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 0.969910083224 Henry Cohn, 2024.
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 0.972579059838 Henry Cohn, 2024.
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 0.973166618967 Henry Cohn, 2025.
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 0.975403482592 Henry Cohn, 2024.
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 0.976199213798 Henry Cohn, 2024.
3 287 0.976292535597 Henry Cohn, 2024.
3 288 0.976364794706 Henry Cohn, 2024.
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 0.977140172393 Henry Cohn, 2024.
3 299 0.977214468409 Henry Cohn, 2025.
3 300 0.977219217071 R. H. Hardin, N. J. A. Sloane, and W. D. Smith, Tables of spherical codes with icosahedral symmetry, 1994–2000.
3 301 0.977392313268 Henry Cohn, 2024.
3 302 0.977458631036 Henry Cohn, 2024.
3 303 0.977523371220 Henry Cohn, 2024.
3 304 0.977583884150 Henry Cohn, 2024.
3 305 0.977632490985 Henry Cohn, 2024.
3 306 0.977704320343 Henry Cohn, 2024.
3 307 0.977814535951 Henry Cohn, 2024.
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 0.978122129978 Henry Cohn, 2024.
3 313 0.978231993615 Henry Cohn, 2024.
3 314 0.978279969095 Henry Cohn, 2024.
3 315 0.978359778769 Henry Cohn, 2024.
3 316 0.978410838412 Henry Cohn, 2024.
3 317 0.978487475787 Henry Cohn, 2024.
3 318 0.978544517230 Henry Cohn, 2024.
3 319 0.978603060123 Henry Cohn, 2024.
3 320 0.978663267012 Henry Cohn, 2024.
3 321 0.978701802245 Henry Cohn, 2024.
3 322 0.978826091828 Henry Cohn, 2024.
3 323 0.978911588007 Henry Cohn, 2024.
3 324 0.978995941163 Henry Cohn, 2024.
3 325 0.979043753404 Henry Cohn, 2024.
3 326 0.979098859474 Henry Cohn, 2024.
3 327 0.979175343310 Henry Cohn, 2024.
3 328 0.979227007488 Henry Cohn, 2024.
3 329 0.979277635210 Henry Cohn, 2024.
3 330 0.979324914072 Henry Cohn, 2024.
3 331 0.979373177432 Henry Cohn, 2024.
3 332 0.979423824372 Henry Cohn, 2024.
3 333 0.979491741719 Henry Cohn, 2024.
3 334 0.979582034493 Henry Cohn, 2024.
3 335 0.979642932989 Henry Cohn, 2024.
3 336 0.979690569342 Henry Cohn, 2024.
3 337 0.979751882491 Henry Cohn, 2026.
3 338 0.979838818714 Henry Cohn, 2024.
3 339 0.979904919491 Henry Cohn, 2024.
3 340 0.979949293421 Henry Cohn, 2024.
3 341 0.979999498179 Henry Cohn, 2024.
3 342 0.980044047715 Henry Cohn, 2024.
3 343 0.980089833534 Henry Cohn, 2024.
3 344 0.980135977822 Henry Cohn, 2024.
3 345 0.980198171376 Henry Cohn, 2024.
3 346 0.980275208082 Henry Cohn, 2024.
3 347 0.980349152228 Henry Cohn, 2024.
3 348 0.980406993197 Henry Cohn, 2024.
3 349 0.980468717236 Henry Cohn, 2024.
3 350 0.980516247811 Henry Cohn, 2024.
3 351 0.980576030074 Henry Cohn, 2024.
3 352 0.980619398778 Henry Cohn, 2024.
3 353 0.980684301407 Henry Cohn, 2024.
3 354 0.980732527244 Henry Cohn, 2024.
3 355 0.980776958770 Henry Cohn, 2024.
3 356 0.980824249739 Henry Cohn, 2024.
3 357 0.980871795041 Henry Cohn, 2024.
3 358 0.980901085519 Henry Cohn, 2024.
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 0.981100649639 Henry Cohn, 2024.
3 362 0.981170817619 Henry Cohn, 2024.
3 363 0.981225268927 Henry Cohn, 2024.
3 364 0.981276718466 Henry Cohn, 2024.
3 365 0.981317422056 Henry Cohn, 2024.
3 366 0.981371676585 Henry Cohn, 2024.
3 367 0.981414713592 Henry Cohn, 2024.
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 0.981848936637 Henry Cohn, 2024.
3 377 0.981891941481 Henry Cohn, 2024.
3 378 0.981926575478 Henry Cohn, 2024.
3 379 0.981965339639 Henry Cohn, 2024.
3 380 0.981966079866 Henry Cohn, 2025.
3 381 0.982112878900 Henry Cohn, 2024.
3 382 0.982155902082 Henry Cohn, 2024.
3 383 0.982191165481 Henry Cohn, 2024.
