization.
29 327 0.167419806742 Henry Cohn, 2026, needs more optimization.
29 328 0.167840324487 Henry Cohn, 2026, needs more optimization.
29 329 0.168244666833 Henry Cohn, 2026, needs more optimization.
29 330 0.168897122935 Henry Cohn, 2026, needs more optimization.
29 331 0.169499919243 Henry Cohn, 2026, needs more optimization.
29 332 0.170965719899 Henry Cohn, 2026, needs more optimization.
29 333 0.171163335352 Henry Cohn, 2026, needs more optimization.
29 334 0.172410930224 Henry Cohn, 2026, needs more optimization.
29 335 0.172776810732 Henry Cohn, 2026, needs more optimization.
29 336 0.173853274006 Henry Cohn, 2026, needs more optimization.
29 337 0.174595326266 Henry Cohn, 2026, needs more optimization.
29 338 0.175318766585 Henry Cohn, 2026, needs more optimization.
29 339 0.175812348224 Henry Cohn, 2026, needs more optimization.
29 340 0.176272808068 Henry Cohn, 2026, needs more optimization.
29 341 0.177195339704 Henry Cohn, 2026, needs more optimization.
29 342 0.177768001648 Henry Cohn, 2026, needs more optimization.
29 343 0.178568657836 Henry Cohn, 2026, needs more optimization.
29 344 0.178608331364 Henry Cohn, 2026, needs more optimization.
29 345 0.178633183680 Henry Cohn, 2026, needs more optimization.
29 346 0.178928239521 Henry Cohn, 2026, needs more optimization.
29 347 0.179099918461 Henry Cohn, 2026, needs more optimization.
29 348 0.179889232991 Henry Cohn, 2026, needs more optimization.
29 349 0.179996190352 Henry Cohn, 2026, needs more optimization.
29 350 0.180374503091 Henry Cohn, 2026, needs more optimization.
29 351 0.180474888268 Henry Cohn, 2026, needs more optimization.
29 352 0.180485297069 Henry Cohn, 2026, needs more optimization.
29 353 0.180526830060 Henry Cohn, 2026, needs more optimization.
29 354 0.180980095567 Henry Cohn, 2026, needs more optimization.
29 355 0.181044511252 Henry Cohn, 2026, needs more optimization.
29 356 0.181102783039 Henry Cohn, 2026, needs more optimization.
29 357 0.181250072265 Henry Cohn, 2026, needs more optimization.
29 358 0.181444131126 Henry Cohn, 2026, needs more optimization.
29 359 0.181615098229 Henry Cohn, 2026, needs more optimization.
29 360 0.181651211674 Henry Cohn, 2026, needs more optimization.
29 361 0.184781518349 Henry Cohn, 2026, needs more optimization.
29 362 0.185276684216 Henry Cohn, 2026, needs more optimization.
29 363 0.185866440780 Henry Cohn, 2026, needs more optimization.
29 364 0.186077556551 Henry Cohn, 2026, needs more optimization.
29 365 0.186243213915 Henry Cohn, 2026, needs more optimization.
29 366 0.186784826498 Henry Cohn, 2026, needs more optimization.
29 367 0.187148627799 Henry Cohn, 2026, needs more optimization.
29 368 0.187284767867 Henry Cohn, 2026, needs more optimization.
29 369 0.187685856742 Henry Cohn, 2026, needs more optimization.
29 370 0.187936752517 Henry Cohn, 2026, needs more optimization.
29 371 0.188345522318 Henry Cohn, 2026, needs more optimization.
29 372 0.188562323502 Henry Cohn, 2026, needs more optimization.
29 373 0.188941896274 Henry Cohn, 2026, needs more optimization.
29 374 0.189280825633 Henry Cohn, 2026, needs more optimization.
29 375 0.189526299869 Henry Cohn, 2026, needs more optimization.
29 376 0.189645633327 Henry Cohn, 2026, needs more optimization.
29 377 0.189960155605 Henry Cohn, 2026, needs more optimization.
29 378 0.190246487540 Henry Cohn, 2026, needs more optimization.
29 379 0.190362410871 Henry Cohn, 2026, needs more optimization.
29 380 0.190789557313 Henry Cohn, 2026, needs more optimization.
29 381 0.191118488926 Henry Cohn, 2026, needs more optimization.
29 382 0.191172993771 Henry Cohn, 2026, needs more optimization.
29 383 0.191403339666 Henry Cohn, 2026, needs more optimization.
29 384 0.191567361586 Henry Cohn, 2026, needs more optimization.
29 385 0.191821809364 Henry Cohn, 2026, needs more optimization.
29 386 0.192000984498 Henry Cohn, 2026, needs more optimization.
29 387 0.192175716606 Henry Cohn, 2026, needs more optimization.
29 388 0.192283745329 Henry Cohn, 2026, needs more optimization.
29 389 0.192769658485 Henry Cohn, 2026, needs more optimization.
29 390 0.192913656076 Henry Cohn, 2026, needs more optimization.
29 391 0.193245039908 Henry Cohn, 2026, needs more optimization.
29 392 0.193553163335 Henry Cohn, 2026, needs more optimization.
29 393 0.193895342210 Henry Cohn, 2026, needs more optimization.
29 394 0.194025586012 Henry Cohn, 2026, needs more optimization.
29 395 0.194288265046 Henry Cohn, 2026, needs more optimization.
29 396 0.194374453167 Henry Cohn, 2026, needs more optimization.
29 451 0.194630872484 Henry Cohn, 2026, needs more optimization.
149⁢x−29
29 452 0.196846963825 Henry Cohn, 2026, needs more optimization.
29 454 0.199323951507 Henry Cohn, 2026, needs more optimization.
29 455 0.199337794410 Henry Cohn, 2026, needs more optimization.
29 456 0.199346820125 Henry Cohn, 2026, needs more optimization.
29 457 0.199378686404 Henry Cohn, 2026, needs more optimization.
29 458 0.199402346560 Henry Cohn, 2026, needs more optimization.
29 459 0.199431209967 Henry Cohn, 2026, needs more optimization.
29 461 0.199439189637 Henry Cohn, 2026, needs more optimization.
29 462 0.199456864725 Henry Cohn, 2026, needs more optimization.
29 463 0.199487988142 Henry Cohn, 2026, needs more optimization.
29 464 0.199500186842 Henry Cohn, 2026, needs more optimization.
29 465 0.199535154885 Henry Cohn, 2026, needs more optimization.
29 466 0.199556946487 Henry Cohn, 2026, needs more optimization.
29 467 0.199596521287 Henry Cohn, 2026, needs more optimization.
29 468 0.199598979388 Henry Cohn, 2026, needs more optimization.
29 469 0.199622221413 Henry Cohn, 2026, needs more optimization.
29 470 0.199634255051 Henry Cohn, 2026, needs more optimization.
29 471 0.199658700940 Henry Cohn, 2026, needs more optimization.
29 472 0.199665736625 Henry Cohn, 2026, needs more optimization.
29 473 0.199676710417 Henry Cohn, 2026, needs more optimization.
29 475 0.199683388276 Henry Cohn, 2026, needs more optimization.
29 476 0.199686949383 Henry Cohn, 2026, needs more optimization.
29 477 0.199695240457 Henry Cohn, 2026, needs more optimization.
29 478 0.199712182127 Henry Cohn, 2026, needs more optimization.
29 479 0.199726058318 Henry Cohn, 2026, needs more optimization.
29 480 0.199731814272 Henry Cohn, 2026, needs more optimization.
29 481 0.199739667841 Henry Cohn, 2026, needs more optimization.
29 482 0.199751049438 Henry Cohn, 2026, needs more optimization.
29 483 0.199766829313 Henry Cohn, 2026, needs more optimization.
29 484 0.199778876964 Henry Cohn, 2026, needs more optimization.
29 485 0.199802974244 Henry Cohn, 2026, needs more optimization.
29 486 0.199818164930 Henry Cohn, 2026, needs more optimization.
29 487 0.199838829647 Henry Cohn, 2026, needs more optimization.
29 488 0.199849218337 Henry Cohn, 2026, needs more optimization.
29 489 0.199863660649 Henry Cohn, 2026, needs more optimization.
29 490 0.199865295521 Henry Cohn, 2026, needs more optimization.
29 491 0.199870296490 Henry Cohn, 2026, needs more optimization.
29 492 0.199889618957 Henry Cohn, 2026, needs more optimization.
29 493 0.199896152768 Henry Cohn, 2026, needs more optimization.
29 494 0.199900546127 Henry Cohn, 2026, needs more optimization.
29 495 0.199915076080 Henry Cohn, 2026, needs more optimization.
29 496 0.199939914762 Henry Cohn, 2026, needs more optimization.
29 576 0.2 Henry Cohn, 2026.
5⁢x−1
29 582 0.200000937047 Henry Cohn, 2026, needs more optimization.
29 587 0.200001264164 Henry Cohn, 2026, needs more optimization.
29 588 0.200001509263 Henry Cohn, 2026, needs more optimization.
29 592 0.200002050030 Henry Cohn, 2026, needs more optimization.
29 593 0.200002050570 Henry Cohn, 2026, needs more optimization.
29 594 0.200002773396 Henry Cohn, 2026, needs more optimization.
29 596 0.200006672509 Henry Cohn, 2026, needs more optimization.
29 597 0.200007142410 Henry Cohn, 2026, needs more optimization.
29 599 0.200011621596 Henry Cohn, 2026, needs more optimization.
29 600 0.200018147696 Henry Cohn, 2026, needs more optimization.
29 601 0.200025428539 Henry Cohn, 2026, needs more optimization.
29 602 0.200048467937 Henry Cohn, 2026, needs more optimization.
29 603 0.200343494689 Henry Cohn, 2026, needs more optimization.
29 604 0.234601344698 Henry Cohn, 2026, needs more optimization.
29 605 0.234604784836 Henry Cohn, 2026, needs more optimization.
29 606 0.234687174537 Henry Cohn, 2026, needs more optimization.
29 609 0.234870579107 Henry Cohn, 2026, needs more optimization.
29 611 0.235147892060 Henry Cohn, 2026, needs more optimization.
29 613 0.235265925834 Henry Cohn, 2026, needs more optimization.
29 617 0.235466019792 Henry Cohn, 2026, needs more optimization.
29 620 0.235792377842 Henry Cohn, 2026, needs more optimization.
29 621 0.235810403917 Henry Cohn, 2026, needs more optimization.
29 622 0.235867674779 Henry Cohn, 2026, needs more optimization.
29 623 0.235915110475 Henry Cohn, 2026, needs more optimization.
29 628 0.236191186006 Henry Cohn, 2026, needs more optimization.
29 633 0.236360648366 Henry Cohn, 2026, needs more optimization.
29 634 0.237041143653 Henry Cohn, 2026, needs more optimization.
29 636 0.237339040626 Henry Cohn, 2026, needs more optimization.
29 637 0.237435718008 Henry Cohn, 2026, needs more optimization.
29 641 0.237456052898 Henry Cohn, 2026, needs more optimization.
29 646 0.237516444528 Henry Cohn, 2026, needs more optimization.
29 647 0.237530075643 Henry Cohn, 2026, needs more optimization.
29 652 0.237578701928 Henry Cohn, 2026, needs more optimization.
29 653 0.237578711391 Henry Cohn, 2026, needs more optimization.
29 655 0.237578854626 Henry Cohn, 2026, needs more optimization.
29 657 0.237639467121 Henry Cohn, 2026, needs more optimization.
29 658 0.237639703265 Henry Cohn, 2026, needs more optimization.
29 661 0.237968665038 Henry Cohn, 2026, needs more optimization.
29 669 0.237973571850 Henry Cohn, 2026, needs more optimization.
29 677 0.237984581455 Henry Cohn, 2026, needs more optimization.
29 679 0.237984621992 Henry Cohn, 2026, needs more optimization.
29 683 0.237995363406 Henry Cohn, 2026, needs more optimization.
29 684 0.237999075599 Henry Cohn, 2026, needs more optimization.
29 685 0.238005918011 Henry Cohn, 2026, needs more optimization.
29 688 0.238016604355 Henry Cohn, 2026, needs more optimization.
29 690 0.238020717926 Henry Cohn, 2026, needs more optimization.
29 691 0.238026370125 Henry Cohn, 2026, needs more optimization.
29 692 0.238047018427 Henry Cohn, 2026, needs more optimization.
29 700 0.238071708367 Henry Cohn, 2026, needs more optimization.
29 702 0.238085226129 Henry Cohn, 2026, needs more optimization.
29 705 0.238088825238 Henry Cohn, 2026, needs more optimization.
29 707 0.238093729139 Henry Cohn, 2026, needs more optimization.
29 711 0.238100231382 Henry Cohn, 2026, needs more optimization.
29 712 0.238115138553 Henry Cohn, 2026, needs more optimization.
29 713 0.238185729640 Henry Cohn, 2026, needs more optimization.
29 715 0.238225708010 Henry Cohn, 2026, needs more optimization.
29 716 0.238255154327 Henry Cohn, 2026, needs more optimization.
29 717 0.238271311207 Henry Cohn, 2026, needs more optimization.
29 718 0.238324979431 Henry Cohn, 2026, needs more optimization.
29 719 0.240936295290 Henry Cohn, 2026, needs more optimization.
29 720 0.241045743626 Henry Cohn, 2026, needs more optimization.
29 722 0.241156374094 Henry Cohn, 2026, needs more optimization.
29 724 0.241231631004 Henry Cohn, 2026, needs more optimization.
29 728 0.241476859019 Henry Cohn, 2026, needs more optimization.
29 729 0.241749548440 Henry Cohn, 2026, needs more optimization.
29 730 0.241893585796 Henry Cohn, 2026, needs more optimization.
29 731 0.241906056415 Henry Cohn, 2026, needs more optimization.
29 733 0.241937610429 Henry Cohn, 2026, needs more optimization.
29 735 0.242133349191 Henry Cohn, 2026, needs more optimization.
29 736 0.242223897206 Henry Cohn, 2026, needs more optimization.
29 737 0.242435126356 Henry Cohn, 2026, needs more optimization.
29 738 0.242554689311 Henry Cohn, 2026, needs more optimization.
29 739 0.242765393689 Henry Cohn, 2026, needs more optimization.
29 741 0.242860466458 Henry Cohn, 2026, needs more optimization.
29 742 0.242993116948 Henry Cohn, 2026, needs more optimization.
29 744 0.243006875072 Henry Cohn, 2026, needs more optimization.
29 745 0.243132779367 Henry Cohn, 2026, needs more optimization.
29 747 0.243253874600 Henry Cohn, 2026, needs more optimization.
29 748 0.243412355184 Henry Cohn, 2026, needs more optimization.
29 749 0.243649495610 Henry Cohn, 2026, needs more optimization.
29 750 0.243728934592 Henry Cohn, 2026, needs more optimization.
29 751 0.243829780697 Henry Cohn, 2026, needs more optimization.
29 752 0.243917528234 Henry Cohn, 2026, needs more optimization.
29 753 0.244004078275 Henry Cohn, 2026, needs more optimization.
29 755 0.244214064994 Henry Cohn, 2026, needs more optimization.
29 760 0.244225593103 Henry Cohn, 2026, needs more optimization.
29 761 0.244354315651 Henry Cohn, 2026, needs more optimization.
29 762 0.244525342327 Henry Cohn, 2026, needs more optimization.
29 763 0.244648259073 Henry Cohn, 2026, needs more optimization.
29 764 0.244660168459 Henry Cohn, 2026, needs more optimization.
29 765 0.244890003544 Henry Cohn, 2026, needs more optimization.
29 766 0.244992487363 Henry Cohn, 2026, needs more optimization.
29 769 0.245125558737 Henry Cohn, 2026, needs more optimization.
29 770 0.245219399820 Henry Cohn, 2026, needs more optimization.
29 771 0.245307463744 Henry Cohn, 2026, needs more optimization.
29 772 0.245519766658 Henry Cohn, 2026, needs more optimization.
29 773 0.245654627623 Henry Cohn, 2026, needs more optimization.
29 774 0.245809501360 Henry Cohn, 2026, needs more optimization.
29 775 0.245864014026 Henry Cohn, 2026, needs more optimization.
29 776 0.245920320723 Henry Cohn, 2026, needs more optimization.
29 778 0.245960517606 Henry Cohn, 2026, needs more optimization.
29 779 0.246073395299 Henry Cohn, 2026, needs more optimization.
29 780 0.246226245679 Henry Cohn, 2026, needs more optimization.
29 781 0.246297638876 Henry Cohn, 2026, needs more optimization.
29 782 0.246387127259 Henry Cohn, 2026, needs more optimization.
29 783 0.246435564981 Henry Cohn, 2026, needs more optimization.
29 784 0.246470039308 Henry Cohn, 2026, needs more optimization.
29 787 0.246553451714 Henry Cohn, 2026, needs more optimization.
29 788 0.246643506414 Henry Cohn, 2026, needs more optimization.
29 790 0.246743064849 Henry Cohn, 2026, needs more optimization.
29 791 0.246787979369 Henry Cohn, 2026, needs more optimization.
29 792 0.246840805261 Henry Cohn, 2026, needs more optimization.
29 793 0.247015519911 Henry Cohn, 2026, needs more optimization.
29 794 0.247108104242 Henry Cohn, 2026, needs more optimization.
29 795 0.247177483698 Henry Cohn, 2026, needs more optimization.
29 798 0.247196831784 Henry Cohn, 2026, needs more optimization.
29 799 0.247305834688 Henry Cohn, 2026, needs more optimization.
29 800 0.247401870670 Henry Cohn, 2026, needs more optimization.
29 801 0.247457339978 Henry Cohn, 2026, needs more optimization.
29 802 0.247534245580 Henry Cohn, 2026, needs more optimization.
29 804 0.247546352079 Henry Cohn, 2026, needs more optimization.
29 805 0.247662241505 Henry Cohn, 2026, needs more optimization.
29 807 0.247774931351 Henry Cohn, 2026, needs more optimization.
29 808 0.247867841606 Henry Cohn, 2026, needs more optimization.
29 809 0.247932019725 Henry Cohn, 2026, needs more optimization.
29 811 0.247941885461 Henry Cohn, 2026, needs more optimization.
29 812 0.248025521693 Henry Cohn, 2026, needs more optimization.
29 813 0.248110127844 Henry Cohn, 2026, needs more optimization.
29 814 0.248176816562 Henry Cohn, 2026, needs more optimization.
29 815 0.248232141595 Henry Cohn, 2026, needs more optimization.
29 822 0.248274393278 Henry Cohn, 2026, needs more optimization.
29 827 0.248420379695 Henry Cohn, 2026, needs more optimization.
29 829 0.248514287052 Henry Cohn, 2026, needs more optimization.
29 830 0.248651571188 Henry Cohn, 2026, needs more optimization.
29 832 0.248688745051 Henry Cohn, 2026, needs more optimization.
29 835 0.248736697982 Henry Cohn, 2026, needs more optimization.
29 836 0.248775370245 Henry Cohn, 2026, needs more optimization.
29 837 0.248789523887 Henry Cohn, 2026, needs more optimization.
29 840 0.248895995335 Henry Cohn, 2026, needs more optimization.
29 841 0.248929505411 Henry Cohn, 2026, needs more optimization.
29 847 0.248952396492 Henry Cohn, 2026, needs more optimization.
29 850 0.249027917739 Henry Cohn, 2026, needs more optimization.
29 851 0.249069899410 Henry Cohn, 2026, needs more optimization.
29 853 0.249103054467 Henry Cohn, 2026, needs more optimization.
29 854 0.249131736112 Henry Cohn, 2026, needs more optimization.
29 855 0.249147684575 Henry Cohn, 2026, needs more optimization.
29 860 0.249194905495 Henry Cohn, 2026, needs more optimization.