3 384 0.982232298421 Henry Cohn, 2024.
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 0.982452801700 Henry Cohn, 2024.
3 390 0.982505534053 Henry Cohn, 2024.
3 391 0.982555955538 Henry Cohn, 2024.
3 392 0.982591195901 Henry Cohn, 2024.
3 393 0.982649357699 Henry Cohn, 2024.
3 394 0.982692375827 Henry Cohn, 2024.
3 395 0.982725465540 Henry Cohn, 2024.
3 396 0.982767271242 Henry Cohn, 2024.
3 397 0.982799147942 Henry Cohn, 2024.
3 398 0.982821049056 Henry Cohn, 2024.
3 399 0.982857394032 Henry Cohn, 2024.
3 400 0.982915172693 Henry Cohn, 2024.
3 401 0.982950664530 Henry Cohn, 2024.
3 402 0.982983355551 Henry Cohn, 2024.
3 403 0.983049964328 Henry Cohn, 2024.
3 404 0.983111162319 Henry Cohn, 2024.
3 405 0.983168565133 Henry Cohn, 2024.
3 406 0.983206265163 Henry Cohn, 2024.
3 407 0.983247933087 Henry Cohn, 2024.
3 408 0.983288123210 Henry Cohn, 2024.
3 409 0.983324857501 Henry Cohn, 2024.
3 410 0.983356947085 Henry Cohn, 2024.
3 411 0.983397760620 Henry Cohn, 2024.
3 412 0.983428600189 Henry Cohn, 2024.
3 413 0.983461427167 Henry Cohn, 2024.
3 414 0.983495155996 Henry Cohn, 2024.
3 415 0.983545319874 Henry Cohn, 2024.
3 416 0.983572356049 Henry Cohn, 2024.
3 417 0.983606629507 Henry Cohn, 2024.
3 418 0.983668285529 Henry Cohn, 2024.
3 419 0.983709311243 Henry Cohn, 2024.
3 420 0.983735772266 Henry Cohn, 2024.
3 421 0.983801876824 Henry Cohn, 2024.
3 422 0.983837084033 Henry Cohn, 2024.
3 423 0.983879327689 Henry Cohn, 2024.
3 424 0.983915009758 Henry Cohn, 2024.
3 425 0.983947724258 Henry Cohn, 2024.
3 426 0.983967656850 Henry Cohn, 2024.
3 427 0.984017759902 Henry Cohn, 2024.
3 428 0.984060532882 Henry Cohn, 2024.
3 429 0.984101619024 Henry Cohn, 2024.
3 430 0.984134891966 Henry Cohn, 2024.
3 431 0.984165514392 Henry Cohn, 2024.
3 432 0.984201636678 Henry Cohn, 2024.
3 433 0.984246511178 Henry Cohn, 2024.
3 434 0.984282456244 Henry Cohn, 2024.
3 435 0.984322511170 Henry Cohn, 2024.
3 436 0.984359381087 Henry Cohn, 2024.
3 437 0.984376596212 Henry Cohn, 2024.
3 438 0.984419779873 Henry Cohn, 2024.
3 439 0.984459277522 Henry Cohn, 2024.
3 440 0.984472421765 Henry Cohn, 2024.
3 441 0.984527980944 Henry Cohn, 2024.
3 442 0.984559589051 Henry Cohn, 2024.
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 0.984813716313 Henry Cohn, 2024.
3 450 0.984846922701 Henry Cohn, 2024.
3 451 0.984872959879 Henry Cohn, 2024.
3 452 0.984911000119 Henry Cohn, 2024.
3 453 0.984942286924 Henry Cohn, 2024.
3 454 0.984966631268 Henry Cohn, 2024.
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 0.985126768610 Henry Cohn, 2024.
3 460 0.985155490467 Henry Cohn, 2024.
3 461 0.985198380759 Henry Cohn, 2024.
3 462 0.985225068423 Henry Cohn, 2024.
3 463 0.985261648362 Henry Cohn, 2024.
3 464 0.985297019485 Henry Cohn, 2024.
3 465 0.985321750708 Henry Cohn, 2024.
3 466 0.985359897849 Henry Cohn, 2024.
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 0.985527599242 Henry Cohn, 2024.
3 473 0.985558412595 Henry Cohn, 2024.
3 474 0.985607101360 Henry Cohn, 2024.
3 475 0.985630320536 Henry Cohn, 2024.
3 476 0.985665218249 Henry Cohn, 2024.
3 477 0.985693505781 Henry Cohn, 2024.
3 478 0.985716117012 Henry Cohn, 2026.
3 479 0.985721775338 Henry Cohn, 2024.
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 0.985812248918 Henry Cohn, 2024.
3 482 0.985842699690 Henry Cohn, 2024.
3 483 0.985872483761 Henry Cohn, 2024.
3 484 0.985900122939 Henry Cohn, 2024.
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 0.986063292599 Henry Cohn, 2024.
3 491 0.986099610800 Henry Cohn, 2024.
3 492 0.986121929372 Henry Cohn, 2024.
3 493 0.986156796272 Henry Cohn, 2024.
3 494 0.986186402493 Henry Cohn, 2024.
3 495 0.986213487487 Henry Cohn, 2024.
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 0.986349227234 Henry Cohn, 2024.
3 501 0.986372404028 Henry Cohn, 2024.
3 502 0.986403542281 Henry Cohn, 2024.
3 503 0.986428428291 Henry Cohn, 2024.
3 504 0.986455469484 Henry Cohn, 2024.
3 505 0.986479196655 Henry Cohn, 2024.
3 506 0.986508558172 Henry Cohn, 2024.
3 507 0.986527855040 Henry Cohn, 2024.
3 508 0.986562688022 Henry Cohn, 2024.
3 510 0.986562950498 Henry Cohn, 2025.
3 511 0.986645870423 Henry Cohn, 2024.
3 512 0.986668364004 Henry Cohn, 2024.
3 513 0.986700077118 Henry Cohn, 2024.
3 514 0.986720532797 Henry Cohn, 2024.
3 515 0.986749064827 Henry Cohn, 2024.
3 516 0.986773903019 Henry Cohn, 2024.
3 517 0.986799492641 Henry Cohn, 2024.
3 518 0.986819754209 Henry Cohn, 2024.
3 519 0.986848175284 Henry Cohn, 2024.
3 520 0.986876145782 Henry Cohn, 2024.
3 521 0.986900278325 Henry Cohn, 2024.
3 522 0.986922575232 Henry Cohn, 2024.
3 523 0.986951778704 Henry Cohn, 2024.
3 524 0.986971561505 Henry Cohn, 2024.
3 525 0.986995199336 Henry Cohn, 2024.
3 526 0.987019236077 Henry Cohn, 2024.
3 527 0.987049033347 Henry Cohn, 2024.
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 0.987234674397 Henry Cohn, 2024.
3 536 0.987259191622 Henry Cohn, 2024.
3 537 0.987271183218 Henry Cohn, 2024.
3 538 0.987304975991 Henry Cohn, 2024.
3 539 0.987336486625 Henry Cohn, 2024.
3 540 0.987351430022 Henry Cohn, 2024.
3 541 0.987380165789 Henry Cohn, 2024.
3 542 0.987388996662 Henry Cohn, 2024.
3 543 0.987425682607 Henry Cohn, 2024.
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 0.987583836919 Henry Cohn, 2024.
3 551 0.987606449640 Henry Cohn, 2024.
3 552 0.987622742921 R. H. Hardin, N. J. A. Sloane, and W. D. Smith, Tables of spherical codes with icosahedral symmetry, 1994–2000.
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 0.987735307385 Henry Cohn, 2024.
3 558 0.987761309685 Henry Cohn, 2024.
3 559 0.987786834005 Henry Cohn, 2024.
3 560 0.987804065628 Henry Cohn, 2024.
3 561 0.987825037070 Henry Cohn, 2024.
3 562 0.987842915448 Henry Cohn, 2024.
3 563 0.987867088796 Henry Cohn, 2024.
3 564 0.987888189116 Henry Cohn, 2024.
3 565 0.987910412219 Henry Cohn, 2024.
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 0.988010035988 Henry Cohn, 2024.
3 571 0.988036994032 Henry Cohn, 2024.
3 572 0.988045143812 Henry Cohn, 2025.
3 573 0.988071465154 Henry Cohn, 2024.
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 0.988371988004 Henry Cohn, 2024.
3 589 0.988390327285 Henry Cohn, 2024.
3 590 0.988413417033 Henry Cohn, 2024.
3 591 0.988431548471 Henry Cohn, 2024.
3 592 0.988452036069 Henry Cohn, 2024.
3 593 0.988468804433 Henry Cohn, 2024.
3 594 0.988492055682 Henry Cohn, 2024.
3 595 0.988509243514 Henry Cohn, 2024.
3 596 0.988527025270 Henry Cohn, 2024.
3 597 0.988546258113 Henry Cohn, 2024.
3 598 0.988563711650 Henry Cohn, 2024.
3 599 0.988581647683 Henry Cohn, 2024.
3 600 0.988601034993 Henry Cohn, 2024.
3 601 0.988621946438 Henry Cohn, 2024.
3 602 0.988641437112 Henry Cohn, 2024.
3 603 0.988656942485 Henry Cohn, 2024.
3 604 0.988675027867 Henry Cohn, 2024.
3 605 0.988700462515 Henry Cohn, 2024.
3 606 0.988712847782 Henry Cohn, 2024.