29 861 0.249223706932 Henry Cohn, 2026, needs more optimization.
29 862 0.249255015116 Henry Cohn, 2026, needs more optimization.
29 863 0.249291798391 Henry Cohn, 2026, needs more optimization.
29 868 0.249365832452 Henry Cohn, 2026, needs more optimization.
29 869 0.249366687084 Henry Cohn, 2026, needs more optimization.
29 873 0.249458692161 Henry Cohn, 2026, needs more optimization.
29 877 0.249520378941 Henry Cohn, 2026, needs more optimization.
29 878 0.249534856100 Henry Cohn, 2026, needs more optimization.
29 882 0.249541679507 Henry Cohn, 2026, needs more optimization.
29 884 0.249561586109 Henry Cohn, 2026, needs more optimization.
29 889 0.249611571571 Henry Cohn, 2026, needs more optimization.
29 890 0.249614363915 Henry Cohn, 2026, needs more optimization.
29 891 0.249616072579 Henry Cohn, 2026, needs more optimization.
29 893 0.249632996504 Henry Cohn, 2026, needs more optimization.
29 894 0.249649884479 Henry Cohn, 2026, needs more optimization.
29 895 0.249661907153 Henry Cohn, 2026, needs more optimization.
29 897 0.249687008058 Henry Cohn, 2026, needs more optimization.
29 898 0.249696113946 Henry Cohn, 2026, needs more optimization.
29 899 0.249710163089 Henry Cohn, 2026, needs more optimization.
29 900 0.249727592069 Henry Cohn, 2026, needs more optimization.
29 901 0.249733514277 Henry Cohn, 2026, needs more optimization.
29 902 0.249746619314 Henry Cohn, 2026, needs more optimization.
29 903 0.249752072042 Henry Cohn, 2026, needs more optimization.
29 904 0.249764272648 Henry Cohn, 2026, needs more optimization.
29 905 0.249780653141 Henry Cohn, 2026, needs more optimization.
29 982 0.249999663831 Henry Cohn, 2026, needs more optimization.
29 988 0.249999848779 Henry Cohn, 2026, needs more optimization.
29 999 0.250000684891 Henry Cohn, 2026, needs more optimization.
29 1000 0.250001136173 Henry Cohn, 2026, needs more optimization.
29 1006 0.250001326478 Henry Cohn, 2026, needs more optimization.
29 1010 0.250004376218 Henry Cohn, 2026, needs more optimization.
29 1011 0.250004967094 Henry Cohn, 2026, needs more optimization.
29 1013 0.250007672034 Henry Cohn, 2026, needs more optimization.
29 1015 0.250008376276 Henry Cohn, 2026, needs more optimization.
29 1016 0.250011800695 Henry Cohn, 2026, needs more optimization.
29 1018 0.250015292875 Henry Cohn, 2026, needs more optimization.
29 1022 0.250023105241 Henry Cohn, 2026, needs more optimization.
29 1024 0.250024102972 Henry Cohn, 2026, needs more optimization.
30 61 0.026884307091 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
23520⁢x3−900⁢x2−30⁢x+1
30 62 0.031274698397 Henry Cohn, 2026.
30 63 0.037893320316 Henry Cohn, 2026.
30 64 0.038348157236 Henry Cohn, 2026.
30 65 0.038479664975 Henry Cohn, 2026.
30 66 0.042441820097 Henry Cohn, 2026, needs more optimization.
30 67 0.043917025854 Henry Cohn, 2026, needs more optimization.
30 68 0.044555720231 Henry Cohn, 2026, needs more optimization.
30 69 0.044563591251 Henry Cohn, 2026, needs more optimization.
30 70 0.044757397041 Henry Cohn, 2026.
30 71 0.049847164675 Henry Cohn, 2026.
30 72 0.051255783604 Henry Cohn, 2026, needs more optimization.
30 73 0.052421148566 Henry Cohn, 2026, needs more optimization.
30 74 0.054131831046 Henry Cohn, 2026, needs more optimization.
30 75 0.056243908098 Henry Cohn, 2026, needs more optimization.
30 76 0.057552662592 Henry Cohn, 2026, needs more optimization.
30 77 0.059053175487 Henry Cohn, 2026, needs more optimization.
30 78 0.060498966169 Henry Cohn, 2026, needs more optimization.
30 79 0.062140014429 Henry Cohn, 2026, needs more optimization.
30 80 0.062584000316 Henry Cohn, 2026, needs more optimization.
30 81 0.062832433925 Henry Cohn, 2026, needs more optimization.
30 82 0.064272764167 Henry Cohn, 2026, needs more optimization.
30 83 0.065104551573 Henry Cohn, 2026, needs more optimization.
30 84 0.066453461702 Henry Cohn, 2026, needs more optimization.
30 85 0.068027669175 Henry Cohn, 2026, needs more optimization.
30 86 0.069487665016 Henry Cohn, 2026, needs more optimization.
30 87 0.070938292076 Henry Cohn, 2026, needs more optimization.
30 88 0.072505464092 Henry Cohn, 2026, needs more optimization.
30 89 0.073901964491 Henry Cohn, 2026, needs more optimization.
30 90 0.074428780472 Henry Cohn, 2026, needs more optimization.
30 91 0.075426915931 Henry Cohn, 2026, needs more optimization.
30 92 0.076276608691 Henry Cohn, 2026, needs more optimization.
30 93 0.076879532078 Henry Cohn, 2026, needs more optimization.
30 94 0.076887748871 Henry Cohn, 2026, needs more optimization.
30 95 0.076930065749 Henry Cohn, 2026, needs more optimization.
30 96 0.077017060701 Henry Cohn, 2026, needs more optimization.
30 97 0.077172781887 Henry Cohn, 2026, needs more optimization.
30 98 0.077272034954 Henry Cohn, 2026, needs more optimization.
30 99 0.077380622721 Henry Cohn, 2026, needs more optimization.
30 100 0.077768398460 Henry Cohn, 2026, needs more optimization.
30 101 0.077928681920 Henry Cohn, 2026, needs more optimization.
30 102 0.078182380812 Henry Cohn, 2026, needs more optimization.
30 103 0.078810396139 Henry Cohn, 2026, needs more optimization.
30 104 0.079143980007 Henry Cohn, 2026, needs more optimization.
30 105 0.079624847038 Henry Cohn, 2026, needs more optimization.
30 106 0.080489221030 Henry Cohn, 2026, needs more optimization.
30 107 0.080664883365 Henry Cohn, 2026, needs more optimization.
30 108 0.080812789307 Henry Cohn, 2026, needs more optimization.
30 109 0.081520875148 Henry Cohn, 2026, needs more optimization.
30 110 0.082107997655 Henry Cohn, 2026, needs more optimization.
30 111 0.082302654415 Henry Cohn, 2026, needs more optimization.
30 112 0.083254192309 Henry Cohn, 2026, needs more optimization.
30 113 0.085102368520 Henry Cohn, 2026, needs more optimization.
30 114 0.086333380579 Orthogonal union of 112 points in 29 dimensions and 2 points in 1 dimension.
111⁢x2+2⁢x−1
30 115 0.087944973913 Henry Cohn, 2026, needs more optimization.
30 116 0.088185356311 Henry Cohn, 2026, needs more optimization.
30 117 0.088551280333 Henry Cohn, 2026, needs more optimization.
30 118 0.089018460490 Henry Cohn, 2026, needs more optimization.
30 119 0.089353701842 Henry Cohn, 2026, needs more optimization.
30 120 0.089662042894 Henry Cohn, 2026, needs more optimization.
30 121 0.089965216680 Henry Cohn, 2026, needs more optimization.
30 122 0.090222720784 Henry Cohn, 2026, needs more optimization.
30 123 0.090518060111 Henry Cohn, 2026, needs more optimization.
30 124 0.090775950635 Henry Cohn, 2026, needs more optimization.
30 125 0.090956360885 Henry Cohn, 2026, needs more optimization.
30 126 0.091623896488 Henry Cohn, 2026, needs more optimization.
30 127 0.092700883674 Henry Cohn, 2026, needs more optimization.
30 128 0.094001976904 Henry Cohn, 2026, needs more optimization.
30 129 0.095273773315 Henry Cohn, 2026, needs more optimization.
30 130 0.097292741745 Henry Cohn, 2026, needs more optimization.
30 131 0.098503012697 Henry Cohn, 2026, needs more optimization.
30 132 0.099543740544 Henry Cohn, 2026, needs more optimization.
30 133 0.100616786012 Henry Cohn, 2026, needs more optimization.
30 134 0.102003243645 Henry Cohn, 2026, needs more optimization.
30 135 0.102471621253 Henry Cohn, 2026, needs more optimization.
30 136 0.102542990215 Henry Cohn, 2026, needs more optimization.
30 137 0.102565191138 Henry Cohn, 2026, needs more optimization.
30 138 0.102572134000 Henry Cohn, 2026, needs more optimization.
30 139 0.102602939419 Henry Cohn, 2026, needs more optimization.
30 140 0.102650767805 Henry Cohn, 2026, needs more optimization.
30 141 0.102665234195 Henry Cohn, 2026, needs more optimization.
30 142 0.103623366785 Henry Cohn, 2026, needs more optimization.
30 143 0.105315794616 Henry Cohn, 2026, needs more optimization.
30 144 0.106156524938 Henry Cohn, 2026, needs more optimization.
30 145 0.107192824717 Henry Cohn, 2026, needs more optimization.
30 146 0.108220462246 Henry Cohn, 2026, needs more optimization.
30 147 0.108866104718 Henry Cohn, 2026, needs more optimization.
30 148 0.109073451910 Henry Cohn, 2026, needs more optimization.
30 149 0.109649935137 Henry Cohn, 2026, needs more optimization.
30 150 0.110161292255 Henry Cohn, 2026, needs more optimization.
30 151 0.110742427349 Henry Cohn, 2026, needs more optimization.
30 152 0.111073040840 Henry Cohn, 2026, needs more optimization.
30 153 0.111086788515 Henry Cohn, 2026, needs more optimization.
30 154 0.111092292250 Henry Cohn, 2026, needs more optimization.
30 155 0.111099609806 Henry Cohn, 2026, needs more optimization.
30 156 0.111108882890 Henry Cohn, 2026, needs more optimization.
30 157 0.111112454427 Henry Cohn, 2026, needs more optimization.
30 158 0.111113469944 Henry Cohn, 2026, needs more optimization.
30 159 0.112281097424 Henry Cohn, 2026, needs more optimization.
30 160 0.113646286827 Henry Cohn, 2026, needs more optimization.
30 161 0.115772980440 Henry Cohn, 2026, needs more optimization.
30 162 0.117269804499 Henry Cohn, 2026, needs more optimization.
30 163 0.118948034505 Henry Cohn, 2026, needs more optimization.
30 164 0.120039011804 Henry Cohn, 2026, needs more optimization.
30 165 0.120962187656 Henry Cohn, 2026, needs more optimization.
30 166 0.121723182416 Henry Cohn, 2026, needs more optimization.
30 167 0.121975475521 Henry Cohn, 2026, needs more optimization.
30 168 0.122829219876 Henry Cohn, 2026, needs more optimization.
30 169 0.123550450680 Henry Cohn, 2026, needs more optimization.
30 170 0.124634171762 Henry Cohn, 2026, needs more optimization.
30 171 0.126575955819 Henry Cohn, 2026, needs more optimization.
30 172 0.127612427241 Henry Cohn, 2026, needs more optimization.
30 173 0.128233380173 Henry Cohn, 2026, needs more optimization.
30 186 0.128238684469 Orthogonal union of 182 points in 28 dimensions and 4 points in 2 dimensions.
92⁢x2−4⁢x−1
30 187 0.128239137542 Henry Cohn, 2026, needs more optimization.
30 188 0.128240365154 Henry Cohn, 2026, needs more optimization.
30 189 0.128372012892 Henry Cohn, 2026, needs more optimization.
30 190 0.129244288919 Henry Cohn, 2026, needs more optimization.
30 191 0.130279030567 Henry Cohn, 2026, needs more optimization.
30 192 0.131434523851 Henry Cohn, 2026, needs more optimization.
30 193 0.131434533157 Henry Cohn, 2026, needs more optimization.
30 194 0.131434546320 Henry Cohn, 2026, needs more optimization.
30 195 0.131439457377 Henry Cohn, 2026, needs more optimization.
30 196 0.131439458364 Henry Cohn, 2026, needs more optimization.
30 197 0.137956900955 Henry Cohn, 2026, needs more optimization.
30 198 0.138516890830 Henry Cohn, 2026, needs more optimization.
30 199 0.139404142021 Henry Cohn, 2026, needs more optimization.
30 200 0.140306315435 Henry Cohn, 2026, needs more optimization.
30 201 0.141134672369 Henry Cohn, 2026, needs more optimization.
30 202 0.141166521568 Henry Cohn, 2026, needs more optimization.
30 203 0.141261028357 Henry Cohn, 2026, needs more optimization.
30 204 0.141300085415 Henry Cohn, 2026, needs more optimization.
30 205 0.141396234125 Henry Cohn, 2026, needs more optimization.
30 206 0.141502686351 Henry Cohn, 2026, needs more optimization.
30 207 0.141550256469 Henry Cohn, 2026, needs more optimization.
30 208 0.141631169088 Henry Cohn, 2026, needs more optimization.
30 209 0.141826679179 Henry Cohn, 2026, needs more optimization.
30 210 0.141962961278 Henry Cohn, 2026, needs more optimization.
30 211 0.142150684378 Henry Cohn, 2026, needs more optimization.
30 212 0.142275740518 Henry Cohn, 2026, needs more optimization.
30 213 0.142289970029 Henry Cohn, 2026, needs more optimization.
30 214 0.142343722612 Henry Cohn, 2026, needs more optimization.
30 215 0.142505268806 Henry Cohn, 2026, needs more optimization.
30 216 0.142825561973 Henry Cohn, 2026, needs more optimization.
30 217 0.142863779805 Henry Cohn, 2026, needs more optimization.
30 218 0.143126453580 Henry Cohn, 2026, needs more optimization.
30 219 0.143708247448 Henry Cohn, 2026, needs more optimization.
30 220 0.143959826542 Henry Cohn, 2026, needs more optimization.
30 221 0.144389951345 Henry Cohn, 2026, needs more optimization.
30 222 0.144502015219 Henry Cohn, 2026, needs more optimization.
30 223 0.144842055775 Henry Cohn, 2026, needs more optimization.
30 224 0.144975400611 Henry Cohn, 2026, needs more optimization.
30 225 0.145185465722 Henry Cohn, 2026, needs more optimization.
30 226 0.145340551428 Henry Cohn, 2026, needs more optimization.
30 227 0.145537735382 Henry Cohn, 2026, needs more optimization.
30 228 0.145892372469 Henry Cohn, 2026, needs more optimization.
30 229 0.146409380917 Henry Cohn, 2026, needs more optimization.
30 230 0.146480800369 Henry Cohn, 2026, needs more optimization.
30 231 0.146581191962 Henry Cohn, 2026, needs more optimization.
30 232 0.146724305223 Henry Cohn, 2026, needs more optimization.
30 233 0.146881227471 Henry Cohn, 2026, needs more optimization.
30 234 0.146881228837 Henry Cohn, 2026, needs more optimization.
30 235 0.147028390224 Henry Cohn, 2026, needs more optimization.
30 237 0.147102976680 Orthogonal union of 235 points in 29 dimensions and 2 points in 1 dimension.
87⁢x2−6⁢x−1
30 238 0.147103933710 Henry Cohn, 2026, needs more optimization.
30 239 0.147104261163 Henry Cohn, 2026, needs more optimization.
30 240 0.147117549617 Henry Cohn, 2026, needs more optimization.
30 241 0.147141480316 Henry Cohn, 2026, needs more optimization.
30 242 0.147806948403 Henry Cohn, 2026, needs more optimization.
30 243 0.147824471507 Henry Cohn, 2026, needs more optimization.
30 244 0.147861213251 Henry Cohn, 2026, needs more optimization.
30 245 0.147868977495 Henry Cohn, 2026, needs more optimization.
30 246 0.147915136077 Henry Cohn, 2026, needs more optimization.
30 247 0.147928698528 Henry Cohn, 2026, needs more optimization.
30 248 0.147978290549 Henry Cohn, 2026, needs more optimization.
30 249 0.147984192605 Henry Cohn, 2026, needs more optimization.
30 250 0.148001470459 Henry Cohn, 2026, needs more optimization.
30 251 0.148065491848 Henry Cohn, 2026, needs more optimization.
30 252 0.148301544901 Henry Cohn, 2026, needs more optimization.
30 253 0.148454667484 Henry Cohn, 2026, needs more optimization.
30 254 0.148937617388 Henry Cohn, 2026, needs more optimization.
30 255 0.149525161851 Henry Cohn, 2026, needs more optimization.
30 256 0.149894785808 Henry Cohn, 2026, needs more optimization.
30 257 0.150623197463 Henry Cohn, 2026, needs more optimization.
30 258 0.150831490871 Henry Cohn, 2026, needs more optimization.
30 259 0.151539376030 Henry Cohn, 2026, needs more optimization.
30 260 0.152168172707 Henry Cohn, 2026, needs more optimization.
30 261 0.153123037388 Henry Cohn, 2026, needs more optimization.
30 262 0.153629792651 Henry Cohn, 2026, needs more optimization.
30 263 0.154172220799 Henry Cohn, 2026, needs more optimization.
30 264 0.154824202641 Henry Cohn, 2026, needs more optimization.
30 265 0.155268729763 Henry Cohn, 2026, needs more optimization.
30 266 0.155974625954 Henry Cohn, 2026, needs more optimization.
30 267 0.156631899381 Henry Cohn, 2026, needs more optimization.
30 268 0.157437127401 Henry Cohn, 2026, needs more optimization.
30 269 0.158209123656 Henry Cohn, 2026, needs more optimization.
30 270 0.158917559432 Henry Cohn, 2026, needs more optimization.
30 271 0.159528447314 Henry Cohn, 2026, needs more optimization.
30 272 0.160092996355 Henry Cohn, 2026, needs more optimization.
30 273 0.160707312317 Henry Cohn, 2026, needs more optimization.
30 274 0.161440710220 Henry Cohn, 2026, needs more optimization.
30 275 0.161772836584 Henry Cohn, 2026, needs more optimization.
30 276 0.161814122727 Henry Cohn, 2026, needs more optimization.
30 277 0.161835083080 Henry Cohn, 2026, needs more optimization.
30 278 0.161878900896 Henry Cohn, 2026, needs more optimization.
30 279 0.161882553562 Henry Cohn, 2026, needs more optimization.
30 280 0.161910358682 Henry Cohn, 2026, needs more optimization.
30 281 0.161971519181 Henry Cohn, 2026, needs more optimization.
30 282 0.162004913584 Henry Cohn, 2026, needs more optimization.
30 283 0.162120346023 Henry Cohn, 2026, needs more optimization.
30 284 0.162252616248 Henry Cohn, 2026, needs more optimization.
30 285 0.162388891461 Henry Cohn, 2026, needs more optimization.
30 286 0.162526277503 Henry Cohn, 2026, needs more optimization.
30 287 0.162774919268 Henry Cohn, 2026, needs more optimization.
30 288 0.162877501270 Henry Cohn, 2026, needs more optimization.
30 289 0.163000501757 Henry Cohn, 2026, needs more optimization.
30 290 0.163066514917 Henry Cohn, 2026, needs more optimization.
30 291 0.163189247081 Henry Cohn, 2026, needs more optimization.
30 292 0.163330297832 Henry Cohn, 2026, needs more optimization.
30 293 0.163352919039 Henry Cohn, 2026, needs more optimization.
30 294 0.163441577747 Henry Cohn, 2026, needs more optimization.
30 295 0.163568324650 Henry Cohn, 2026, needs more optimization.