3 607 0.988727431487 Henry Cohn, 2024.
3 608 0.988756306926 Henry Cohn, 2024.
3 609 0.988760157529 Henry Cohn, 2024.
3 610 0.988792706244 Henry Cohn, 2024.
3 611 0.988803996797 Henry Cohn, 2024.
3 612 0.988822833992 Henry Cohn, 2024.
3 613 0.988842455232 Henry Cohn, 2024.
3 614 0.988857096430 Henry Cohn, 2024.
3 615 0.988875778474 Henry Cohn, 2024.
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 0.989000876941 Henry Cohn, 2024.
3 623 0.989012818314 Henry Cohn, 2024.
3 624 0.989034528790 Henry Cohn, 2024.
3 625 0.989054157149 Henry Cohn, 2024.
3 626 0.989070144515 Henry Cohn, 2024.
3 627 0.989088135354 Henry Cohn, 2024.
3 628 0.989105386471 Henry Cohn, 2024.
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 0.989202420209 Henry Cohn, 2024.
3 635 0.989219790718 Henry Cohn, 2024.
3 636 0.989242196163 Henry Cohn, 2024.
3 637 0.989258990501 Henry Cohn, 2024.
3 638 0.989267204518 Henry Cohn, 2024.
3 639 0.989290088613 Henry Cohn, 2024.
3 640 0.989301986015 Henry Cohn, 2024.
3 641 0.989321411266 Henry Cohn, 2024.
3 642 0.989332573182 Henry Cohn, 2024.
3 643 0.989352773976 Henry Cohn, 2024.
3 644 0.989371069478 Henry Cohn, 2024.
3 645 0.989382485431 Henry Cohn, 2024.
3 646 0.989398690989 Henry Cohn, 2024.
3 647 0.989413119239 Henry Cohn, 2024.
3 648 0.989433849301 Henry Cohn, 2024.
3 649 0.989453044562 Henry Cohn, 2024.
3 650 0.989463904615 Henry Cohn, 2024.
3 651 0.989485039605 Henry Cohn, 2024.
3 652 0.989500668198 Henry Cohn, 2024.
3 653 0.989517659733 Henry Cohn, 2024.
3 654 0.989528389272 Henry Cohn, 2024.
3 655 0.989547002612 Henry Cohn, 2024.
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 0.989626363395 Henry Cohn, 2024.
3 661 0.989640005006 Henry Cohn, 2024.
3 662 0.989658469367 Henry Cohn, 2024.
3 663 0.989668542979 Henry Cohn, 2024.
3 664 0.989681374062 Henry Cohn, 2024.
3 665 0.989702032269 Henry Cohn, 2024.
3 666 0.989717535361 Henry Cohn, 2024.
3 667 0.989731743795 Henry Cohn, 2024.
3 668 0.989745751462 Henry Cohn, 2024.
3 669 0.989761473114 Henry Cohn, 2024.
3 670 0.989765777159 Henry Cohn, 2024.
3 671 0.989792890413 Henry Cohn, 2024.
3 672 0.989799643833 Henry Cohn, 2024.
3 673 0.989818330488 Henry Cohn, 2024.
3 674 0.989833722485 Henry Cohn, 2024.
3 675 0.989852452169 Henry Cohn, 2024.
3 676 0.989861529212 Henry Cohn, 2024.
3 678 0.989879779829 Henry Cohn, 2024.
3 679 0.989905728538 Henry Cohn, 2024.
3 680 0.989921085378 Henry Cohn, 2024.
3 681 0.989936920244 Henry Cohn, 2024.
3 682 0.989955559541 Henry Cohn, 2024.
3 683 0.989973015974 Henry Cohn, 2024.
3 684 0.989976827933 Henry Cohn, 2024.
3 685 0.990001449211 Henry Cohn, 2024.
3 686 0.990006418271 Henry Cohn, 2024.
3 687 0.990025982355 Henry Cohn, 2024.
3 688 0.990037853003 Henry Cohn, 2024.
3 689 0.990051064090 Henry Cohn, 2024.
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 0.990108022437 Henry Cohn, 2024.
3 694 0.990123873541 Henry Cohn, 2024.
3 695 0.990138225464 Henry Cohn, 2024.
3 696 0.990144937712 Henry Cohn, 2024.
3 697 0.990164610569 Henry Cohn, 2024.
3 698 0.990178131415 Henry Cohn, 2024.
3 699 0.990196847589 Henry Cohn, 2024.
3 700 0.990204754056 Henry Cohn, 2024.
3 702 0.990207507930 Henry Cohn, 2025.
3 703 0.990246510087 Henry Cohn, 2024.
3 704 0.990264421603 Henry Cohn, 2024.
3 705 0.990275791331 Henry Cohn, 2024.
3 706 0.990290378683 Henry Cohn, 2024.