30 296 0.163586525536 Henry Cohn, 2026, needs more optimization.
30 297 0.163650981240 Henry Cohn, 2026, needs more optimization.
30 298 0.163738341719 Henry Cohn, 2026, needs more optimization.
30 299 0.163838281415 Henry Cohn, 2026, needs more optimization.
30 300 0.163913584934 Henry Cohn, 2026, needs more optimization.
30 301 0.164030128810 Henry Cohn, 2026, needs more optimization.
30 302 0.164122063369 Henry Cohn, 2026, needs more optimization.
30 303 0.164386398485 Henry Cohn, 2026, needs more optimization.
30 304 0.164523195656 Henry Cohn, 2026, needs more optimization.
30 305 0.164619849647 Henry Cohn, 2026, needs more optimization.
30 306 0.164709296137 Henry Cohn, 2026, needs more optimization.
30 307 0.164774093713 Henry Cohn, 2026, needs more optimization.
30 308 0.164917482249 Henry Cohn, 2026, needs more optimization.
30 309 0.164991851434 Henry Cohn, 2026, needs more optimization.
30 310 0.165062688399 Henry Cohn, 2026, needs more optimization.
30 311 0.165159340799 Henry Cohn, 2026, needs more optimization.
30 312 0.165196985121 Henry Cohn, 2026, needs more optimization.
30 313 0.165258613213 Henry Cohn, 2026, needs more optimization.
30 314 0.165327145331 Henry Cohn, 2026, needs more optimization.
30 315 0.165451135155 Henry Cohn, 2026, needs more optimization.
30 316 0.165536157506 Henry Cohn, 2026, needs more optimization.
30 317 0.165624354120 Henry Cohn, 2026, needs more optimization.
30 318 0.165648874613 Henry Cohn, 2026, needs more optimization.
30 319 0.165729688858 Henry Cohn, 2026, needs more optimization.
30 321 0.165845204854 Henry Cohn, 2026, needs more optimization.
30 322 0.166042547614 Henry Cohn, 2026, needs more optimization.
30 323 0.166143604073 Henry Cohn, 2026, needs more optimization.
30 324 0.166213286775 Henry Cohn, 2026, needs more optimization.
30 325 0.166351765326 Henry Cohn, 2026, needs more optimization.
30 326 0.166504365512 Henry Cohn, 2026, needs more optimization.
30 327 0.166560227017 Henry Cohn, 2026, needs more optimization.
30 329 0.166609038212 Henry Cohn, 2026, needs more optimization.
30 330 0.166611770456 Henry Cohn, 2026, needs more optimization.
30 331 0.166649261014 Henry Cohn, 2026, needs more optimization.
30 332 0.166672016028 Henry Cohn, 2026, needs more optimization.
30 333 0.166677400861 Henry Cohn, 2026, needs more optimization.
30 334 0.166744189007 Henry Cohn, 2026, needs more optimization.
30 335 0.166831976744 Henry Cohn, 2026, needs more optimization.
30 336 0.167007779116 Henry Cohn, 2026, needs more optimization.
30 337 0.167169837644 Henry Cohn, 2026, needs more optimization.
30 338 0.167259558723 Henry Cohn, 2026, needs more optimization.
30 339 0.167372026900 Henry Cohn, 2026, needs more optimization.
30 340 0.167744703322 Henry Cohn, 2026, needs more optimization.
30 341 0.168059918925 Henry Cohn, 2026, needs more optimization.
30 342 0.168366517503 Henry Cohn, 2026, needs more optimization.
30 343 0.169668683852 Henry Cohn, 2026, needs more optimization.
30 344 0.170174922586 Henry Cohn, 2026, needs more optimization.
30 345 0.171255671720 Henry Cohn, 2026, needs more optimization.
30 346 0.171706970072 Henry Cohn, 2026, needs more optimization.
30 347 0.172541623002 Henry Cohn, 2026, needs more optimization.
30 348 0.172767920575 Henry Cohn, 2026, needs more optimization.
30 349 0.173907895363 Henry Cohn, 2026, needs more optimization.
30 350 0.174539092867 Henry Cohn, 2026, needs more optimization.
30 351 0.174828529035 Henry Cohn, 2026, needs more optimization.
30 352 0.175785622384 Henry Cohn, 2026, needs more optimization.
30 353 0.176381222125 Henry Cohn, 2026, needs more optimization.
30 354 0.176987133640 Henry Cohn, 2026, needs more optimization.
30 355 0.177440835272 Henry Cohn, 2026, needs more optimization.
30 356 0.178184486796 Henry Cohn, 2026, needs more optimization.
30 357 0.178682235562 Henry Cohn, 2026, needs more optimization.
30 358 0.179180903171 Henry Cohn, 2026, needs more optimization.
30 359 0.179789470582 Henry Cohn, 2026, needs more optimization.
30 360 0.180414553640 Henry Cohn, 2026, needs more optimization.
30 361 0.180672413600 Henry Cohn, 2026, needs more optimization.
30 362 0.181130389098 Henry Cohn, 2026, needs more optimization.
30 363 0.181411088336 Henry Cohn, 2026, needs more optimization.
30 364 0.181866360304 Henry Cohn, 2026, needs more optimization.
30 365 0.182221045799 Henry Cohn, 2026, needs more optimization.
30 366 0.182770785048 Henry Cohn, 2026, needs more optimization.
30 367 0.183023057260 Henry Cohn, 2026, needs more optimization.
30 368 0.183257844109 Henry Cohn, 2026, needs more optimization.
30 369 0.183482426664 Henry Cohn, 2026, needs more optimization.
30 370 0.184940911031 Henry Cohn, 2026, needs more optimization.
30 371 0.185088292720 Henry Cohn, 2026, needs more optimization.
30 372 0.185429901422 Henry Cohn, 2026, needs more optimization.
30 373 0.185539158058 Henry Cohn, 2026, needs more optimization.
30 374 0.185576241200 Henry Cohn, 2026, needs more optimization.
30 375 0.186704644017 Henry Cohn, 2026, needs more optimization.
30 376 0.186916026808 Henry Cohn, 2026, needs more optimization.
30 377 0.187073298328 Henry Cohn, 2026, needs more optimization.
30 378 0.187111888225 Henry Cohn, 2026, needs more optimization.
30 379 0.187284166837 Henry Cohn, 2026, needs more optimization.
30 380 0.187343434297 Henry Cohn, 2026, needs more optimization.
30 381 0.187353919740 Henry Cohn, 2026, needs more optimization.
30 382 0.187362726679 Henry Cohn, 2026, needs more optimization.
30 383 0.187504714872 Henry Cohn, 2026, needs more optimization.
30 384 0.187803524235 Henry Cohn, 2026, needs more optimization.
30 385 0.187865203131 Henry Cohn, 2026, needs more optimization.
30 386 0.187889941199 Henry Cohn, 2026, needs more optimization.
30 387 0.187973619787 Henry Cohn, 2026, needs more optimization.
30 388 0.188519911437 Henry Cohn, 2026, needs more optimization.
30 389 0.188596242464 Henry Cohn, 2026, needs more optimization.
30 390 0.188607785974 Henry Cohn, 2026, needs more optimization.
30 391 0.189078920106 Henry Cohn, 2026, needs more optimization.
30 392 0.189127362657 Henry Cohn, 2026, needs more optimization.
30 393 0.189242596139 Henry Cohn, 2026, needs more optimization.
30 394 0.189274674873 Henry Cohn, 2026, needs more optimization.
30 395 0.189834728410 Henry Cohn, 2026, needs more optimization.
30 396 0.190019054114 Henry Cohn, 2026, needs more optimization.
30 397 0.190080518561 Henry Cohn, 2026, needs more optimization.
30 398 0.190651319337 Henry Cohn, 2026, needs more optimization.
30 399 0.190726337523 Henry Cohn, 2026, needs more optimization.
30 400 0.191105263361 Henry Cohn, 2026, needs more optimization.
30 401 0.191439850332 Henry Cohn, 2026, needs more optimization.
30 402 0.191643729952 Henry Cohn, 2026, needs more optimization.
30 403 0.192137893738 Henry Cohn, 2026, needs more optimization.
30 404 0.192280006766 Henry Cohn, 2026, needs more optimization.
30 405 0.192491150077 Henry Cohn, 2026, needs more optimization.
30 406 0.192799647271 Henry Cohn, 2026, needs more optimization.
30 407 0.193006096885 Henry Cohn, 2026, needs more optimization.
30 408 0.193159303253 Henry Cohn, 2026, needs more optimization.
30 409 0.193539483328 Henry Cohn, 2026, needs more optimization.
30 410 0.193832449194 Henry Cohn, 2026, needs more optimization.
30 411 0.194074992931 Henry Cohn, 2026, needs more optimization.
30 412 0.194348007047 Henry Cohn, 2026, needs more optimization.
30 453 0.194630872484 Orthogonal union of 451 points in 29 dimensions and 2 points in 1 dimension.
149⁢x−29
30 454 0.194633481928 Henry Cohn, 2026, needs more optimization.
30 455 0.197953289166 Henry Cohn, 2026, needs more optimization.
30 456 0.197994749415 Henry Cohn, 2026, needs more optimization.
30 457 0.198028667553 Henry Cohn, 2026, needs more optimization.
30 458 0.198059747513 Henry Cohn, 2026, needs more optimization.
30 459 0.198079686279 Henry Cohn, 2026, needs more optimization.
30 460 0.198161375436 Henry Cohn, 2026, needs more optimization.
30 461 0.198173824763 Henry Cohn, 2026, needs more optimization.
30 462 0.198318889603 Henry Cohn, 2026, needs more optimization.
30 463 0.198420905253 Henry Cohn, 2026, needs more optimization.
30 464 0.198465098936 Henry Cohn, 2026, needs more optimization.
30 465 0.198489340987 Henry Cohn, 2026, needs more optimization.
30 466 0.198512596683 Henry Cohn, 2026, needs more optimization.
30 467 0.198575187935 Henry Cohn, 2026, needs more optimization.
30 468 0.198594519901 Henry Cohn, 2026, needs more optimization.
30 469 0.198637769453 Henry Cohn, 2026, needs more optimization.
30 470 0.198712294012 Henry Cohn, 2026, needs more optimization.
30 471 0.198747102503 Henry Cohn, 2026, needs more optimization.
30 472 0.198818343955 Henry Cohn, 2026, needs more optimization.
30 473 0.198863633518 Henry Cohn, 2026, needs more optimization.
30 474 0.198921263529 Henry Cohn, 2026, needs more optimization.
30 475 0.198981912028 Henry Cohn, 2026, needs more optimization.
30 476 0.199001231957 Henry Cohn, 2026, needs more optimization.
30 477 0.199075719093 Henry Cohn, 2026, needs more optimization.
30 478 0.199105160500 Henry Cohn, 2026, needs more optimization.
30 479 0.199132461201 Henry Cohn, 2026, needs more optimization.
30 480 0.199160767671 Henry Cohn, 2026, needs more optimization.
30 481 0.199199045540 Henry Cohn, 2026, needs more optimization.
30 482 0.199227788926 Henry Cohn, 2026, needs more optimization.
30 483 0.199259808351 Henry Cohn, 2026, needs more optimization.
30 484 0.199262005628 Henry Cohn, 2026, needs more optimization.
30 485 0.199294311754 Henry Cohn, 2026, needs more optimization.
30 486 0.199303263015 Henry Cohn, 2026, needs more optimization.
30 487 0.199326976741 Henry Cohn, 2026, needs more optimization.
30 488 0.199364882470 Henry Cohn, 2026, needs more optimization.
30 489 0.199365817904 Henry Cohn, 2026, needs more optimization.
30 491 0.199371526644 Henry Cohn, 2026, needs more optimization.
30 492 0.199389103222 Henry Cohn, 2026, needs more optimization.
30 493 0.199402409902 Henry Cohn, 2026, needs more optimization.
30 494 0.199424862742 Henry Cohn, 2026, needs more optimization.
30 495 0.199432770354 Henry Cohn, 2026, needs more optimization.
30 496 0.199446246734 Henry Cohn, 2026, needs more optimization.
30 498 0.199454335626 Henry Cohn, 2026, needs more optimization.
30 499 0.199470153745 Henry Cohn, 2026, needs more optimization.
30 500 0.199489294523 Henry Cohn, 2026, needs more optimization.
30 501 0.199497738943 Henry Cohn, 2026, needs more optimization.
30 502 0.199540643100 Henry Cohn, 2026, needs more optimization.
30 503 0.199553900555 Henry Cohn, 2026, needs more optimization.
30 504 0.199568217923 Henry Cohn, 2026, needs more optimization.
30 505 0.199573175226 Henry Cohn, 2026, needs more optimization.
30 506 0.199577472587 Henry Cohn, 2026, needs more optimization.
30 507 0.199596277719 Henry Cohn, 2026, needs more optimization.
30 508 0.199615760314 Henry Cohn, 2026, needs more optimization.
30 509 0.199646341647 Henry Cohn, 2026, needs more optimization.
30 510 0.199655100280 Henry Cohn, 2026, needs more optimization.
30 511 0.199674451230 Henry Cohn, 2026, needs more optimization.
30 512 0.199721954080 Henry Cohn, 2026, needs more optimization.
30 513 0.199738507682 Henry Cohn, 2026, needs more optimization.
30 514 0.199746548714 Henry Cohn, 2026, needs more optimization.
30 515 0.199756382202 Henry Cohn, 2026, needs more optimization.
30 516 0.199765444409 Henry Cohn, 2026, needs more optimization.
30 518 0.199771448081 Henry Cohn, 2026, needs more optimization.
30 519 0.199794030723 Henry Cohn, 2026, needs more optimization.
30 520 0.199797041214 Henry Cohn, 2026, needs more optimization.
30 521 0.199809436348 Henry Cohn, 2026, needs more optimization.
30 522 0.199817094649 Henry Cohn, 2026, needs more optimization.
30 523 0.199824482241 Henry Cohn, 2026, needs more optimization.
30 524 0.199837257088 Henry Cohn, 2026, needs more optimization.
30 525 0.199856427948 Henry Cohn, 2026, needs more optimization.
30 526 0.199868713076 Henry Cohn, 2026, needs more optimization.
30 528 0.199879039438 Henry Cohn, 2026, needs more optimization.
30 529 0.199884326518 Henry Cohn, 2026, needs more optimization.
30 530 0.199893048307 Henry Cohn, 2026, needs more optimization.
30 531 0.199899461300 Henry Cohn, 2026, needs more optimization.
30 533 0.199913202444 Henry Cohn, 2026, needs more optimization.
30 534 0.199917003282 Henry Cohn, 2026, needs more optimization.
30 536 0.199926490740 Henry Cohn, 2026, needs more optimization.
30 537 0.199929622995 Henry Cohn, 2026, needs more optimization.
30 538 0.199943245294 Henry Cohn, 2026, needs more optimization.
30 539 0.199957877337 Henry Cohn, 2026, needs more optimization.
30 540 0.199965494895 Henry Cohn, 2026, needs more optimization.
30 656 0.2 Henry Cohn, 2026.
5⁢x−1
30 657 0.203357314611 Henry Cohn, 2026, needs more optimization.
30 668 0.236314226398 Henry Cohn, 2026, needs more optimization.
30 672 0.236377261200 Henry Cohn, 2026, needs more optimization.
30 673 0.236918284945 Henry Cohn, 2026, needs more optimization.
30 674 0.236920422534 Henry Cohn, 2026, needs more optimization.
30 678 0.236925951928 Henry Cohn, 2026, needs more optimization.
30 681 0.237001677348 Henry Cohn, 2026, needs more optimization.
30 691 0.237009720244 Henry Cohn, 2026, needs more optimization.
30 693 0.237081525824 Henry Cohn, 2026, needs more optimization.
30 696 0.237089914130 Henry Cohn, 2026, needs more optimization.
30 700 0.237187964978 Henry Cohn, 2026, needs more optimization.
30 701 0.237221909388 Henry Cohn, 2026, needs more optimization.
30 702 0.237288749806 Henry Cohn, 2026, needs more optimization.
30 703 0.237435500065 Henry Cohn, 2026, needs more optimization.
30 705 0.237459609039 Henry Cohn, 2026, needs more optimization.
30 706 0.237475999095 Henry Cohn, 2026, needs more optimization.
30 710 0.237728567165 Henry Cohn, 2026, needs more optimization.
30 714 0.237756970643 Henry Cohn, 2026, needs more optimization.
30 719 0.237776789094 Henry Cohn, 2026, needs more optimization.
30 720 0.237865178635 Henry Cohn, 2026, needs more optimization.
30 721 0.238736224205 Henry Cohn, 2026, needs more optimization.
30 722 0.238756977195 Henry Cohn, 2026, needs more optimization.
30 724 0.238761202535 Henry Cohn, 2026, needs more optimization.
30 726 0.239067212617 Henry Cohn, 2026, needs more optimization.
30 728 0.239067244233 Henry Cohn, 2026, needs more optimization.
30 730 0.239094778813 Henry Cohn, 2026, needs more optimization.
30 731 0.239166627991 Henry Cohn, 2026, needs more optimization.
30 732 0.239206589686 Henry Cohn, 2026, needs more optimization.
30 733 0.239481826296 Henry Cohn, 2026, needs more optimization.
30 734 0.239488236158 Henry Cohn, 2026, needs more optimization.
30 735 0.239521361274 Henry Cohn, 2026, needs more optimization.
30 737 0.239591135665 Henry Cohn, 2026, needs more optimization.
30 738 0.239758265430 Henry Cohn, 2026, needs more optimization.
30 740 0.239903138003 Henry Cohn, 2026, needs more optimization.
30 741 0.240016212448 Henry Cohn, 2026, needs more optimization.
30 742 0.240047397818 Henry Cohn, 2026, needs more optimization.
30 743 0.240137136336 Henry Cohn, 2026, needs more optimization.
30 744 0.240161697120 Henry Cohn, 2026, needs more optimization.
30 745 0.240360569008 Henry Cohn, 2026, needs more optimization.
30 746 0.240451247765 Henry Cohn, 2026, needs more optimization.
30 747 0.240484685957 Henry Cohn, 2026, needs more optimization.
30 748 0.240528313917 Henry Cohn, 2026, needs more optimization.
30 749 0.240554430614 Henry Cohn, 2026, needs more optimization.
30 763 0.240703991244 Henry Cohn, 2026, needs more optimization.
30 770 0.241342155304 Henry Cohn, 2026, needs more optimization.
30 773 0.241530816684 Henry Cohn, 2026, needs more optimization.
30 776 0.241978171180 Henry Cohn, 2026, needs more optimization.
30 777 0.242107773030 Henry Cohn, 2026, needs more optimization.
30 778 0.242359802488 Henry Cohn, 2026, needs more optimization.
30 779 0.242430430831 Henry Cohn, 2026, needs more optimization.
30 780 0.242509873167 Henry Cohn, 2026, needs more optimization.
30 781 0.242601852111 Henry Cohn, 2026, needs more optimization.
30 782 0.242758045414 Henry Cohn, 2026, needs more optimization.
30 785 0.242798770621 Henry Cohn, 2026, needs more optimization.
30 786 0.242887759806 Henry Cohn, 2026, needs more optimization.
30 787 0.242993087457 Henry Cohn, 2026, needs more optimization.
30 788 0.243024560779 Henry Cohn, 2026, needs more optimization.
30 792 0.243105200208 Henry Cohn, 2026, needs more optimization.
30 793 0.243245344327 Henry Cohn, 2026, needs more optimization.
30 794 0.243348399571 Henry Cohn, 2026, needs more optimization.
30 795 0.243388491791 Henry Cohn, 2026, needs more optimization.
30 796 0.243529680129 Henry Cohn, 2026, needs more optimization.
30 797 0.243624522288 Henry Cohn, 2026, needs more optimization.
30 798 0.243798852530 Henry Cohn, 2026, needs more optimization.
30 801 0.243890530328 Henry Cohn, 2026, needs more optimization.
30 802 0.244015893997 Henry Cohn, 2026, needs more optimization.
30 803 0.244170339962 Henry Cohn, 2026, needs more optimization.
30 804 0.244325283674 Henry Cohn, 2026, needs more optimization.
30 805 0.244447395768 Henry Cohn, 2026, needs more optimization.
30 806 0.244573440964 Henry Cohn, 2026, needs more optimization.
30 808 0.244690421155 Henry Cohn, 2026, needs more optimization.
30 809 0.244779688501 Henry Cohn, 2026, needs more optimization.
30 810 0.244922725219 Henry Cohn, 2026, needs more optimization.
30 812 0.244965585856 Henry Cohn, 2026, needs more optimization.
30 813 0.245155935684 Henry Cohn, 2026, needs more optimization.
30 814 0.245186754454 Henry Cohn, 2026, needs more optimization.
30 815 0.245239378165 Henry Cohn, 2026, needs more optimization.
30 816 0.245366165984 Henry Cohn, 2026, needs more optimization.
30 817 0.245366211987 Henry Cohn, 2026, needs more optimization.
30 820 0.245522335431 Henry Cohn, 2026, needs more optimization.
30 821 0.245677951805 Henry Cohn, 2026, needs more optimization.
30 825 0.245791982728 Henry Cohn, 2026, needs more optimization.
30 826 0.245933341306 Henry Cohn, 2026, needs more optimization.
30 827 0.246073879364 Henry Cohn, 2026, needs more optimization.
30 828 0.246141859367 Henry Cohn, 2026, needs more optimization.
30 831 0.246177388603 Henry Cohn, 2026, needs more optimization.
30 832 0.246349731549 Henry Cohn, 2026, needs more optimization.
30 834 0.246399789707 Henry Cohn, 2026, needs more optimization.
30 836 0.246449952489 Henry Cohn, 2026, needs more optimization.
30 837 0.246533529710 Henry Cohn, 2026, needs more optimization.
30 838 0.246617519818 Henry Cohn, 2026, needs more optimization.
30 839 0.246629052009 Henry Cohn, 2026, needs more optimization.
30 842 0.246715201341 Henry Cohn, 2026, needs more optimization.
30 843 0.246814450356 Henry Cohn, 2026, needs more optimization.
30 844 0.246879098535 Henry Cohn, 2026, needs more optimization.
30 845 0.247040587943 Henry Cohn, 2026, needs more optimization.
30 846 0.247125530744 Henry Cohn, 2026, needs more optimization.
30 847 0.247195365237 Henry Cohn, 2026, needs more optimization.
30 848 0.247288097729 Henry Cohn, 2026, needs more optimization.
30 849 0.247292207696 Henry Cohn, 2026, needs more optimization.
30 850 0.247363148060 Henry Cohn, 2026, needs more optimization.
30 851 0.247434753393 Henry Cohn, 2026, needs more optimization.
30 852 0.247452518800 Henry Cohn, 2026, needs more optimization.
30 855 0.247502862754 Henry Cohn, 2026, needs more optimization.
30 856 0.247571670819 Henry Cohn, 2026, needs more optimization.
30 858 0.247585275996 Henry Cohn, 2026, needs more optimization.
30 861 0.247652816676 Henry Cohn, 2026, needs more optimization.
30 862 0.247692030522 Henry Cohn, 2026, needs more optimization.
30 863 0.247769883253 Henry Cohn, 2026, needs more optimization.
30 864 0.247823832792 Henry Cohn, 2026, needs more optimization.
30 865 0.247895185171 Henry Cohn, 2026, needs more optimization.
30 867 0.247948674489 Henry Cohn, 2026, needs more optimization.
30 869 0.247976152399 Henry Cohn, 2026, needs more optimization.
30 870 0.248018216175 Henry Cohn, 2026, needs more optimization.
30 871 0.248081817209 Henry Cohn, 2026, needs more optimization.
30 872 0.248128050401 Henry Cohn, 2026, needs more optimization.
30 873 0.248146039395 Henry Cohn, 2026, needs more optimization.
30 874 0.248157828945 Henry Cohn, 2026, needs more optimization.
30 877 0.248191743618 Henry Cohn, 2026, needs more optimization.
30 878 0.248248989610 Henry Cohn, 2026, needs more optimization.
30 879 0.248297624133 Henry Cohn, 2026, needs more optimization.
30 881 0.248346989631 Henry Cohn, 2026, needs more optimization.
30 883 0.248386883292 Henry Cohn, 2026, needs more optimization.
30 884 0.248437926495 Henry Cohn, 2026, needs more optimization.
30 886 0.248465079514 Henry Cohn, 2026, needs more optimization.
30 887 0.248499171926 Henry Cohn, 2026, needs more optimization.
30 888 0.248548069054 Henry Cohn, 2026, needs more optimization.
30 889 0.248586975629 Henry Cohn, 2026, needs more optimization.
30 890 0.248616255672 Henry Cohn, 2026, needs more optimization.
30 894 0.248636183852 Henry Cohn, 2026, needs more optimization.
30 896 0.248692997527 Henry Cohn, 2026, needs more optimization.
30 897 0.248712270099 Henry Cohn, 2026, needs more optimization.
30 898 0.248736955107 Henry Cohn, 2026, needs more optimization.
30 899 0.248764773929 Henry Cohn, 2026, needs more optimization.
30 900 0.248777216355 Henry Cohn, 2026, needs more optimization.
30 901 0.248817605001 Henry Cohn, 2026, needs more optimization.
30 902 0.248859929428 Henry Cohn, 2026, needs more optimization.
30 904 0.248893290762 Henry Cohn, 2026, needs more optimization.
30 905 0.248894959067 Henry Cohn, 2026, needs more optimization.
30 908 0.248928798760 Henry Cohn, 2026, needs more optimization.
30 909 0.248966070368 Henry Cohn, 2026, needs more optimization.
30 910 0.249002627148 Henry Cohn, 2026, needs more optimization.
30 911 0.249017146761 Henry Cohn, 2026, needs more optimization.
30 915 0.249020307232 Henry Cohn, 2026, needs more optimization.
30 916 0.249028834996 Henry Cohn, 2026, needs more optimization.
30 917 0.249054019841 Henry Cohn, 2026, needs more optimization.
30 918 0.249063223588 Henry Cohn, 2026, needs more optimization.
30 922 0.249134375250 Henry Cohn, 2026, needs more optimization.
30 923 0.249178882584 Henry Cohn, 2026, needs more optimization.
30 927 0.249185953942 Henry Cohn, 2026, needs more optimization.
30 928 0.249205628996 Henry Cohn, 2026, needs more optimization.
30 929 0.249226203565 Henry Cohn, 2026, needs more optimization.
30 930 0.249243578616 Henry Cohn, 2026, needs more optimization.
30 940 0.249277269939 Henry Cohn, 2026, needs more optimization.
30 942 0.249286240491 Henry Cohn, 2026, needs more optimization.
30 945 0.249341667319 Henry Cohn, 2026, needs more optimization.
30 946 0.249358924108 Henry Cohn, 2026, needs more optimization.
30 947 0.249396018719 Henry Cohn, 2026, needs more optimization.
30 958 0.249413248686 Henry Cohn, 2026, needs more optimization.
30 960 0.249519250469 Henry Cohn, 2026, needs more optimization.
30 972 0.249519250473 Henry Cohn, 2026, needs more optimization.
30 973 0.249524609753 Henry Cohn, 2026, needs more optimization.
30 977 0.249582546924 Henry Cohn, 2026, needs more optimization.
30 978 0.249589848677 Henry Cohn, 2026, needs more optimization.
30 981 0.249604041453 Henry Cohn, 2026, needs more optimization.
30 982 0.249608609306 Henry Cohn, 2026, needs more optimization.
30 983 0.249612366695 Henry Cohn, 2026, needs more optimization.
30 984 0.249620220872 Henry Cohn, 2026, needs more optimization.
30 985 0.249656155181 Henry Cohn, 2026, needs more optimization.
30 986 0.249656876161 Henry Cohn, 2026, needs more optimization.
30 987 0.249665877373 Henry Cohn, 2026, needs more optimization.
30 988 0.249684408556 Henry Cohn, 2026, needs more optimization.
30 996 0.249715754763 Henry Cohn, 2026, needs more optimization.
30 997 0.249763899178 Henry Cohn, 2026, needs more optimization.
30 998 0.249774645917 Henry Cohn, 2026, needs more optimization.
30 1001 0.249775744585 Henry Cohn, 2026, needs more optimization.
30 1024 0.249928145007 Henry Cohn, 2026, needs more optimization.
31 63 0.026092422671 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
26071⁢x3−961⁢x2−31⁢x+1
31 64 0.030325190881 Henry Cohn, 2026.
31 65 0.037285566163 Henry Cohn, 2026.
31 66 0.037768798212 Henry Cohn, 2026.
31 67 0.038109705419 Henry Cohn, 2026, needs more optimization.
31 68 0.041215744725 Henry Cohn, 2026, needs more optimization.
31 69 0.043538391987 Henry Cohn, 2026.
31 70 0.043787493764 Henry Cohn, 2026, needs more optimization.
31 71 0.044034146773 Henry Cohn, 2026, needs more optimization.
31 72 0.044582818669 Henry Cohn, 2026, needs more optimization.
31 73 0.048631532114 Henry Cohn, 2026, needs more optimization.
31 74 0.050062100884 Henry Cohn, 2026, needs more optimization.
31 75 0.051024214945 Henry Cohn, 2026, needs more optimization.
31 76 0.052577066844 Henry Cohn, 2026, needs more optimization.
31 77 0.054426884298 Henry Cohn, 2026, needs more optimization.
31 78 0.055755020834 Henry Cohn, 2026, needs more optimization.
31 79 0.057284623728 Henry Cohn, 2026, needs more optimization.
31 80 0.058637531392 Henry Cohn, 2026, needs more optimization.
31 81 0.060011299846 Henry Cohn, 2026, needs more optimization.
31 82 0.061357120245 Henry Cohn, 2026, needs more optimization.
31 83 0.061674403313 Henry Cohn, 2026, needs more optimization.
31 84 0.062330750235 Henry Cohn, 2026, needs more optimization.
31 85 0.063445927592 Henry Cohn, 2026, needs more optimization.
31 86 0.064362380190 Henry Cohn, 2026, needs more optimization.
31 87 0.065615624659 Henry Cohn, 2026, needs more optimization.
31 88 0.067039610179 Henry Cohn, 2026, needs more optimization.
31 89 0.068506494757 Henry Cohn, 2026, needs more optimization.
31 90 0.069720921068 Henry Cohn, 2026, needs more optimization.
31 91 0.071598803746 Henry Cohn, 2026, needs more optimization.
31 92 0.072712083799 Henry Cohn, 2026, needs more optimization.
31 93 0.074055368828 Henry Cohn, 2026, needs more optimization.
31 94 0.074942126721 Henry Cohn, 2026, needs more optimization.
31 95 0.075273135809 Henry Cohn, 2026, needs more optimization.
31 96 0.075939747317 Henry Cohn, 2026, needs more optimization.
31 97 0.076159916596 Henry Cohn, 2026, needs more optimization.
31 98 0.076805767970 Henry Cohn, 2026, needs more optimization.
31 99 0.076860741510 Henry Cohn, 2026, needs more optimization.
31 100 0.076921146546 Henry Cohn, 2026, needs more optimization.
31 101 0.076984650247 Henry Cohn, 2026, needs more optimization.
31 102 0.077145708117 Henry Cohn, 2026, needs more optimization.
31 103 0.077287797096 Henry Cohn, 2026, needs more optimization.
31 104 0.077395981890 Henry Cohn, 2026, needs more optimization.
31 105 0.077813784516 Henry Cohn, 2026, needs more optimization.
31 106 0.078225854536 Henry Cohn, 2026, needs more optimization.
31 107 0.078676677442 Henry Cohn, 2026, needs more optimization.
31 108 0.079518381296 Henry Cohn, 2026, needs more optimization.
31 109 0.079832479835 Henry Cohn, 2026, needs more optimization.
31 110 0.080290691161 Henry Cohn, 2026, needs more optimization.
31 111 0.080622730435 Henry Cohn, 2026, needs more optimization.
31 112 0.080735257584 Henry Cohn, 2026, needs more optimization.
31 113 0.081335639701 Henry Cohn, 2026, needs more optimization.
31 114 0.081692980281 Henry Cohn, 2026, needs more optimization.
31 115 0.082453702884 Henry Cohn, 2026, needs more optimization.
31 116 0.083365429156 Henry Cohn, 2026, needs more optimization.
31 117 0.084477618007 Henry Cohn, 2026, needs more optimization.
31 120 0.084959387951 Henry Cohn, 2026.
115⁢x2+2⁢x−1
31 121 0.088280523807 Henry Cohn, 2026, needs more optimization.
31 122 0.088681596669 Henry Cohn, 2026, needs more optimization.
31 123 0.088839360666 Henry Cohn, 2026, needs more optimization.
31 124 0.089147393600 Henry Cohn, 2026, needs more optimization.
31 125 0.089579244825 Henry Cohn, 2026, needs more optimization.
31 126 0.089915482079 Henry Cohn, 2026, needs more optimization.
31 127 0.090288109813 Henry Cohn, 2026, needs more optimization.
31 128 0.090373087504 Henry Cohn, 2026, needs more optimization.
31 129 0.090746282741 Henry Cohn, 2026, needs more optimization.
31 130 0.091274921879 Henry Cohn, 2026, needs more optimization.
31 131 0.092148790945 Henry Cohn, 2026, needs more optimization.
31 132 0.093185745683 Henry Cohn, 2026, needs more optimization.
31 133 0.094603425758 Henry Cohn, 2026, needs more optimization.
31 134 0.095446492633 Henry Cohn, 2026, needs more optimization.
31 135 0.096343283771 Henry Cohn, 2026, needs more optimization.
31 136 0.097754486724 Henry Cohn, 2026, needs more optimization.
31 137 0.098799761728 Henry Cohn, 2026, needs more optimization.
31 138 0.099759169654 Henry Cohn, 2026, needs more optimization.
31 139 0.100441857520 Henry Cohn, 2026, needs more optimization.
31 140 0.101617334460 Henry Cohn, 2026, needs more optimization.
31 141 0.102422090255 Henry Cohn, 2026, needs more optimization.
31 142 0.102449892044 Henry Cohn, 2026, needs more optimization.
31 143 0.102497370842 Henry Cohn, 2026, needs more optimization.
31 144 0.102555111851 Henry Cohn, 2026, needs more optimization.
31 145 0.102555112096 Henry Cohn, 2026, needs more optimization.
31 146 0.102846173591 Henry Cohn, 2026, needs more optimization.
31 147 0.103818600059 Henry Cohn, 2026, needs more optimization.
31 148 0.104750072194 Henry Cohn, 2026, needs more optimization.
31 149 0.105239923843 Henry Cohn, 2026, needs more optimization.
31 150 0.106265188041 Henry Cohn, 2026, needs more optimization.
31 151 0.106990228860 Henry Cohn, 2026, needs more optimization.
31 152 0.107761952531 Henry Cohn, 2026, needs more optimization.
31 153 0.108593087869 Henry Cohn, 2026, needs more optimization.
31 154 0.109323202581 Henry Cohn, 2026, needs more optimization.
31 155 0.109955078169 Henry Cohn, 2026, needs more optimization.
31 156 0.110150193963 Henry Cohn, 2026, needs more optimization.
31 157 0.110354589252 Henry Cohn, 2026, needs more optimization.
31 158 0.110456173210 Henry Cohn, 2026, needs more optimization.
31 159 0.110681329322 Henry Cohn, 2026, needs more optimization.
31 160 0.111016675626 Henry Cohn, 2026, needs more optimization.
31 161 0.111512858029 Henry Cohn, 2026, needs more optimization.
31 162 0.111966055312 Henry Cohn, 2026, needs more optimization.
31 163 0.113070676059 Henry Cohn, 2026, needs more optimization.
31 164 0.113822129189 Henry Cohn, 2026, needs more optimization.
31 165 0.114366610289 Henry Cohn, 2026, needs more optimization.
31 166 0.115472340048 Henry Cohn, 2026, needs more optimization.
31 167 0.116367688596 Henry Cohn, 2026, needs more optimization.
31 168 0.117334619213 Henry Cohn, 2026, needs more optimization.
31 169 0.118278596134 Henry Cohn, 2026, needs more optimization.
31 170 0.119300570890 Henry Cohn, 2026, needs more optimization.
31 171 0.120183440460 Henry Cohn, 2026, needs more optimization.
31 172 0.121257618483 Henry Cohn, 2026, needs more optimization.
31 173 0.122372782253 Henry Cohn, 2026, needs more optimization.
31 174 0.123654081020 Henry Cohn, 2026, needs more optimization.
31 175 0.124761087498 Henry Cohn, 2026, needs more optimization.
31 176 0.125711817018 Henry Cohn, 2026, needs more optimization.
31 177 0.126360261699 Henry Cohn, 2026, needs more optimization.
31 178 0.127052830051 Henry Cohn, 2026, needs more optimization.
31 179 0.127663957418 Henry Cohn, 2026, needs more optimization.
31 180 0.127816144964 Henry Cohn, 2026, needs more optimization.
31 181 0.128013700047 Henry Cohn, 2026, needs more optimization.
31 182 0.128094035568 Henry Cohn, 2026, needs more optimization.
31 183 0.128107989663 Henry Cohn, 2026, needs more optimization.
31 184 0.128170522658 Henry Cohn, 2026, needs more optimization.
31 188 0.128237513434 Henry Cohn, 2026, needs more optimization.
31 189 0.128239137542 Orthogonal union of 187 points in 30 dimensions and 2 points in 1 dimension.
31 190 0.128239923510 Henry Cohn, 2026, needs more optimization.
31 191 0.128239923512 Henry Cohn, 2026, needs more optimization.
31 192 0.128240631311 Henry Cohn, 2026, needs more optimization.
31 193 0.128253078961 Henry Cohn, 2026, needs more optimization.
31 194 0.128419113486 Henry Cohn, 2026, needs more optimization.
31 195 0.128954799825 Henry Cohn, 2026, needs more optimization.
31 196 0.129729094256 Henry Cohn, 2026, needs more optimization.
31 197 0.130244257934 Henry Cohn, 2026, needs more optimization.
31 198 0.130246440826 Henry Cohn, 2026, needs more optimization.
31 199 0.131370211290 Henry Cohn, 2026, needs more optimization.
31 200 0.131390933578 Henry Cohn, 2026, needs more optimization.
31 201 0.135033235769 Henry Cohn, 2026, needs more optimization.
31 202 0.135898563417 Henry Cohn, 2026, needs more optimization.
31 203 0.136747432166 Henry Cohn, 2026, needs more optimization.
31 204 0.137361486234 Henry Cohn, 2026, needs more optimization.
31 205 0.137534137818 Henry Cohn, 2026, needs more optimization.
31 206 0.138236205136 Henry Cohn, 2026, needs more optimization.
31 207 0.138689257934 Henry Cohn, 2026, needs more optimization.
31 208 0.138972515824 Henry Cohn, 2026, needs more optimization.
31 209 0.139726803299 Henry Cohn, 2026, needs more optimization.
31 210 0.140499371851 Henry Cohn, 2026, needs more optimization.
31 211 0.140534130599 Henry Cohn, 2026, needs more optimization.
31 212 0.140643804157 Henry Cohn, 2026, needs more optimization.
31 213 0.140685797752 Henry Cohn, 2026, needs more optimization.
31 214 0.140906173950 Henry Cohn, 2026, needs more optimization.