3 707 0.990307749113 Henry Cohn, 2024.
3 708 0.990313284691 Henry Cohn, 2024.
3 709 0.990331708341 Henry Cohn, 2024.
3 711 0.990345295659 Henry Cohn, 2024.
3 712 0.990368376224 Henry Cohn, 2024.
3 713 0.990383651488 Henry Cohn, 2024.
3 714 0.990391904853 Henry Cohn, 2024.
3 715 0.990408038650 Henry Cohn, 2024.
3 716 0.990424201178 Henry Cohn, 2024.
3 717 0.990437124471 Henry Cohn, 2024.
3 718 0.990448237688 Henry Cohn, 2024.
3 719 0.990461529899 Henry Cohn, 2024.
3 720 0.990474919274 Henry Cohn, 2024.
3 721 0.990491371173 Henry Cohn, 2024.
3 722 0.990499809958 Henry Cohn, 2024.
3 723 0.990516894560 Henry Cohn, 2024.
3 724 0.990532198847 Henry Cohn, 2024.
3 725 0.990534529638 Henry Cohn, 2024.
3 726 0.990553141663 Henry Cohn, 2024.
3 727 0.990566965324 Henry Cohn, 2024.
3 728 0.990571284239 Henry Cohn, 2024.
3 729 0.990587255137 Henry Cohn, 2024.
3 730 0.990603287439 Henry Cohn, 2024.
3 731 0.990612626443 Henry Cohn, 2024.
3 732 0.990621413211 Henry Cohn, 2025.
3 733 0.990643551144 Henry Cohn, 2024.
3 734 0.990660617632 Henry Cohn, 2024.
3 735 0.990668792728 Henry Cohn, 2024.
3 736 0.990681732803 Henry Cohn, 2024.
3 737 0.990695306177 Henry Cohn, 2024.
3 738 0.990704677084 Henry Cohn, 2024.
3 739 0.990713057195 Henry Cohn, 2024.
3 740 0.990728865941 Henry Cohn, 2024.
3 741 0.990742245221 Henry Cohn, 2024.
3 742 0.990755361153 Henry Cohn, 2024.
3 743 0.990770576230 Henry Cohn, 2024.
3 744 0.990780046428 Henry Cohn, 2024.
3 745 0.990791226838 Henry Cohn, 2024.
3 746 0.990807128963 Henry Cohn, 2024.
3 747 0.990816878553 Henry Cohn, 2024.
3 748 0.990830906878 Henry Cohn, 2024.
3 749 0.990838053202 Henry Cohn, 2024.
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 0.990872395915 Henry Cohn, 2024.
3 753 0.990883514545 Henry Cohn, 2024.
3 754 0.990901296816 Henry Cohn, 2024.
3 755 0.990905033119 Henry Cohn, 2024.
3 756 0.990922227516 Henry Cohn, 2024.
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 0.990976123095 Henry Cohn, 2024.
3 762 0.990993252010 Henry Cohn, 2024.
3 763 0.991002546962 Henry Cohn, 2024.
3 764 0.991020776255 Henry Cohn, 2024.
3 765 0.991029933301 Henry Cohn, 2024.
3 766 0.991038039796 Henry Cohn, 2024.
3 767 0.991054850991 Henry Cohn, 2024.
3 768 0.991063858891 Henry Cohn, 2024.
3 769 0.991073054499 Henry Cohn, 2024.
3 770 0.991085755280 Henry Cohn, 2024.
3 771 0.991097098258 Henry Cohn, 2024.
3 772 0.991107834438 Henry Cohn, 2024.
3 773 0.991120324668 Henry Cohn, 2024.
3 774 0.991132071939 Henry Cohn, 2024.
3 775 0.991145898664 Henry Cohn, 2024.
3 776 0.991156697126 Henry Cohn, 2024.
3 777 0.991161697853 Henry Cohn, 2024.
3 778 0.991178514334 Henry Cohn, 2024.
3 779 0.991188403576 Henry Cohn, 2024.
3 780 0.991195467101 Henry Cohn, 2024.
3 781 0.991212495316 Henry Cohn, 2024.
3 782 0.991221877841 Henry Cohn, 2024.
3 783 0.991227432227 Henry Cohn, 2024.
3 784 0.991237581418 Henry Cohn, 2024.
3 785 0.991250704363 Henry Cohn, 2024.
3 786 0.991265609504 Henry Cohn, 2024.
3 787 0.991279737346 Henry Cohn, 2024.
3 788 0.991287959034 Henry Cohn, 2024.
3 789 0.991298474057 Henry Cohn, 2024.
3 790 0.991311108786 Henry Cohn, 2024.
3 791 0.991319397658 Henry Cohn, 2024.
3 792 0.991327970122 Henry Cohn, 2024.
3 793 0.991343095341 Henry Cohn, 2024.