31 215 0.141002104285 Henry Cohn, 2026, needs more optimization.
31 216 0.141043518100 Henry Cohn, 2026, needs more optimization.
31 217 0.141194306872 Henry Cohn, 2026, needs more optimization.
31 218 0.141299438882 Henry Cohn, 2026, needs more optimization.
31 219 0.141535549563 Henry Cohn, 2026, needs more optimization.
31 220 0.141898196716 Henry Cohn, 2026, needs more optimization.
31 221 0.141960977904 Henry Cohn, 2026, needs more optimization.
31 222 0.142036801158 Henry Cohn, 2026, needs more optimization.
31 223 0.142087140050 Henry Cohn, 2026, needs more optimization.
31 224 0.142157248961 Henry Cohn, 2026, needs more optimization.
31 225 0.142402596084 Henry Cohn, 2026, needs more optimization.
31 226 0.142820242868 Henry Cohn, 2026, needs more optimization.
31 227 0.142970277316 Henry Cohn, 2026, needs more optimization.
31 228 0.143197406776 Henry Cohn, 2026, needs more optimization.
31 229 0.143790628677 Henry Cohn, 2026, needs more optimization.
31 230 0.144361517486 Henry Cohn, 2026, needs more optimization.
31 231 0.144763465014 Henry Cohn, 2026, needs more optimization.
31 232 0.144900582615 Henry Cohn, 2026, needs more optimization.
31 233 0.145126151013 Henry Cohn, 2026, needs more optimization.
31 234 0.145322341245 Henry Cohn, 2026, needs more optimization.
31 235 0.145397171491 Henry Cohn, 2026, needs more optimization.
31 236 0.145513681913 Henry Cohn, 2026, needs more optimization.
31 237 0.145627495637 Henry Cohn, 2026, needs more optimization.
31 238 0.145772157764 Henry Cohn, 2026, needs more optimization.
31 239 0.145895467989 Henry Cohn, 2026, needs more optimization.
31 240 0.146019526881 Henry Cohn, 2026, needs more optimization.
31 241 0.146039834721 Henry Cohn, 2026, needs more optimization.
31 242 0.146205982235 Henry Cohn, 2026, needs more optimization.
31 243 0.146415039952 Henry Cohn, 2026, needs more optimization.
31 244 0.146528397415 Henry Cohn, 2026, needs more optimization.
31 245 0.146619489110 Henry Cohn, 2026, needs more optimization.
31 246 0.146732053827 Henry Cohn, 2026, needs more optimization.
31 247 0.146831712905 Henry Cohn, 2026, needs more optimization.
31 248 0.146902597777 Henry Cohn, 2026, needs more optimization.
31 249 0.147158446042 Henry Cohn, 2026, needs more optimization.
31 250 0.147195420205 Henry Cohn, 2026, needs more optimization.
31 251 0.147268145934 Henry Cohn, 2026, needs more optimization.
31 252 0.147328232900 Henry Cohn, 2026, needs more optimization.
31 253 0.147507516409 Henry Cohn, 2026, needs more optimization.
31 254 0.147571635436 Henry Cohn, 2026, needs more optimization.
31 255 0.147651852476 Henry Cohn, 2026, needs more optimization.
31 256 0.147825253569 Henry Cohn, 2026, needs more optimization.
31 257 0.147968345833 Henry Cohn, 2026, needs more optimization.
31 258 0.148277752911 Henry Cohn, 2026, needs more optimization.
31 259 0.148601520866 Henry Cohn, 2026, needs more optimization.
31 260 0.148609276458 Henry Cohn, 2026, needs more optimization.
31 261 0.148644948228 Henry Cohn, 2026, needs more optimization.
31 262 0.149117514884 Henry Cohn, 2026, needs more optimization.
31 263 0.149287089552 Henry Cohn, 2026, needs more optimization.
31 264 0.149732555875 Henry Cohn, 2026, needs more optimization.
31 265 0.150237776785 Henry Cohn, 2026, needs more optimization.
31 266 0.150573893375 Henry Cohn, 2026, needs more optimization.
31 267 0.150843935009 Henry Cohn, 2026, needs more optimization.
31 268 0.151041962608 Henry Cohn, 2026, needs more optimization.
31 269 0.151401411575 Henry Cohn, 2026, needs more optimization.
31 270 0.152144475851 Henry Cohn, 2026, needs more optimization.
31 271 0.152742121421 Henry Cohn, 2026, needs more optimization.
31 272 0.153078145507 Henry Cohn, 2026, needs more optimization.
31 273 0.154341281875 Henry Cohn, 2026, needs more optimization.
31 274 0.154503288004 Henry Cohn, 2026, needs more optimization.
31 275 0.154679069213 Henry Cohn, 2026, needs more optimization.
31 276 0.155433823340 Henry Cohn, 2026, needs more optimization.
31 277 0.156130780053 Henry Cohn, 2026, needs more optimization.
31 278 0.156473178121 Henry Cohn, 2026, needs more optimization.
31 279 0.156888408159 Henry Cohn, 2026, needs more optimization.
31 280 0.157536637333 Henry Cohn, 2026, needs more optimization.
31 281 0.158305035817 Henry Cohn, 2026, needs more optimization.
31 282 0.158882811040 Henry Cohn, 2026, needs more optimization.
31 283 0.159178195000 Henry Cohn, 2026, needs more optimization.
31 284 0.159667109469 Henry Cohn, 2026, needs more optimization.
31 285 0.160163304774 Henry Cohn, 2026, needs more optimization.
31 286 0.160550519777 Henry Cohn, 2026, needs more optimization.
31 287 0.161062425928 Henry Cohn, 2026, needs more optimization.
31 288 0.161640002440 Henry Cohn, 2026, needs more optimization.
31 289 0.161672546835 Henry Cohn, 2026, needs more optimization.
31 290 0.161714384711 Henry Cohn, 2026, needs more optimization.
31 291 0.161717425027 Henry Cohn, 2026, needs more optimization.
31 292 0.161780922598 Henry Cohn, 2026, needs more optimization.
31 293 0.161793759055 Henry Cohn, 2026, needs more optimization.
31 294 0.161803347682 Henry Cohn, 2026, needs more optimization.
31 295 0.161828090495 Henry Cohn, 2026, needs more optimization.
31 296 0.161854091544 Henry Cohn, 2026, needs more optimization.
31 297 0.161903004637 Henry Cohn, 2026, needs more optimization.
31 298 0.161947057807 Henry Cohn, 2026, needs more optimization.
31 299 0.162050187392 Henry Cohn, 2026, needs more optimization.
31 300 0.162139789291 Henry Cohn, 2026, needs more optimization.
31 301 0.162180867947 Henry Cohn, 2026, needs more optimization.
31 302 0.162344475435 Henry Cohn, 2026, needs more optimization.
31 303 0.162477759244 Henry Cohn, 2026, needs more optimization.
31 304 0.162502032770 Henry Cohn, 2026, needs more optimization.
31 305 0.162794689884 Henry Cohn, 2026, needs more optimization.
31 306 0.162957076224 Henry Cohn, 2026, needs more optimization.
31 307 0.163097732869 Henry Cohn, 2026, needs more optimization.
31 308 0.163196549645 Henry Cohn, 2026, needs more optimization.
31 309 0.163319038105 Henry Cohn, 2026, needs more optimization.
31 310 0.163523401836 Henry Cohn, 2026, needs more optimization.
31 311 0.163679022034 Henry Cohn, 2026, needs more optimization.
31 312 0.163772037050 Henry Cohn, 2026, needs more optimization.
31 313 0.163844651838 Henry Cohn, 2026, needs more optimization.
31 314 0.163936502297 Henry Cohn, 2026, needs more optimization.
31 315 0.163988052466 Henry Cohn, 2026, needs more optimization.
31 316 0.164101363662 Henry Cohn, 2026, needs more optimization.
31 317 0.164202130529 Henry Cohn, 2026, needs more optimization.
31 318 0.164239867802 Henry Cohn, 2026, needs more optimization.
31 319 0.164364098599 Henry Cohn, 2026, needs more optimization.
31 320 0.164494123494 Henry Cohn, 2026, needs more optimization.
31 321 0.164510421016 Henry Cohn, 2026, needs more optimization.
31 322 0.164584566293 Henry Cohn, 2026, needs more optimization.
31 323 0.164627942038 Henry Cohn, 2026, needs more optimization.
31 324 0.164697518698 Henry Cohn, 2026, needs more optimization.
31 325 0.164758630234 Henry Cohn, 2026, needs more optimization.
31 326 0.164851633698 Henry Cohn, 2026, needs more optimization.
31 327 0.164924205071 Henry Cohn, 2026, needs more optimization.
31 328 0.165066856975 Henry Cohn, 2026, needs more optimization.
31 329 0.165191479746 Henry Cohn, 2026, needs more optimization.
31 330 0.165224750477 Henry Cohn, 2026, needs more optimization.
31 331 0.165337160174 Henry Cohn, 2026, needs more optimization.
31 332 0.165411395132 Henry Cohn, 2026, needs more optimization.
31 333 0.165495767805 Henry Cohn, 2026, needs more optimization.
31 334 0.165552825138 Henry Cohn, 2026, needs more optimization.
31 335 0.165655138250 Henry Cohn, 2026, needs more optimization.
31 336 0.165725231605 Henry Cohn, 2026, needs more optimization.
31 337 0.165883408305 Henry Cohn, 2026, needs more optimization.
31 338 0.165960119802 Henry Cohn, 2026, needs more optimization.
31 339 0.166127688506 Henry Cohn, 2026, needs more optimization.
31 340 0.166253238175 Henry Cohn, 2026, needs more optimization.
31 341 0.166460538403 Henry Cohn, 2026, needs more optimization.
31 342 0.166524636217 Henry Cohn, 2026, needs more optimization.
31 343 0.166600432488 Henry Cohn, 2026, needs more optimization.
31 344 0.166649100310 Henry Cohn, 2026, needs more optimization.
31 345 0.166719326405 Henry Cohn, 2026, needs more optimization.
31 346 0.166763153372 Henry Cohn, 2026, needs more optimization.
31 347 0.166810965494 Henry Cohn, 2026, needs more optimization.
31 348 0.166916663517 Henry Cohn, 2026, needs more optimization.
31 349 0.166992619107 Henry Cohn, 2026, needs more optimization.
31 350 0.167094091055 Henry Cohn, 2026, needs more optimization.
31 351 0.167464624711 Henry Cohn, 2026, needs more optimization.
31 352 0.168440258172 Henry Cohn, 2026, needs more optimization.
31 353 0.168658409065 Henry Cohn, 2026, needs more optimization.
31 354 0.168922665001 Henry Cohn, 2026, needs more optimization.
31 355 0.169151217088 Henry Cohn, 2026, needs more optimization.
31 356 0.170040634690 Henry Cohn, 2026, needs more optimization.
31 357 0.170376180079 Henry Cohn, 2026, needs more optimization.
31 358 0.171054617681 Henry Cohn, 2026, needs more optimization.
31 359 0.171408214243 Henry Cohn, 2026, needs more optimization.
31 360 0.171764550177 Henry Cohn, 2026, needs more optimization.
31 361 0.178319833970 Henry Cohn, 2026, needs more optimization.
31 362 0.178329383049 Henry Cohn, 2026, needs more optimization.
31 363 0.178371171247 Henry Cohn, 2026, needs more optimization.
31 364 0.178417908535 Henry Cohn, 2026, needs more optimization.
31 365 0.178425302733 Henry Cohn, 2026, needs more optimization.
31 366 0.178548106239 Henry Cohn, 2026, needs more optimization.
31 367 0.178605678121 Henry Cohn, 2026, needs more optimization.
31 368 0.178651484586 Henry Cohn, 2026, needs more optimization.
31 369 0.178729520712 Henry Cohn, 2026, needs more optimization.
31 370 0.178887320262 Henry Cohn, 2026, needs more optimization.
31 371 0.179043153457 Henry Cohn, 2026, needs more optimization.
31 372 0.179378004276 Henry Cohn, 2026, needs more optimization.
31 373 0.179465711182 Henry Cohn, 2026, needs more optimization.
31 374 0.180091710426 Henry Cohn, 2026, needs more optimization.
31 375 0.180427618381 Henry Cohn, 2026, needs more optimization.
31 376 0.180594639937 Henry Cohn, 2026, needs more optimization.
31 377 0.180975600954 Henry Cohn, 2026, needs more optimization.
31 378 0.181566681204 Henry Cohn, 2026, needs more optimization.
31 379 0.181681663799 Henry Cohn, 2026, needs more optimization.
31 380 0.181722551896 Henry Cohn, 2026, needs more optimization.
31 381 0.181729933735 Henry Cohn, 2026, needs more optimization.
31 382 0.181959762469 Henry Cohn, 2026, needs more optimization.
31 383 0.182001575716 Henry Cohn, 2026, needs more optimization.
31 384 0.182083106656 Henry Cohn, 2026, needs more optimization.
31 386 0.182270253513 Henry Cohn, 2026, needs more optimization.
31 387 0.182290850601 Henry Cohn, 2026, needs more optimization.
31 388 0.182550466477 Henry Cohn, 2026, needs more optimization.
31 389 0.182699075297 Henry Cohn, 2026, needs more optimization.
31 390 0.182824479789 Henry Cohn, 2026, needs more optimization.
31 391 0.182978885347 Henry Cohn, 2026, needs more optimization.
31 392 0.183417443851 Henry Cohn, 2026, needs more optimization.
31 393 0.183584398350 Henry Cohn, 2026, needs more optimization.
31 394 0.183813928514 Henry Cohn, 2026, needs more optimization.
31 395 0.183962740199 Henry Cohn, 2026, needs more optimization.
31 396 0.184406462779 Henry Cohn, 2026, needs more optimization.
31 397 0.184692991859 Henry Cohn, 2026, needs more optimization.
31 398 0.184914444366 Henry Cohn, 2026, needs more optimization.
31 399 0.185369814767 Henry Cohn, 2026, needs more optimization.
31 400 0.185889495032 Henry Cohn, 2026, needs more optimization.
31 401 0.185990943528 Henry Cohn, 2026, needs more optimization.
31 402 0.186071192131 Henry Cohn, 2026, needs more optimization.
31 403 0.186295528531 Henry Cohn, 2026, needs more optimization.
31 404 0.186514632595 Henry Cohn, 2026, needs more optimization.
31 405 0.186920008330 Henry Cohn, 2026, needs more optimization.
31 406 0.187157188431 Henry Cohn, 2026, needs more optimization.
31 407 0.187355242961 Henry Cohn, 2026, needs more optimization.
31 408 0.187622622591 Henry Cohn, 2026, needs more optimization.
31 409 0.187718264098 Henry Cohn, 2026, needs more optimization.
31 410 0.187904299047 Henry Cohn, 2026, needs more optimization.
31 411 0.188184703800 Henry Cohn, 2026, needs more optimization.
31 412 0.188486871901 Henry Cohn, 2026, needs more optimization.
31 413 0.188687298815 Henry Cohn, 2026, needs more optimization.
31 414 0.188972756633 Henry Cohn, 2026, needs more optimization.
31 415 0.189140025568 Henry Cohn, 2026, needs more optimization.
31 416 0.189281511888 Henry Cohn, 2026, needs more optimization.
31 417 0.189533556109 Henry Cohn, 2026, needs more optimization.
31 418 0.189706954627 Henry Cohn, 2026, needs more optimization.
31 419 0.190032528147 Henry Cohn, 2026, needs more optimization.
31 420 0.190197553797 Henry Cohn, 2026, needs more optimization.
31 421 0.190395044770 Henry Cohn, 2026, needs more optimization.
31 422 0.190604707089 Henry Cohn, 2026, needs more optimization.
31 423 0.190842204505 Henry Cohn, 2026, needs more optimization.
31 424 0.191095063804 Henry Cohn, 2026, needs more optimization.
31 425 0.191324553420 Henry Cohn, 2026, needs more optimization.
31 426 0.191621738942 Henry Cohn, 2026, needs more optimization.
31 427 0.191784647319 Henry Cohn, 2026, needs more optimization.
31 428 0.191812697307 Henry Cohn, 2026, needs more optimization.
31 429 0.192009769134 Henry Cohn, 2026, needs more optimization.
31 430 0.192133422013 Henry Cohn, 2026, needs more optimization.
31 431 0.192427068785 Henry Cohn, 2026, needs more optimization.
31 432 0.192643525614 Henry Cohn, 2026, needs more optimization.
31 433 0.192956470742 Henry Cohn, 2026, needs more optimization.
31 434 0.193164279462 Henry Cohn, 2026, needs more optimization.
31 435 0.193251507474 Henry Cohn, 2026, needs more optimization.
31 436 0.193423195016 Henry Cohn, 2026, needs more optimization.
31 437 0.193684748324 Henry Cohn, 2026, needs more optimization.
31 438 0.193800115061 Henry Cohn, 2026, needs more optimization.
31 439 0.193999157166 Henry Cohn, 2026, needs more optimization.
31 455 0.194630872484 Orthogonal union of 451 points in 29 dimensions and 4 points in 2 dimensions.
149⁢x−29
31 456 0.194631802812 Henry Cohn, 2026, needs more optimization.
31 457 0.195834894726 Henry Cohn, 2026, needs more optimization.
31 458 0.195921495031 Henry Cohn, 2026, needs more optimization.
31 459 0.195979184989 Henry Cohn, 2026, needs more optimization.
31 460 0.196177940714 Henry Cohn, 2026, needs more optimization.
31 461 0.196384403965 Henry Cohn, 2026, needs more optimization.
31 462 0.196473506741 Henry Cohn, 2026, needs more optimization.
31 463 0.196641219299 Henry Cohn, 2026, needs more optimization.
31 464 0.196728952000 Henry Cohn, 2026, needs more optimization.
31 465 0.196885290257 Henry Cohn, 2026, needs more optimization.
31 466 0.196958470128 Henry Cohn, 2026, needs more optimization.
31 467 0.197130196122 Henry Cohn, 2026, needs more optimization.
31 468 0.197274959642 Henry Cohn, 2026, needs more optimization.
31 469 0.197347481058 Henry Cohn, 2026, needs more optimization.
31 470 0.197428610843 Henry Cohn, 2026, needs more optimization.
31 471 0.197503021760 Henry Cohn, 2026, needs more optimization.
31 472 0.197573506585 Henry Cohn, 2026, needs more optimization.
31 473 0.197607512768 Henry Cohn, 2026, needs more optimization.
31 474 0.197609938392 Henry Cohn, 2026, needs more optimization.
31 475 0.197722788779 Henry Cohn, 2026, needs more optimization.
31 476 0.197793234884 Henry Cohn, 2026, needs more optimization.
31 477 0.197857429189 Henry Cohn, 2026, needs more optimization.
31 478 0.197894494993 Henry Cohn, 2026, needs more optimization.
31 482 0.198007976314 Henry Cohn, 2026, needs more optimization.
31 484 0.198137453435 Henry Cohn, 2026, needs more optimization.
31 485 0.198193504851 Henry Cohn, 2026, needs more optimization.
31 486 0.198229119604 Henry Cohn, 2026, needs more optimization.
31 487 0.198337681761 Henry Cohn, 2026, needs more optimization.
31 488 0.198357279729 Henry Cohn, 2026, needs more optimization.
31 489 0.198479626464 Henry Cohn, 2026, needs more optimization.
31 490 0.198486353178 Henry Cohn, 2026, needs more optimization.
31 491 0.198560336426 Henry Cohn, 2026, needs more optimization.
31 492 0.198591604159 Henry Cohn, 2026, needs more optimization.
31 493 0.198636005526 Henry Cohn, 2026, needs more optimization.
31 494 0.198665795837 Henry Cohn, 2026, needs more optimization.
31 495 0.198761962271 Henry Cohn, 2026, needs more optimization.