3 794 0.991355598368 Henry Cohn, 2024.
3 795 0.991362648296 Henry Cohn, 2024.
3 796 0.991373620973 Henry Cohn, 2024.
3 797 0.991382382844 Henry Cohn, 2024.
3 798 0.991394391213 Henry Cohn, 2024.
3 799 0.991408093880 Henry Cohn, 2024.
3 800 0.991414851715 Henry Cohn, 2024.
3 801 0.991425603623 Henry Cohn, 2024.
3 802 0.991437819695 Henry Cohn, 2024.
3 803 0.991450003639 Henry Cohn, 2024.
3 804 0.991459924550 Henry Cohn, 2024.
3 805 0.991468080347 Henry Cohn, 2024.
3 806 0.991480017656 Henry Cohn, 2024.
3 807 0.991488929993 Henry Cohn, 2024.
3 808 0.991499472524 Henry Cohn, 2024.
3 809 0.991513039166 Henry Cohn, 2024.
3 810 0.991520665687 Henry Cohn, 2024.
3 811 0.991534887804 Henry Cohn, 2024.
3 812 0.991541771500 Henry Cohn, 2024.
3 813 0.991547822510 Henry Cohn, 2024.
3 814 0.991561861128 Henry Cohn, 2024.
3 815 0.991569264349 Henry Cohn, 2024.
3 816 0.991580342934 Henry Cohn, 2024.
3 817 0.991591011326 Henry Cohn, 2024.
3 818 0.991606217466 Henry Cohn, 2024.
3 819 0.991611831024 Henry Cohn, 2024.
3 820 0.991624044122 Henry Cohn, 2024.
3 821 0.991631483847 Henry Cohn, 2024.
3 822 0.991640340040 Henry Cohn, 2024.
3 823 0.991650165081 Henry Cohn, 2024.
3 824 0.991660076581 Henry Cohn, 2024.
3 825 0.991671265549 Henry Cohn, 2024.
3 826 0.991681742391 Henry Cohn, 2024.
3 827 0.991695448495 Henry Cohn, 2024.
3 828 0.991700756929 Henry Cohn, 2024.
3 829 0.991713398461 Henry Cohn, 2024.
3 830 0.991721621394 Henry Cohn, 2024.
3 831 0.991727218135 Henry Cohn, 2024.
3 832 0.991735674478 Henry Cohn, 2024.
3 833 0.991757657241 Henry Cohn, 2024.
3 834 0.991761234909 Henry Cohn, 2024.
3 835 0.991775366198 Henry Cohn, 2024.
3 836 0.991780274903 Henry Cohn, 2024.
3 837 0.991787929640 Henry Cohn, 2024.
3 838 0.991802634344 Henry Cohn, 2024.
3 840 0.991804916272 R. H. Hardin, N. J. A. Sloane, and W. D. Smith, Tables of spherical codes with icosahedral symmetry, 1994–2000.
3 841 0.991829212367 Henry Cohn, 2024.
3 842 0.991840819373 Henry Cohn, 2024.
3 843 0.991847889329 Henry Cohn, 2024.
3 844 0.991857775147 Henry Cohn, 2024.
3 845 0.991863629186 Henry Cohn, 2024.
3 846 0.991878532857 Henry Cohn, 2025.
3 847 0.991886320624 Henry Cohn, 2025.
3 848 0.991897746584 Henry Cohn, 2025.
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 0.991942749939 Henry Cohn, 2025.
3 854 0.991951631435 Henry Cohn, 2025.
3 855 0.991962531819 Henry Cohn, 2025.
3 856 0.991972423212 Henry Cohn, 2025.
3 857 0.991979003112 Henry Cohn, 2025.
3 858 0.991987713948 Henry Cohn, 2025.
3 860 0.992000324488 R. H. Hardin, N. J. A. Sloane, and W. D. Smith, Tables of spherical codes with icosahedral symmetry, 1994–2000.
3 861 0.992015656329 Henry Cohn, 2025.
3 862 0.992022903669 Henry Cohn, 2025.
3 863 0.992039444605 Henry Cohn, 2025.
3 864 0.992045910827 Henry Cohn, 2025.
3 865 0.992052833787 Henry Cohn, 2025.
3 866 0.992064050508 Henry Cohn, 2025.
3 867 0.992072381754 Henry Cohn, 2025.
3 868 0.992080033785 Henry Cohn, 2025.
3 869 0.992091623959 Henry Cohn, 2025.
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 0.992125985753 Henry Cohn, 2025.
3 874 0.992130666610 Henry Cohn, 2025.
3 875 0.992141194210 Henry Cohn, 2025.
3 876 0.992148880613 Henry Cohn, 2025.
3 877 0.992154329715 Henry Cohn, 2025.
3 878 0.992168861340 Henry Cohn, 2025.
3 879 0.992171243331 Henry Cohn, 2025.