31 498 0.198770936019 Henry Cohn, 2026, needs more optimization.
31 499 0.198804821624 Henry Cohn, 2026, needs more optimization.
31 500 0.198834347918 Henry Cohn, 2026, needs more optimization.
31 501 0.198900316957 Henry Cohn, 2026, needs more optimization.
31 502 0.198937776560 Henry Cohn, 2026, needs more optimization.
31 503 0.198982506619 Henry Cohn, 2026, needs more optimization.
31 504 0.199004171527 Henry Cohn, 2026, needs more optimization.
31 505 0.199022917011 Henry Cohn, 2026, needs more optimization.
31 506 0.199058675932 Henry Cohn, 2026, needs more optimization.
31 507 0.199063257237 Henry Cohn, 2026, needs more optimization.
31 509 0.199089187551 Henry Cohn, 2026, needs more optimization.
31 510 0.199104588661 Henry Cohn, 2026, needs more optimization.
31 511 0.199128070450 Henry Cohn, 2026, needs more optimization.
31 512 0.199141277337 Henry Cohn, 2026, needs more optimization.
31 513 0.199195461808 Henry Cohn, 2026, needs more optimization.
31 514 0.199217235978 Henry Cohn, 2026, needs more optimization.
31 515 0.199248705815 Henry Cohn, 2026, needs more optimization.
31 516 0.199284279997 Henry Cohn, 2026, needs more optimization.
31 517 0.199312735910 Henry Cohn, 2026, needs more optimization.
31 518 0.199345822695 Henry Cohn, 2026, needs more optimization.
31 520 0.199381331290 Henry Cohn, 2026, needs more optimization.
31 521 0.199404018895 Henry Cohn, 2026, needs more optimization.
31 522 0.199426066264 Henry Cohn, 2026, needs more optimization.
31 523 0.199454084530 Henry Cohn, 2026, needs more optimization.
31 524 0.199463450519 Henry Cohn, 2026, needs more optimization.
31 525 0.199472819288 Henry Cohn, 2026, needs more optimization.
31 527 0.199500086827 Henry Cohn, 2026, needs more optimization.
31 529 0.199508187575 Henry Cohn, 2026, needs more optimization.
31 530 0.199534627648 Henry Cohn, 2026, needs more optimization.
31 531 0.199555227477 Henry Cohn, 2026, needs more optimization.
31 537 0.199563047853 Henry Cohn, 2026, needs more optimization.
31 538 0.199573886134 Henry Cohn, 2026, needs more optimization.
31 539 0.199588681747 Henry Cohn, 2026, needs more optimization.
31 540 0.199596768873 Henry Cohn, 2026, needs more optimization.
31 541 0.199609475559 Henry Cohn, 2026, needs more optimization.
31 542 0.199634292461 Henry Cohn, 2026, needs more optimization.
31 543 0.199642377845 Henry Cohn, 2026, needs more optimization.
31 544 0.199663353377 Henry Cohn, 2026, needs more optimization.
31 545 0.199668197075 Henry Cohn, 2026, needs more optimization.
31 547 0.199680114357 Henry Cohn, 2026, needs more optimization.
31 548 0.199689739084 Henry Cohn, 2026, needs more optimization.
31 549 0.199702141752 Henry Cohn, 2026, needs more optimization.
31 550 0.199705513971 Henry Cohn, 2026, needs more optimization.
31 551 0.199716955690 Henry Cohn, 2026, needs more optimization.
31 552 0.199726442270 Henry Cohn, 2026, needs more optimization.
31 555 0.199757849597 Henry Cohn, 2026, needs more optimization.
31 557 0.199776119799 Henry Cohn, 2026, needs more optimization.
31 559 0.199783932172 Henry Cohn, 2026, needs more optimization.
31 561 0.199803160000 Henry Cohn, 2026, needs more optimization.
31 562 0.199815330527 Henry Cohn, 2026, needs more optimization.
31 564 0.199820203361 Henry Cohn, 2026, needs more optimization.
31 565 0.199826094307 Henry Cohn, 2026, needs more optimization.
31 566 0.199840711288 Henry Cohn, 2026, needs more optimization.
31 568 0.199857594981 Henry Cohn, 2026, needs more optimization.
31 569 0.199867814196 Henry Cohn, 2026, needs more optimization.
31 570 0.199871458435 Henry Cohn, 2026, needs more optimization.
31 573 0.199902346414 Henry Cohn, 2026, needs more optimization.
31 574 0.199903085177 Henry Cohn, 2026, needs more optimization.
31 575 0.199906165626 Henry Cohn, 2026, needs more optimization.
31 576 0.199908109206 Henry Cohn, 2026, needs more optimization.
31 577 0.199915704084 Henry Cohn, 2026, needs more optimization.
31 579 0.199917724486 Henry Cohn, 2026, needs more optimization.
31 581 0.199923929318 Henry Cohn, 2026, needs more optimization.
31 583 0.199929221202 Henry Cohn, 2026, needs more optimization.
31 584 0.199930777765 Henry Cohn, 2026, needs more optimization.
31 585 0.199956050956 Henry Cohn, 2026, needs more optimization.
31 688 0.2 Henry Cohn, 2026.
5⁢x−1
31 689 0.206391434129 Henry Cohn, 2026, needs more optimization.
31 690 0.216286151279 Henry Cohn, 2026, needs more optimization.
31 691 0.216526158001 Henry Cohn, 2026, needs more optimization.
31 692 0.216916276167 Henry Cohn, 2026, needs more optimization.
31 693 0.217258765567 Henry Cohn, 2026, needs more optimization.
31 694 0.217628082025 Henry Cohn, 2026, needs more optimization.
31 695 0.217855201495 Henry Cohn, 2026, needs more optimization.
31 696 0.218026695605 Henry Cohn, 2026, needs more optimization.
31 697 0.218249083445 Henry Cohn, 2026, needs more optimization.
31 698 0.218486500016 Henry Cohn, 2026, needs more optimization.
31 699 0.218747347666 Henry Cohn, 2026, needs more optimization.
31 700 0.219009774327 Henry Cohn, 2026, needs more optimization.
31 701 0.219255028939 Henry Cohn, 2026, needs more optimization.
31 702 0.219575210217 Henry Cohn, 2026, needs more optimization.
31 703 0.219876436091 Henry Cohn, 2026, needs more optimization.
31 704 0.220176985976 Henry Cohn, 2026, needs more optimization.
31 705 0.220463507926 Henry Cohn, 2026, needs more optimization.
31 706 0.220603868005 Henry Cohn, 2026, needs more optimization.
31 707 0.220851830133 Henry Cohn, 2026, needs more optimization.
31 708 0.221098574636 Henry Cohn, 2026, needs more optimization.
31 709 0.221385731045 Henry Cohn, 2026, needs more optimization.
31 710 0.221689406248 Henry Cohn, 2026, needs more optimization.
31 711 0.221975733553 Henry Cohn, 2026, needs more optimization.
31 712 0.222186648998 Henry Cohn, 2026, needs more optimization.
31 713 0.222469265906 Henry Cohn, 2026, needs more optimization.
31 714 0.222681463849 Henry Cohn, 2026, needs more optimization.
31 715 0.222986602988 Henry Cohn, 2026, needs more optimization.
31 716 0.223217308780 Henry Cohn, 2026, needs more optimization.
31 717 0.223531971236 Henry Cohn, 2026, needs more optimization.
31 718 0.223808747280 Henry Cohn, 2026, needs more optimization.
31 719 0.224078194882 Henry Cohn, 2026, needs more optimization.
31 720 0.224354169120 Henry Cohn, 2026, needs more optimization.
31 721 0.224510987238 Henry Cohn, 2026, needs more optimization.
31 722 0.224832953887 Henry Cohn, 2026, needs more optimization.
31 723 0.225070359697 Henry Cohn, 2026, needs more optimization.
31 724 0.225325894302 Henry Cohn, 2026, needs more optimization.
31 725 0.225444472053 Henry Cohn, 2026, needs more optimization.
31 726 0.225764503461 Henry Cohn, 2026, needs more optimization.
31 727 0.225980755424 Henry Cohn, 2026, needs more optimization.
31 728 0.226187688220 Henry Cohn, 2026, needs more optimization.
31 729 0.226498991291 Henry Cohn, 2026, needs more optimization.
31 730 0.226608553111 Henry Cohn, 2026, needs more optimization.
31 731 0.226872039356 Henry Cohn, 2026, needs more optimization.
31 732 0.227123058662 Henry Cohn, 2026, needs more optimization.
31 733 0.227300740181 Henry Cohn, 2026, needs more optimization.
31 734 0.227573021232 Henry Cohn, 2026, needs more optimization.
31 735 0.227745126377 Henry Cohn, 2026, needs more optimization.
31 736 0.228022248384 Henry Cohn, 2026, needs more optimization.
31 737 0.228251038206 Henry Cohn, 2026, needs more optimization.
31 738 0.228548801770 Henry Cohn, 2026, needs more optimization.
31 739 0.228768150734 Henry Cohn, 2026, needs more optimization.
31 740 0.228988913460 Henry Cohn, 2026, needs more optimization.
31 741 0.229183087372 Henry Cohn, 2026, needs more optimization.
31 742 0.229389115737 Henry Cohn, 2026, needs more optimization.
31 743 0.229682705505 Henry Cohn, 2026, needs more optimization.
31 744 0.229916732429 Henry Cohn, 2026, needs more optimization.
31 745 0.230172987475 Henry Cohn, 2026, needs more optimization.
31 746 0.230387885718 Henry Cohn, 2026, needs more optimization.
31 747 0.230622181196 Henry Cohn, 2026, needs more optimization.
31 748 0.230841557176 Henry Cohn, 2026, needs more optimization.
31 749 0.230992085370 Henry Cohn, 2026, needs more optimization.
31 750 0.231237371154 Henry Cohn, 2026, needs more optimization.
31 751 0.231454203792 Henry Cohn, 2026, needs more optimization.
31 752 0.231681899238 Henry Cohn, 2026, needs more optimization.
31 753 0.231899669208 Henry Cohn, 2026, needs more optimization.
31 754 0.232064853565 Henry Cohn, 2026, needs more optimization.
31 755 0.232232656604 Henry Cohn, 2026, needs more optimization.
31 756 0.232386757068 Henry Cohn, 2026, needs more optimization.
31 757 0.232529005205 Henry Cohn, 2026, needs more optimization.
31 758 0.232722764038 Henry Cohn, 2026, needs more optimization.
31 759 0.232996481746 Henry Cohn, 2026, needs more optimization.
31 760 0.233175274735 Henry Cohn, 2026, needs more optimization.
31 761 0.233413011155 Henry Cohn, 2026, needs more optimization.
31 762 0.233519111387 Henry Cohn, 2026, needs more optimization.
31 763 0.233793303454 Henry Cohn, 2026, needs more optimization.
31 764 0.233954538423 Henry Cohn, 2026, needs more optimization.
31 765 0.234112462688 Henry Cohn, 2026, needs more optimization.
31 766 0.234307414550 Henry Cohn, 2026, needs more optimization.
31 767 0.234500450253 Henry Cohn, 2026, needs more optimization.
31 768 0.234691651354 Henry Cohn, 2026, needs more optimization.
31 769 0.234831113932 Henry Cohn, 2026, needs more optimization.
31 770 0.234982892976 Henry Cohn, 2026, needs more optimization.
31 771 0.235144788434 Henry Cohn, 2026, needs more optimization.
31 772 0.235389666824 Henry Cohn, 2026, needs more optimization.
31 773 0.235589163110 Henry Cohn, 2026, needs more optimization.
31 774 0.235731845553 Henry Cohn, 2026, needs more optimization.
31 775 0.235973036490 Henry Cohn, 2026, needs more optimization.
31 776 0.236118991613 Henry Cohn, 2026, needs more optimization.
31 777 0.236295774127 Henry Cohn, 2026, needs more optimization.
31 778 0.236512100398 Henry Cohn, 2026, needs more optimization.
31 779 0.236692194210 Henry Cohn, 2026, needs more optimization.
31 780 0.236920310412 Henry Cohn, 2026, needs more optimization.
31 781 0.237086663110 Henry Cohn, 2026, needs more optimization.
31 782 0.237289300346 Henry Cohn, 2026, needs more optimization.
31 783 0.237479787839 Henry Cohn, 2026, needs more optimization.
31 784 0.237711597018 Henry Cohn, 2026, needs more optimization.
31 1024 0.238095238096 Henry Cohn, 2026.
21⁢x−5
32 65 0.025347196752 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
28800⁢x3−1024⁢x2−32⁢x+1
32 66 0.029441153101 Henry Cohn, 2026.
32 67 0.036059548939 Henry Cohn, 2026, needs more optimization.
32 68 0.036921898559 Henry Cohn, 2026.
32 69 0.037652090605 Henry Cohn, 2026.
32 70 0.040284468062 Henry Cohn, 2026, needs more optimization.
32 71 0.043041701045 Henry Cohn, 2026, needs more optimization.
32 72 0.043340506635 Henry Cohn, 2026, needs more optimization.
32 73 0.043635192946 Henry Cohn, 2026, needs more optimization.
32 74 0.044312064799 Henry Cohn, 2026, needs more optimization.
32 75 0.046969465718 Henry Cohn, 2026, needs more optimization.
32 76 0.048914805743 Henry Cohn, 2026, needs more optimization.
32 77 0.049877295176 Henry Cohn, 2026, needs more optimization.
32 78 0.051358756718 Henry Cohn, 2026, needs more optimization.
32 79 0.053163786132 Henry Cohn, 2026, needs more optimization.
32 80 0.054716199890 Henry Cohn, 2026, needs more optimization.
32 81 0.055651582257 Henry Cohn, 2026, needs more optimization.
32 82 0.056964486782 Henry Cohn, 2026, needs more optimization.
32 83 0.058223868475 Henry Cohn, 2026, needs more optimization.
32 84 0.059654568961 Henry Cohn, 2026, needs more optimization.
32 85 0.060923971340 Henry Cohn, 2026, needs more optimization.
32 86 0.061924997346 Henry Cohn, 2026, needs more optimization.
32 87 0.063171707740 Henry Cohn, 2026, needs more optimization.
32 88 0.064356780468 Henry Cohn, 2026, needs more optimization.
32 89 0.065580030497 Henry Cohn, 2026, needs more optimization.
32 90 0.066403448391 Henry Cohn, 2026, needs more optimization.
32 91 0.067770523575 Henry Cohn, 2026, needs more optimization.
32 92 0.068706408388 Henry Cohn, 2026, needs more optimization.
32 93 0.069828449024 Henry Cohn, 2026, needs more optimization.
32 94 0.070634404780 Henry Cohn, 2026, needs more optimization.
32 95 0.071715164404 Henry Cohn, 2026, needs more optimization.
32 96 0.072860231407 Henry Cohn, 2026, needs more optimization.
32 97 0.073896152354 Henry Cohn, 2026, needs more optimization.
32 98 0.073972144719 Henry Cohn, 2026, needs more optimization.
32 99 0.074680739138 Henry Cohn, 2026, needs more optimization.
32 100 0.075274765234 Henry Cohn, 2026, needs more optimization.
32 101 0.075926613727 Henry Cohn, 2026, needs more optimization.
32 102 0.076145069326 Henry Cohn, 2026, needs more optimization.
32 103 0.076760110256 Henry Cohn, 2026, needs more optimization.
32 104 0.076940558047 Henry Cohn, 2026, needs more optimization.
32 105 0.077067687954 Henry Cohn, 2026, needs more optimization.
32 106 0.077277290868 Henry Cohn, 2026, needs more optimization.
32 107 0.077416306816 Henry Cohn, 2026, needs more optimization.
32 108 0.077639663168 Henry Cohn, 2026, needs more optimization.
32 109 0.077719065847 Henry Cohn, 2026, needs more optimization.
32 110 0.078036307065 Henry Cohn, 2026, needs more optimization.
32 111 0.078886904251 Henry Cohn, 2026, needs more optimization.
32 112 0.079491976586 Henry Cohn, 2026, needs more optimization.
32 113 0.079891950413 Henry Cohn, 2026, needs more optimization.
32 114 0.080450156888 Henry Cohn, 2026, needs more optimization.
32 115 0.080598500607 Henry Cohn, 2026, needs more optimization.
32 116 0.080906180621 Henry Cohn, 2026, needs more optimization.
32 117 0.080987081247 Henry Cohn, 2026, needs more optimization.
32 118 0.081654858630 Henry Cohn, 2026, needs more optimization.
32 119 0.082498969010 Henry Cohn, 2026, needs more optimization.
32 120 0.083463741862 Henry Cohn, 2026, needs more optimization.
32 121 0.084405217293 Henry Cohn, 2026, needs more optimization.
32 122 0.084959387951 Orthogonal union of 120 points in 31 dimensions and 2 points in 1 dimension.
115⁢x2+2⁢x−1
32 123 0.085677621137 Henry Cohn, 2026, needs more optimization.
32 124 0.086091243515 Henry Cohn, 2026, needs more optimization.
32 125 0.086493345699 Henry Cohn, 2026, needs more optimization.
32 126 0.086717022523 Henry Cohn, 2026, needs more optimization.
32 127 0.088524798428 Henry Cohn, 2026, needs more optimization.
32 128 0.088868270853 Henry Cohn, 2026, needs more optimization.
32 129 0.089185312962 Henry Cohn, 2026, needs more optimization.
32 130 0.089563924908 Henry Cohn, 2026, needs more optimization.
32 131 0.089730958771 Henry Cohn, 2026, needs more optimization.
32 132 0.089779525060 Henry Cohn, 2026, needs more optimization.
32 133 0.089985168850 Henry Cohn, 2026, needs more optimization.
32 134 0.090080012719 Henry Cohn, 2026, needs more optimization.
32 135 0.090186865722 Henry Cohn, 2026, needs more optimization.
32 136 0.090738654927 Henry Cohn, 2026, needs more optimization.
32 137 0.091844019094 Henry Cohn, 2026, needs more optimization.
32 138 0.092897430854 Henry Cohn, 2026, needs more optimization.
32 139 0.093783657395 Henry Cohn, 2026, needs more optimization.
32 140 0.094487233268 Henry Cohn, 2026, needs more optimization.
32 141 0.095595400614 Henry Cohn, 2026, needs more optimization.
32 142 0.096711206336 Henry Cohn, 2026, needs more optimization.
32 143 0.097517187312 Henry Cohn, 2026, needs more optimization.
32 144 0.098659674917 Henry Cohn, 2026, needs more optimization.
32 145 0.099651216156 Henry Cohn, 2026, needs more optimization.
32 146 0.100378534157 Henry Cohn, 2026, needs more optimization.
32 147 0.101193885127 Henry Cohn, 2026, needs more optimization.
32 148 0.101934590215 Henry Cohn, 2026, needs more optimization.
32 150 0.102441532266 Henry Cohn, 2026, needs more optimization.
32 151 0.102468677884 Henry Cohn, 2026, needs more optimization.
32 152 0.102597787204 Henry Cohn, 2026, needs more optimization.
32 153 0.103070461679 Henry Cohn, 2026, needs more optimization.
32 154 0.103775244423 Henry Cohn, 2026, needs more optimization.
32 155 0.104812398447 Henry Cohn, 2026, needs more optimization.
32 156 0.105837798789 Henry Cohn, 2026, needs more optimization.
32 157 0.106398508784 Henry Cohn, 2026, needs more optimization.
32 158 0.106941447635 Henry Cohn, 2026, needs more optimization.
32 159 0.107167315114 Henry Cohn, 2026, needs more optimization.
32 160 0.107543191141 Henry Cohn, 2026, needs more optimization.
32 161 0.107900960190 Henry Cohn, 2026, needs more optimization.
32 162 0.108437898188 Henry Cohn, 2026, needs more optimization.