3 880 0.992185909971 Henry Cohn, 2025.
3 881 0.992192486886 Henry Cohn, 2025.
3 882 0.992198371680 Henry Cohn, 2025.
3 883 0.992209993174 Henry Cohn, 2025.
3 884 0.992219699147 Henry Cohn, 2025.
3 885 0.992231709887 Henry Cohn, 2025.
3 886 0.992239057053 Henry Cohn, 2025.
3 887 0.992242382220 Henry Cohn, 2025.
3 888 0.992258876226 Henry Cohn, 2025.
3 889 0.992268087253 Henry Cohn, 2025.
3 890 0.992270692003 Henry Cohn, 2025.
3 891 0.992282908648 Henry Cohn, 2025.
3 892 0.992289973548 Henry Cohn, 2025.
3 893 0.992298164886 Henry Cohn, 2025.
3 894 0.992309459744 Henry Cohn, 2025.
3 895 0.992316358484 Henry Cohn, 2025.
3 896 0.992319789432 Henry Cohn, 2025.
3 897 0.992332110080 Henry Cohn, 2025.
3 898 0.992338696092 Henry Cohn, 2025.
3 899 0.992349829991 Henry Cohn, 2025.
3 900 0.992360793848 Henry Cohn, 2024.
3 901 0.992366538174 Henry Cohn, 2025.
3 902 0.992377854101 Henry Cohn, 2025.
3 903 0.992382061576 Henry Cohn, 2025.
3 904 0.992392816154 Henry Cohn, 2025.
3 905 0.992400631964 Henry Cohn, 2025.
3 906 0.992409191703 Henry Cohn, 2025.
3 907 0.992416883647 Henry Cohn, 2025.
3 908 0.992422545672 Henry Cohn, 2025.
3 909 0.992432062810 Henry Cohn, 2025.
3 910 0.992437123795 Henry Cohn, 2025.
3 911 0.992443166019 Henry Cohn, 2025.
3 912 0.992454600852 Henry Cohn, 2025.
3 913 0.992469933271 Henry Cohn, 2025.
3 914 0.992471207708 Henry Cohn, 2025.
3 915 0.992482565852 Henry Cohn, 2025.
3 916 0.992492188420 Henry Cohn, 2025.
3 917 0.992500203453 Henry Cohn, 2025.
3 918 0.992507205651 Henry Cohn, 2025.
3 919 0.992516908676 Henry Cohn, 2025.
3 920 0.992518345854 Henry Cohn, 2025.
3 921 0.992532122129 Henry Cohn, 2025.
3 922 0.992539673688 Henry Cohn, 2025.
3 923 0.992547647599 Henry Cohn, 2025.
3 924 0.992553990146 Henry Cohn, 2025.
3 925 0.992565731685 Henry Cohn, 2025.
3 926 0.992569938693 Henry Cohn, 2025.
3 927 0.992580946257 Henry Cohn, 2025.
3 928 0.992583930232 Henry Cohn, 2025.
3 929 0.992590355210 Henry Cohn, 2025.
3 930 0.992602765384 Henry Cohn, 2025.
3 931 0.992610375347 Henry Cohn, 2025.
3 932 0.992616284375 Henry Cohn, 2025.
3 933 0.992624602034 Henry Cohn, 2025.
3 934 0.992631107765 Henry Cohn, 2025.
3 935 0.992640679227 Henry Cohn, 2025.
3 936 0.992649034124 Henry Cohn, 2025.
3 937 0.992657820696 Henry Cohn, 2025.
3 938 0.992665682904 Henry Cohn, 2025.
3 939 0.992672947443 Henry Cohn, 2025.
3 940 0.992677739706 Henry Cohn, 2025.
3 941 0.992688089317 Henry Cohn, 2025.
3 942 0.992696579115 Henry Cohn, 2025.
3 943 0.992702546437 Henry Cohn, 2025.
3 944 0.992713697005 Henry Cohn, 2025.
3 945 0.992717631580 Henry Cohn, 2025.
3 946 0.992723034803 Henry Cohn, 2025.
3 947 0.992729250719 Henry Cohn, 2025.
3 948 0.992740223152 Henry Cohn, 2025.
3 950 0.992751947060 Henry Cohn, 2025.
3 951 0.992767541985 Henry Cohn, 2025.
3 952 0.992771438024 Henry Cohn, 2025.
3 953 0.992778258864 Henry Cohn, 2025.
3 954 0.992786191374 Henry Cohn, 2025.
3 955 0.992791727019 Henry Cohn, 2025.
3 956 0.992801093482 Henry Cohn, 2025.
3 957 0.992810004476 Henry Cohn, 2025.
3 958 0.992817667647 Henry Cohn, 2025.
3 959 0.992826125413 Henry Cohn, 2025.