32 163 0.108908183662 Henry Cohn, 2026, needs more optimization.
32 164 0.109508632751 Henry Cohn, 2026, needs more optimization.
32 165 0.110128676311 Henry Cohn, 2026, needs more optimization.
32 166 0.110630114689 Henry Cohn, 2026, needs more optimization.
32 167 0.111438960617 Henry Cohn, 2026, needs more optimization.
32 168 0.112093559301 Henry Cohn, 2026, needs more optimization.
32 169 0.112755671556 Henry Cohn, 2026, needs more optimization.
32 170 0.113526852778 Henry Cohn, 2026, needs more optimization.
32 171 0.114538873881 Henry Cohn, 2026, needs more optimization.
32 172 0.115404888684 Henry Cohn, 2026, needs more optimization.
32 173 0.116308201126 Henry Cohn, 2026, needs more optimization.
32 174 0.117063736843 Henry Cohn, 2026, needs more optimization.
32 175 0.118176054143 Henry Cohn, 2026, needs more optimization.
32 176 0.119017839533 Henry Cohn, 2026, needs more optimization.
32 177 0.119551831748 Henry Cohn, 2026, needs more optimization.
32 178 0.120416228761 Henry Cohn, 2026, needs more optimization.
32 179 0.121440619030 Henry Cohn, 2026, needs more optimization.
32 180 0.121964906779 Henry Cohn, 2026, needs more optimization.
32 181 0.122750351613 Henry Cohn, 2026, needs more optimization.
32 182 0.123469211836 Henry Cohn, 2026, needs more optimization.
32 183 0.124134672679 Henry Cohn, 2026, needs more optimization.
32 184 0.125017511173 Henry Cohn, 2026, needs more optimization.
32 185 0.125748241495 Henry Cohn, 2026, needs more optimization.
32 186 0.126200042424 Henry Cohn, 2026, needs more optimization.
32 187 0.126978061930 Henry Cohn, 2026, needs more optimization.
32 188 0.127635662433 Henry Cohn, 2026, needs more optimization.
32 190 0.128170897523 Henry Cohn, 2026, needs more optimization.
32 191 0.128221985544 Henry Cohn, 2026, needs more optimization.
32 192 0.128221986291 Henry Cohn, 2026, needs more optimization.
32 194 0.128227297451 Henry Cohn, 2026, needs more optimization.
32 195 0.128227297883 Henry Cohn, 2026, needs more optimization.
32 196 0.128239011538 Henry Cohn, 2026, needs more optimization.
32 197 0.128241132435 Henry Cohn, 2026, needs more optimization.
32 198 0.128276918650 Henry Cohn, 2026, needs more optimization.
32 199 0.128647089936 Henry Cohn, 2026, needs more optimization.
32 200 0.128809324110 Henry Cohn, 2026, needs more optimization.
32 201 0.129240738601 Henry Cohn, 2026, needs more optimization.
32 202 0.129908045145 Henry Cohn, 2026, needs more optimization.
32 203 0.130293973708 Henry Cohn, 2026, needs more optimization.
32 204 0.130294042847 Henry Cohn, 2026, needs more optimization.
32 205 0.130673660116 Henry Cohn, 2026, needs more optimization.
32 206 0.130936384905 Henry Cohn, 2026, needs more optimization.
32 207 0.131055177961 Henry Cohn, 2026, needs more optimization.
32 208 0.131208113863 Henry Cohn, 2026, needs more optimization.
32 209 0.134558136886 Henry Cohn, 2026, needs more optimization.
32 210 0.134990230414 Henry Cohn, 2026, needs more optimization.
32 211 0.135570890706 Henry Cohn, 2026, needs more optimization.
32 212 0.135898854789 Henry Cohn, 2026, needs more optimization.
32 213 0.136447858852 Henry Cohn, 2026, needs more optimization.
32 214 0.136787578416 Henry Cohn, 2026, needs more optimization.
32 215 0.137422336857 Henry Cohn, 2026, needs more optimization.
32 216 0.137930063425 Henry Cohn, 2026, needs more optimization.
32 217 0.138566512870 Henry Cohn, 2026, needs more optimization.
32 218 0.138892548169 Henry Cohn, 2026, needs more optimization.
32 219 0.139252738493 Henry Cohn, 2026, needs more optimization.
32 220 0.139857416233 Henry Cohn, 2026, needs more optimization.
32 221 0.140286287756 Henry Cohn, 2026, needs more optimization.
32 222 0.140444065187 Henry Cohn, 2026, needs more optimization.
32 223 0.140533109961 Henry Cohn, 2026, needs more optimization.
32 224 0.140645449124 Henry Cohn, 2026, needs more optimization.
32 225 0.140750650798 Henry Cohn, 2026, needs more optimization.
32 226 0.140890284933 Henry Cohn, 2026, needs more optimization.
32 227 0.141124012295 Henry Cohn, 2026, needs more optimization.
32 228 0.141238324908 Henry Cohn, 2026, needs more optimization.
32 229 0.141407760181 Henry Cohn, 2026, needs more optimization.
32 230 0.141498667667 Henry Cohn, 2026, needs more optimization.
32 231 0.141747248258 Henry Cohn, 2026, needs more optimization.
32 232 0.141895013532 Henry Cohn, 2026, needs more optimization.
32 233 0.142027326792 Henry Cohn, 2026, needs more optimization.
32 234 0.142127192559 Henry Cohn, 2026, needs more optimization.
32 235 0.142432186016 Henry Cohn, 2026, needs more optimization.
32 236 0.142695355485 Henry Cohn, 2026, needs more optimization.
32 237 0.142773757214 Henry Cohn, 2026, needs more optimization.
32 238 0.142896367058 Henry Cohn, 2026, needs more optimization.
32 239 0.143074611258 Henry Cohn, 2026, needs more optimization.
32 240 0.143623935977 Henry Cohn, 2026, needs more optimization.
32 241 0.143692920812 Henry Cohn, 2026, needs more optimization.
32 242 0.143877727039 Henry Cohn, 2026, needs more optimization.
32 243 0.144042142977 Henry Cohn, 2026, needs more optimization.
32 244 0.144427668222 Henry Cohn, 2026, needs more optimization.
32 245 0.144865966956 Henry Cohn, 2026, needs more optimization.
32 246 0.144955063138 Henry Cohn, 2026, needs more optimization.
32 247 0.145047336923 Henry Cohn, 2026, needs more optimization.
32 248 0.145378904091 Henry Cohn, 2026, needs more optimization.
32 249 0.145533053713 Henry Cohn, 2026, needs more optimization.
32 250 0.145788811370 Henry Cohn, 2026, needs more optimization.
32 251 0.146001263503 Henry Cohn, 2026, needs more optimization.
32 252 0.146049323910 Henry Cohn, 2026, needs more optimization.
32 253 0.146254436409 Henry Cohn, 2026, needs more optimization.
32 254 0.146390897629 Henry Cohn, 2026, needs more optimization.
32 255 0.146478960797 Henry Cohn, 2026, needs more optimization.
32 256 0.146601800947 Henry Cohn, 2026, needs more optimization.
32 257 0.146610015821 Henry Cohn, 2026, needs more optimization.
32 258 0.146718896236 Henry Cohn, 2026, needs more optimization.
32 259 0.146900780060 Henry Cohn, 2026, needs more optimization.
32 260 0.147186757366 Henry Cohn, 2026, needs more optimization.
32 261 0.147463839652 Henry Cohn, 2026, needs more optimization.
32 262 0.147608398402 Henry Cohn, 2026, needs more optimization.
32 263 0.147942507464 Henry Cohn, 2026, needs more optimization.
32 264 0.148056565688 Henry Cohn, 2026, needs more optimization.
32 265 0.148190096983 Henry Cohn, 2026, needs more optimization.
32 266 0.148396166898 Henry Cohn, 2026, needs more optimization.
32 267 0.148456934238 Henry Cohn, 2026, needs more optimization.
32 268 0.148650262087 Henry Cohn, 2026, needs more optimization.
32 269 0.148945453676 Henry Cohn, 2026, needs more optimization.
32 270 0.149150119692 Henry Cohn, 2026, needs more optimization.
32 271 0.149376470158 Henry Cohn, 2026, needs more optimization.
32 272 0.149822115166 Henry Cohn, 2026, needs more optimization.
32 273 0.150466806100 Henry Cohn, 2026, needs more optimization.
32 274 0.150786848820 Henry Cohn, 2026, needs more optimization.
32 275 0.151447471525 Henry Cohn, 2026, needs more optimization.
32 276 0.151945117104 Henry Cohn, 2026, needs more optimization.
32 277 0.152544324231 Henry Cohn, 2026, needs more optimization.
32 278 0.152859384969 Henry Cohn, 2026, needs more optimization.
32 279 0.153125080817 Henry Cohn, 2026, needs more optimization.
32 280 0.153233666557 Henry Cohn, 2026, needs more optimization.
32 281 0.153722924518 Henry Cohn, 2026, needs more optimization.
32 282 0.153938420904 Henry Cohn, 2026, needs more optimization.
32 283 0.154411846741 Henry Cohn, 2026, needs more optimization.
32 284 0.154941753343 Henry Cohn, 2026, needs more optimization.
32 285 0.155406579306 Henry Cohn, 2026, needs more optimization.
32 286 0.155879540941 Henry Cohn, 2026, needs more optimization.
32 287 0.156410991841 Henry Cohn, 2026, needs more optimization.
32 288 0.156713802658 Henry Cohn, 2026, needs more optimization.
32 289 0.157123087281 Henry Cohn, 2026, needs more optimization.
32 290 0.157504915735 Henry Cohn, 2026, needs more optimization.
32 291 0.157659753897 Henry Cohn, 2026, needs more optimization.
32 292 0.158268033050 Henry Cohn, 2026, needs more optimization.
32 293 0.158555285517 Henry Cohn, 2026, needs more optimization.
32 294 0.159028240030 Henry Cohn, 2026, needs more optimization.
32 295 0.159368028322 Henry Cohn, 2026, needs more optimization.
32 296 0.159863951725 Henry Cohn, 2026, needs more optimization.
32 297 0.160120566446 Henry Cohn, 2026, needs more optimization.
32 298 0.160639913043 Henry Cohn, 2026, needs more optimization.
32 299 0.160940857011 Henry Cohn, 2026, needs more optimization.
32 300 0.160956023010 Henry Cohn, 2026, needs more optimization.
32 301 0.160991503394 Henry Cohn, 2026, needs more optimization.
32 302 0.161093822951 Henry Cohn, 2026, needs more optimization.
32 303 0.161257155707 Henry Cohn, 2026, needs more optimization.
32 304 0.161405374033 Henry Cohn, 2026, needs more optimization.
32 306 0.161492280659 Henry Cohn, 2026, needs more optimization.
32 307 0.161609401432 Henry Cohn, 2026, needs more optimization.
32 308 0.161675009189 Henry Cohn, 2026, needs more optimization.
32 309 0.161763359112 Henry Cohn, 2026, needs more optimization.
32 310 0.161817311278 Henry Cohn, 2026, needs more optimization.
32 311 0.161874296641 Henry Cohn, 2026, needs more optimization.
32 312 0.161924417419 Henry Cohn, 2026, needs more optimization.
32 313 0.161972636060 Henry Cohn, 2026, needs more optimization.
32 314 0.162025456302 Henry Cohn, 2026, needs more optimization.
32 315 0.162061367051 Henry Cohn, 2026, needs more optimization.
32 316 0.162149311445 Henry Cohn, 2026, needs more optimization.
32 317 0.162241314921 Henry Cohn, 2026, needs more optimization.
32 318 0.162288103877 Henry Cohn, 2026, needs more optimization.
32 319 0.162381523994 Henry Cohn, 2026, needs more optimization.
32 320 0.162451458866 Henry Cohn, 2026, needs more optimization.
32 321 0.162523577097 Henry Cohn, 2026, needs more optimization.
32 322 0.162598055620 Henry Cohn, 2026, needs more optimization.
32 323 0.162690547950 Henry Cohn, 2026, needs more optimization.
32 324 0.162799778904 Henry Cohn, 2026, needs more optimization.
32 325 0.162936504959 Henry Cohn, 2026, needs more optimization.
32 326 0.163041685656 Henry Cohn, 2026, needs more optimization.
32 327 0.163127129741 Henry Cohn, 2026, needs more optimization.
32 328 0.163179527766 Henry Cohn, 2026, needs more optimization.
32 329 0.163290943273 Henry Cohn, 2026, needs more optimization.
32 330 0.163373386854 Henry Cohn, 2026, needs more optimization.
32 331 0.163465998735 Henry Cohn, 2026, needs more optimization.
32 332 0.163556154907 Henry Cohn, 2026, needs more optimization.
32 333 0.163706313397 Henry Cohn, 2026, needs more optimization.
32 334 0.163800739882 Henry Cohn, 2026, needs more optimization.
32 335 0.163868623674 Henry Cohn, 2026, needs more optimization.
32 336 0.163978741348 Henry Cohn, 2026, needs more optimization.
32 337 0.164101805356 Henry Cohn, 2026, needs more optimization.
32 338 0.164213724283 Henry Cohn, 2026, needs more optimization.
32 339 0.164413775280 Henry Cohn, 2026, needs more optimization.
32 340 0.164482994105 Henry Cohn, 2026, needs more optimization.
32 341 0.164568222475 Henry Cohn, 2026, needs more optimization.
32 342 0.164634649726 Henry Cohn, 2026, needs more optimization.
32 343 0.164791079883 Henry Cohn, 2026, needs more optimization.
32 344 0.164875943725 Henry Cohn, 2026, needs more optimization.
32 345 0.164882837203 Henry Cohn, 2026, needs more optimization.
32 346 0.165026534349 Henry Cohn, 2026, needs more optimization.
32 347 0.165162777109 Henry Cohn, 2026, needs more optimization.
32 348 0.165272290212 Henry Cohn, 2026, needs more optimization.
32 349 0.165386714758 Henry Cohn, 2026, needs more optimization.
32 350 0.165562676935 Henry Cohn, 2026, needs more optimization.
32 351 0.165671913390 Henry Cohn, 2026, needs more optimization.
32 352 0.165837135226 Henry Cohn, 2026, needs more optimization.
32 353 0.165955670398 Henry Cohn, 2026, needs more optimization.
32 354 0.166162671737 Henry Cohn, 2026, needs more optimization.
32 355 0.166339846752 Henry Cohn, 2026, needs more optimization.
32 356 0.166691861075 Henry Cohn, 2026, needs more optimization.
32 357 0.166708364482 Henry Cohn, 2026, needs more optimization.
32 358 0.166717845310 Henry Cohn, 2026, needs more optimization.
32 359 0.166803343688 Henry Cohn, 2026, needs more optimization.
32 360 0.167057650232 Henry Cohn, 2026, needs more optimization.
32 361 0.167365079553 Henry Cohn, 2026, needs more optimization.
32 362 0.167416207304 Henry Cohn, 2026, needs more optimization.
32 363 0.177216215198 Henry Cohn, 2026, needs more optimization.
32 364 0.177279736755 Henry Cohn, 2026, needs more optimization.
32 365 0.177302911380 Henry Cohn, 2026, needs more optimization.
32 366 0.177330022029 Henry Cohn, 2026, needs more optimization.
32 367 0.177358988609 Henry Cohn, 2026, needs more optimization.
32 368 0.177836914618 Henry Cohn, 2026, needs more optimization.
32 369 0.177857503797 Henry Cohn, 2026, needs more optimization.
32 370 0.177888780235 Henry Cohn, 2026, needs more optimization.
32 371 0.177916123709 Henry Cohn, 2026, needs more optimization.
32 372 0.177941613685 Henry Cohn, 2026, needs more optimization.
32 373 0.178054276822 Henry Cohn, 2026, needs more optimization.
32 374 0.178103808130 Henry Cohn, 2026, needs more optimization.
32 375 0.178152858690 Henry Cohn, 2026, needs more optimization.
32 376 0.178210688125 Henry Cohn, 2026, needs more optimization.
32 377 0.178235145283 Henry Cohn, 2026, needs more optimization.
32 378 0.178255122880 Henry Cohn, 2026, needs more optimization.
32 379 0.178302899915 Henry Cohn, 2026, needs more optimization.
32 380 0.178494693335 Henry Cohn, 2026, needs more optimization.
32 381 0.178506253554 Henry Cohn, 2026, needs more optimization.
32 382 0.178510268603 Henry Cohn, 2026, needs more optimization.
32 383 0.178533256439 Henry Cohn, 2026, needs more optimization.
32 384 0.178538037098 Henry Cohn, 2026, needs more optimization.
32 385 0.178564390484 Henry Cohn, 2026, needs more optimization.
32 386 0.178572647208 Henry Cohn, 2026, needs more optimization.
32 387 0.178580597096 Henry Cohn, 2026, needs more optimization.
32 388 0.178621560318 Henry Cohn, 2026, needs more optimization.
32 389 0.178634483823 Henry Cohn, 2026, needs more optimization.
32 390 0.178657903025 Henry Cohn, 2026, needs more optimization.
32 391 0.178701983056 Henry Cohn, 2026, needs more optimization.
32 392 0.178754074145 Henry Cohn, 2026, needs more optimization.
32 393 0.178802981783 Henry Cohn, 2026, needs more optimization.
32 394 0.178821005461 Henry Cohn, 2026, needs more optimization.
32 395 0.178860870732 Henry Cohn, 2026, needs more optimization.
32 396 0.178916911576 Henry Cohn, 2026, needs more optimization.
32 397 0.179054893904 Henry Cohn, 2026, needs more optimization.
32 398 0.179453444140 Henry Cohn, 2026, needs more optimization.
32 399 0.179601594765 Henry Cohn, 2026, needs more optimization.
32 400 0.180078300554 Henry Cohn, 2026, needs more optimization.
32 401 0.180207991051 Henry Cohn, 2026, needs more optimization.
32 402 0.180431560804 Henry Cohn, 2026, needs more optimization.
32 403 0.180888399642 Henry Cohn, 2026, needs more optimization.
32 404 0.180951319316 Henry Cohn, 2026, needs more optimization.
32 405 0.181292744314 Henry Cohn, 2026, needs more optimization.
32 406 0.181426378111 Henry Cohn, 2026, needs more optimization.
32 407 0.181603499429 Henry Cohn, 2026, needs more optimization.
32 408 0.182298802401 Henry Cohn, 2026, needs more optimization.
32 409 0.182402791437 Henry Cohn, 2026, needs more optimization.
32 410 0.182605521127 Henry Cohn, 2026, needs more optimization.
32 411 0.182893601813 Henry Cohn, 2026, needs more optimization.
32 412 0.183002490180 Henry Cohn, 2026, needs more optimization.
32 413 0.183171112464 Henry Cohn, 2026, needs more optimization.
32 414 0.183297747781 Henry Cohn, 2026, needs more optimization.
32 415 0.183589124506 Henry Cohn, 2026, needs more optimization.
32 416 0.183966635534 Henry Cohn, 2026, needs more optimization.
32 417 0.184152470055 Henry Cohn, 2026, needs more optimization.
32 418 0.184665459785 Henry Cohn, 2026, needs more optimization.
32 419 0.184985712180 Henry Cohn, 2026, needs more optimization.
32 420 0.185145410353 Henry Cohn, 2026, needs more optimization.
32 421 0.185688127841 Henry Cohn, 2026, needs more optimization.
32 422 0.185928584855 Henry Cohn, 2026, needs more optimization.
32 423 0.186164694568 Henry Cohn, 2026, needs more optimization.
32 424 0.186187191729 Henry Cohn, 2026, needs more optimization.
32 425 0.186275940573 Henry Cohn, 2026, needs more optimization.
32 426 0.186369317803 Henry Cohn, 2026, needs more optimization.
32 427 0.186623315167 Henry Cohn, 2026, needs more optimization.
32 428 0.187138819338 Henry Cohn, 2026, needs more optimization.
32 429 0.187390391368 Henry Cohn, 2026, needs more optimization.
32 430 0.187570883685 Henry Cohn, 2026, needs more optimization.
32 431 0.187726788771 Henry Cohn, 2026, needs more optimization.
32 432 0.188167842429 Henry Cohn, 2026, needs more optimization.
32 433 0.188288448986 Henry Cohn, 2026, needs more optimization.
32 434 0.188480383707 Henry Cohn, 2026, needs more optimization.
32 435 0.188567770793 Henry Cohn, 2026, needs more optimization.
32 436 0.188896479508 Henry Cohn, 2026, needs more optimization.
32 437 0.188923688117 Henry Cohn, 2026, needs more optimization.
32 438 0.189099334128 Henry Cohn, 2026, needs more optimization.
32 439 0.189253179304 Henry Cohn, 2026, needs more optimization.
32 440 0.189490651434 Henry Cohn, 2026, needs more optimization.
32 441 0.189609370450 Henry Cohn, 2026, needs more optimization.
32 442 0.189864505395 Henry Cohn, 2026, needs more optimization.
32 443 0.189950480894 Henry Cohn, 2026, needs more optimization.
32 444 0.189950480963 Henry Cohn, 2026, needs more optimization.
32 445 0.190051727376 Henry Cohn, 2026, needs more optimization.
32 446 0.190164133123 Henry Cohn, 2026, needs more optimization.
32 447 0.190433004663 Henry Cohn, 2026, needs more optimization.
32 448 0.190659159138 Henry Cohn, 2026, needs more optimization.
32 449 0.191111383850 Henry Cohn, 2026, needs more optimization.
32 450 0.191244006801 Henry Cohn, 2026, needs more optimization.
32 451 0.191452888350 Henry Cohn, 2026, needs more optimization.
32 452 0.191538845843 Henry Cohn, 2026, needs more optimization.
32 453 0.191627691490 Henry Cohn, 2026, needs more optimization.
32 454 0.191668255204 Henry Cohn, 2026, needs more optimization.
32 455 0.191831320134 Henry Cohn, 2026, needs more optimization.
32 456 0.192062579696 Henry Cohn, 2026, needs more optimization.
32 457 0.192143544999 Henry Cohn, 2026, needs more optimization.
32 458 0.192186743564 Henry Cohn, 2026, needs more optimization.
32 459 0.192448398126 Henry Cohn, 2026, needs more optimization.
32 460 0.192590593100 Henry Cohn, 2026, needs more optimization.
32 461 0.192657776320 Henry Cohn, 2026, needs more optimization.
32 462 0.192893835777 Henry Cohn, 2026, needs more optimization.
32 463 0.192987912824 Henry Cohn, 2026, needs more optimization.
32 464 0.193174395663 Henry Cohn, 2026, needs more optimization.
32 465 0.193256011749 Henry Cohn, 2026, needs more optimization.
32 466 0.193498095337 Henry Cohn, 2026, needs more optimization.
32 467 0.193642630106 Henry Cohn, 2026, needs more optimization.
32 468 0.193742993710 Henry Cohn, 2026, needs more optimization.
32 469 0.194025300516 Henry Cohn, 2026, needs more optimization.
32 470 0.194083965165 Henry Cohn, 2026, needs more optimization.
32 471 0.194132752349 Henry Cohn, 2026, needs more optimization.
32 472 0.194143893898 Henry Cohn, 2026, needs more optimization.
32 473 0.194323681840 Henry Cohn, 2026, needs more optimization.
32 474 0.194413624066 Henry Cohn, 2026, needs more optimization.
32 475 0.194467349743 Henry Cohn, 2026, needs more optimization.
32 476 0.194529824524 Henry Cohn, 2026, needs more optimization.
32 477 0.194696655430 Henry Cohn, 2026, needs more optimization.
32 478 0.194790627486 Henry Cohn, 2026, needs more optimization.
32 479 0.194902167130 Henry Cohn, 2026, needs more optimization.
32 528 0.195121951220 Henry Cohn, 2026.
41⁢x−8
32 529 0.199360713872 Henry Cohn, 2026, needs more optimization.
32 530 0.199368297905 Henry Cohn, 2026, needs more optimization.
32 532 0.199373261029 Henry Cohn, 2026, needs more optimization.
32 534 0.199379310667 Henry Cohn, 2026, needs more optimization.
32 535 0.199388101198 Henry Cohn, 2026, needs more optimization.
32 536 0.199402779754 Henry Cohn, 2026, needs more optimization.
32 537 0.199404081918 Henry Cohn, 2026, needs more optimization.
32 538 0.199418249772 Henry Cohn, 2026, needs more optimization.
32 539 0.199424530392 Henry Cohn, 2026, needs more optimization.
32 540 0.199434883550 Henry Cohn, 2026, needs more optimization.
32 541 0.199446558001 Henry Cohn, 2026, needs more optimization.
32 542 0.199512655075 Henry Cohn, 2026, needs more optimization.
32 543 0.199517476272 Henry Cohn, 2026, needs more optimization.
32 544 0.199587254774 Henry Cohn, 2026, needs more optimization.
32 545 0.199601591566 Henry Cohn, 2026, needs more optimization.
32 546 0.199606670214 Henry Cohn, 2026, needs more optimization.
32 547 0.199610093314 Henry Cohn, 2026, needs more optimization.
32 548 0.199610281937 Henry Cohn, 2026, needs more optimization.
32 549 0.199614334668 Henry Cohn, 2026, needs more optimization.
32 551 0.199621362608 Henry Cohn, 2026, needs more optimization.
32 552 0.199627111508 Henry Cohn, 2026, needs more optimization.
32 553 0.199630833378 Henry Cohn, 2026, needs more optimization.
32 554 0.199632081074 Henry Cohn, 2026, needs more optimization.
32 557 0.199635385631 Henry Cohn, 2026, needs more optimization.
32 558 0.199638512278 Henry Cohn, 2026, needs more optimization.
32 559 0.199641353700 Henry Cohn, 2026, needs more optimization.
32 560 0.199641359405 Henry Cohn, 2026, needs more optimization.
32 562 0.199649257601 Henry Cohn, 2026, needs more optimization.
32 563 0.199663313853 Henry Cohn, 2026, needs more optimization.
32 564 0.199672621744 Henry Cohn, 2026, needs more optimization.
32 565 0.199705190655 Henry Cohn, 2026, needs more optimization.
32 566 0.199708261733 Henry Cohn, 2026, needs more optimization.
32 567 0.199716431799 Henry Cohn, 2026, needs more optimization.
32 568 0.199720502628 Henry Cohn, 2026, needs more optimization.
32 570 0.199721694128 Henry Cohn, 2026, needs more optimization.
32 571 0.199727030745 Henry Cohn, 2026, needs more optimization.
32 573 0.199728559056 Henry Cohn, 2026, needs more optimization.
32 576 0.199744161656 Henry Cohn, 2026, needs more optimization.
32 577 0.199752965220 Henry Cohn, 2026, needs more optimization.
32 578 0.199761290884 Henry Cohn, 2026, needs more optimization.
32 579 0.199765225951 Henry Cohn, 2026, needs more optimization.
32 581 0.199768505918 Henry Cohn, 2026, needs more optimization.
32 582 0.199773214406 Henry Cohn, 2026, needs more optimization.
32 585 0.199811164498 Henry Cohn, 2026, needs more optimization.
32 587 0.199818949413 Henry Cohn, 2026, needs more optimization.
32 588 0.199822465257 Henry Cohn, 2026, needs more optimization.
32 590 0.199830498228 Henry Cohn, 2026, needs more optimization.
32 591 0.199840250188 Henry Cohn, 2026, needs more optimization.
32 594 0.199859552652 Henry Cohn, 2026, needs more optimization.
32 595 0.199873081288 Henry Cohn, 2026, needs more optimization.
32 596 0.199881079072 Henry Cohn, 2026, needs more optimization.
32 597 0.199963384531 Henry Cohn, 2026, needs more optimization.
32 599 0.199965011383 Henry Cohn, 2026, needs more optimization.
32 601 0.199965350580 Henry Cohn, 2026, needs more optimization.
32 605 0.199966534515 Henry Cohn, 2026, needs more optimization.
32 608 0.199967101108 Henry Cohn, 2026, needs more optimization.
32 609 0.199969967547 Henry Cohn, 2026, needs more optimization.
32 610 0.199971626944 Henry Cohn, 2026, needs more optimization.
32 611 0.199972628657 Henry Cohn, 2026, needs more optimization.
32 612 0.199976502999 Henry Cohn, 2026, needs more optimization.
32 615 0.199977540863 Henry Cohn, 2026, needs more optimization.
32 616 0.199980781125 Henry Cohn, 2026, needs more optimization.
32 618 0.199984961651 Henry Cohn, 2026, needs more optimization.
32 619 0.199986659203 Henry Cohn, 2026, needs more optimization.
32 620 0.199987328433 Henry Cohn, 2026, needs more optimization.
32 704 0.2 Henry Cohn, 2026.
5⁢x−1
32 705 0.209391158534 Henry Cohn, 2026, needs more optimization.
32 706 0.212767262764 Henry Cohn, 2026, needs more optimization.
32 707 0.212849406140 Henry Cohn, 2026, needs more optimization.
32 708 0.213123647040 Henry Cohn, 2026, needs more optimization.
32 709 0.213215250962 Henry Cohn, 2026, needs more optimization.
32 710 0.214317946738 Henry Cohn, 2026, needs more optimization.
32 711 0.214542020953 Henry Cohn, 2026, needs more optimization.
32 712 0.214635686399 Henry Cohn, 2026, needs more optimization.
32 713 0.214756629845 Henry Cohn, 2026, needs more optimization.
32 714 0.214925604452 Henry Cohn, 2026, needs more optimization.
32 715 0.214974332299 Henry Cohn, 2026, needs more optimization.
32 716 0.215218419158 Henry Cohn, 2026, needs more optimization.
32 717 0.215315419273 Henry Cohn, 2026, needs more optimization.
32 718 0.216495371475 Henry Cohn, 2026, needs more optimization.
32 719 0.216567035399 Henry Cohn, 2026, needs more optimization.
32 720 0.216718698669 Henry Cohn, 2026, needs more optimization.
32 721 0.216782338501 Henry Cohn, 2026, needs more optimization.
32 722 0.217151729033 Henry Cohn, 2026, needs more optimization.
32 723 0.217241657250 Henry Cohn, 2026, needs more optimization.
32 724 0.217652985750 Henry Cohn, 2026, needs more optimization.
32 725 0.217748272667 Henry Cohn, 2026, needs more optimization.
32 726 0.218096989435 Henry Cohn, 2026, needs more optimization.
32 727 0.218157423683 Henry Cohn, 2026, needs more optimization.
32 728 0.218179174204 Henry Cohn, 2026, needs more optimization.
32 729 0.218265876450 Henry Cohn, 2026, needs more optimization.
32 730 0.218322925900 Henry Cohn, 2026, needs more optimization.
32 731 0.219193568101 Henry Cohn, 2026, needs more optimization.
32 732 0.219373278335 Henry Cohn, 2026, needs more optimization.
32 733 0.219472739577 Henry Cohn, 2026, needs more optimization.
32 734 0.219725141163 Henry Cohn, 2026, needs more optimization.
32 735 0.219760065280 Henry Cohn, 2026, needs more optimization.
32 736 0.220109993829 Henry Cohn, 2026, needs more optimization.
32 737 0.220230522837 Henry Cohn, 2026, needs more optimization.
32 738 0.220449151804 Henry Cohn, 2026, needs more optimization.
32 739 0.220559624297 Henry Cohn, 2026, needs more optimization.
32 740 0.220651474350 Henry Cohn, 2026, needs more optimization.
32 741 0.221516671717 Henry Cohn, 2026, needs more optimization.
32 742 0.221617673889 Henry Cohn, 2026, needs more optimization.
32 743 0.221721537402 Henry Cohn, 2026, needs more optimization.
32 744 0.221787786000 Henry Cohn, 2026, needs more optimization.
32 745 0.221951198492 Henry Cohn, 2026, needs more optimization.
32 746 0.222000979783 Henry Cohn, 2026, needs more optimization.
32 747 0.222152669136 Henry Cohn, 2026, needs more optimization.
32 748 0.222200508757 Henry Cohn, 2026, needs more optimization.
32 749 0.222268908715 Henry Cohn, 2026, needs more optimization.
32 750 0.223390390575 Henry Cohn, 2026, needs more optimization.
32 751 0.223458179127 Henry Cohn, 2026, needs more optimization.
32 752 0.223580976958 Henry Cohn, 2026, needs more optimization.
32 753 0.223703948111 Henry Cohn, 2026, needs more optimization.
32 754 0.223771685960 Henry Cohn, 2026, needs more optimization.
32 755 0.223923009412 Henry Cohn, 2026, needs more optimization.
32 756 0.223995680107 Henry Cohn, 2026, needs more optimization.
32 757 0.224154664840 Henry Cohn, 2026, needs more optimization.
32 758 0.224355831030 Henry Cohn, 2026, needs more optimization.
32 759 0.225182247691 Henry Cohn, 2026, needs more optimization.
32 760 0.225268581194 Henry Cohn, 2026, needs more optimization.
32 761 0.225405000732 Henry Cohn, 2026, needs more optimization.
32 762 0.225419132991 Henry Cohn, 2026, needs more optimization.
32 763 0.225598776566 Henry Cohn, 2026, needs more optimization.
32 764 0.225651055475 Henry Cohn, 2026, needs more optimization.
32 765 0.225712734086 Henry Cohn, 2026, needs more optimization.
32 766 0.226335667899 Henry Cohn, 2026, needs more optimization.
32 767 0.226445864241 Henry Cohn, 2026, needs more optimization.
32 768 0.226512768293 Henry Cohn, 2026, needs more optimization.
32 769 0.226692598417 Henry Cohn, 2026, needs more optimization.
32 770 0.226765002224 Henry Cohn, 2026, needs more optimization.
32 771 0.227734014355 Henry Cohn, 2026, needs more optimization.
32 772 0.227780274954 Henry Cohn, 2026, needs more optimization.
32 773 0.227915813092 Henry Cohn, 2026, needs more optimization.
32 774 0.227953339922 Henry Cohn, 2026, needs more optimization.
32 775 0.227980667585 Henry Cohn, 2026, needs more optimization.
32 776 0.228169557750 Henry Cohn, 2026, needs more optimization.
32 777 0.228348110463 Henry Cohn, 2026, needs more optimization.
32 778 0.228400750868 Henry Cohn, 2026, needs more optimization.
32 779 0.228638156905 Henry Cohn, 2026, needs more optimization.
32 780 0.228769694797 Henry Cohn, 2026, needs more optimization.
32 781 0.228878807003 Henry Cohn, 2026, needs more optimization.
32 782 0.228920978997 Henry Cohn, 2026, needs more optimization.
32 783 0.228960264407 Henry Cohn, 2026, needs more optimization.
32 784 0.229059826188 Henry Cohn, 2026, needs more optimization.
32 785 0.229217402822 Henry Cohn, 2026, needs more optimization.
32 786 0.231309370451 Henry Cohn, 2026, needs more optimization.
32 787 0.231508915214 Henry Cohn, 2026, needs more optimization.
32 788 0.231576437155 Henry Cohn, 2026, needs more optimization.
32 789 0.231718153985 Henry Cohn, 2026, needs more optimization.
32 790 0.231813207139 Henry Cohn, 2026, needs more optimization.
32 791 0.231944048320 Henry Cohn, 2026, needs more optimization.
32 792 0.231991191696 Henry Cohn, 2026, needs more optimization.
32 793 0.232037536156 Henry Cohn, 2026, needs more optimization.
32 794 0.232101327564 Henry Cohn, 2026, needs more optimization.
32 795 0.232222686657 Henry Cohn, 2026, needs more optimization.
32 796 0.232320086074 Henry Cohn, 2026, needs more optimization.
32 797 0.232404097222 Henry Cohn, 2026, needs more optimization.
32 798 0.232550725640 Henry Cohn, 2026, needs more optimization.
32 799 0.232664196714 Henry Cohn, 2026, needs more optimization.
32 800 0.232820836318 Henry Cohn, 2026, needs more optimization.
32 801 0.232950868955 Henry Cohn, 2026, needs more optimization.
32 802 0.233137115625 Henry Cohn, 2026, needs more optimization.
32 803 0.233248426653 Henry Cohn, 2026, needs more optimization.
32 804 0.233416693001 Henry Cohn, 2026, needs more optimization.
32 805 0.233540596973 Henry Cohn, 2026, needs more optimization.
32 806 0.233706016132 Henry Cohn, 2026, needs more optimization.
32 807 0.233852502853 Henry Cohn, 2026, needs more optimization.
32 808 0.234058995527 Henry Cohn, 2026, needs more optimization.
32 809 0.234201607351 Henry Cohn, 2026, needs more optimization.
32 810 0.234413108549 Henry Cohn, 2026, needs more optimization.
32 811 0.234543351428 Henry Cohn, 2026, needs more optimization.
32 812 0.234706341401 Henry Cohn, 2026, needs more optimization.
32 813 0.234817636995 Henry Cohn, 2026, needs more optimization.
32 814 0.235003921131 Henry Cohn, 2026, needs more optimization.
32 815 0.235162015005 Henry Cohn, 2026, needs more optimization.
32 816 0.235298983178 Henry Cohn, 2026, needs more optimization.
32 817 0.235520676427 Henry Cohn, 2026, needs more optimization.
32 818 0.235660834602 Henry Cohn, 2026, needs more optimization.
32 819 0.235782783792 Henry Cohn, 2026, needs more optimization.
32 820 0.235925010183 Henry Cohn, 2026, needs more optimization.
32 821 0.236069573945 Henry Cohn, 2026, needs more optimization.
32 822 0.236227986328 Henry Cohn, 2026, needs more optimization.
32 823 0.236338396334 Henry Cohn, 2026, needs more optimization.
32 824 0.236472007541 Henry Cohn, 2026, needs more optimization.
32 825 0.236677069393 Henry Cohn, 2026, needs more optimization.
32 826 0.236809347967 Henry Cohn, 2026, needs more optimization.
32 827 0.236970572540 Henry Cohn, 2026, needs more optimization.
32 828 0.237159405939 Henry Cohn, 2026, needs more optimization.
32 829 0.237343280741 Henry Cohn, 2026, needs more optimization.
32 830 0.237474114340 Henry Cohn, 2026, needs more optimization.
32 831 0.237655323751 Henry Cohn, 2026, needs more optimization.
32 832 0.237704799333 Henry Cohn, 2026, needs more optimization.
32 833 0.237895750381 Henry Cohn, 2026, needs more optimization.
32 1024 0.238095238096 Code with 1024 points in 31 dimensions.
21⁢x−5
52 325* 0.0625 P. J. Cameron, J. M. Goethals, and J. J. Seidel, Strongly regular graphs having strongly regular subconstituents, J. Algebra 55 (1978), 257–280, doi:10.1016/0021-8693(78)90220-X; V. I. Levenshtein, Designs as maximum codes in polynomial metric spaces, Acta Appl. Math. 29 (1992), 1–82, doi:10.1007/BF00053379.
16⁢x−1
64 4224* 0.125 V. I. Levenšteĭn, Bounds for the maximal cardinality of a code with bounded modulus of the inner product (Russian), Dokl. Akad. Nauk SSSR 263 (1982), 1303–1308, English translation in Soviet Math. Dokl. 25 (1982), 526–531; H. Cohn, D. de Laat, and N. Leijenhorst, Optimality of spherical codes via exact semidefinite programming bounds, preprint, 2024, arXiv:2403.16874.
8⁢x−1