3 960 0.992830967656 Henry Cohn, 2024.
3 961 0.992838773549 Henry Cohn, 2025.
3 962 0.992843794794 Henry Cohn, 2025.
3 963 0.992852425763 Henry Cohn, 2025.
3 964 0.992860398135 Henry Cohn, 2025.
3 965 0.992871354421 Henry Cohn, 2025.
3 966 0.992875386015 Henry Cohn, 2025.
3 967 0.992882714198 Henry Cohn, 2025.
3 968 0.992886923604 Henry Cohn, 2025.
3 969 0.992896341783 Henry Cohn, 2025.
3 970 0.992903243757 Henry Cohn, 2025.
3 971 0.992910234827 Henry Cohn, 2025.
3 972 0.992915598654 Henry Cohn, 2025.
3 974 0.992925603203 Henry Cohn, 2025.
3 975 0.992935839740 Henry Cohn, 2025.
3 976 0.992946637569 Henry Cohn, 2025.
3 977 0.992953433939 Henry Cohn, 2025.
3 978 0.992962810288 Henry Cohn, 2025.
3 979 0.992968433192 Henry Cohn, 2025.
3 980 0.992974636259 Henry Cohn, 2024.
3 981 0.992982747599 Henry Cohn, 2025.
3 982 0.992988090846 Henry Cohn, 2025.
3 983 0.992998353831 Henry Cohn, 2025.
3 984 0.993003417762 Henry Cohn, 2025.
3 985 0.993011691492 Henry Cohn, 2025.
3 986 0.993015554264 Henry Cohn, 2025.
3 988 0.993023719135 Henry Cohn, 2025.
3 989 0.993037184620 Henry Cohn, 2025.
3 990 0.993045751650 Henry Cohn, 2025.
3 991 0.993050187813 Henry Cohn, 2025.
3 992 0.993061792827 Henry Cohn, 2025.
3 993 0.993062803097 Henry Cohn, 2025.
3 994 0.993075914352 Henry Cohn, 2025.
3 995 0.993078560947 Henry Cohn, 2025.
3 996 0.993085371709 Henry Cohn, 2025.
3 997 0.993095368942 Henry Cohn, 2025.
3 998 0.993098230447 Henry Cohn, 2025.
3 999 0.993106913603 Henry Cohn, 2025.
3 1000 0.993111266855 Henry Cohn, 2025.
3 1001 0.993123068371 Henry Cohn, 2025.
3 1002 0.993125622347 Henry Cohn, 2025.
3 1003 0.993132170420 Henry Cohn, 2025.
3 1004 0.993141407134 Henry Cohn, 2025.
3 1005 0.993148911123 Henry Cohn, 2025.
3 1006 0.993152122720 Henry Cohn, 2025.
3 1008 0.993159005478 Henry Cohn, 2025.
3 1010 0.993176753480 R. H. Hardin, N. J. A. Sloane, and W. D. Smith, Tables of spherical codes with icosahedral symmetry, 1994–2000.
3 1011 0.993185799668 Henry Cohn, 2025.
3 1012 0.993195967770 Henry Cohn, 2025.
3 1013 0.993202916215 Henry Cohn, 2025.
3 1014 0.993210002788 Henry Cohn, 2025.
3 1015 0.993213366518 Henry Cohn, 2025.
3 1016 0.993220747476 Henry Cohn, 2025.
3 1017 0.993224054059 Henry Cohn, 2025.
3 1018 0.993234793239 Henry Cohn, 2025.
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 0.993256895835 Henry Cohn, 2025.
3 1022 0.993258630946 Henry Cohn, 2025.
3 1023 0.993269506578 Henry Cohn, 2025.
3 1024 0.993274985225 Henry Cohn, 2025.
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 0.843251223216 Henry Cohn, 2025.
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 0.856498246684 Henry Cohn, 2025.
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 0.861356896238 Henry Cohn, 2026, needs more optimization.
4 171 0.861877205800 Henry Cohn, 2025.
4 172 0.862358805352 Henry Cohn, 2025.
4 173 0.862725307388 Henry Cohn, 2025.
4 174 0.863246308920 Henry Cohn, 2025.
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 0.867174335033 Henry Cohn, 2025.
4 183 0.867335807322 Henry Cohn, 2025.
4 184 0.867763055785 Henry Cohn, 2025.
4 185 0.868224155431 Henry Cohn, 2025.
4 186 0.868518800651 Henry Cohn, 2025.
4 187 0.868845310389 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 0.871341712847 Henry Cohn, 2025.
4 193 0.871545546243 Henry Cohn, 2025.
4 194 0.871792013221 Henry Cohn, 2025.
4 195 0.872106376131 Henry Cohn, 2025.
4 196 0.872623946731 Henry Cohn, 2025.
4 197 0.873487426793 Henry Cohn, 2025.
4 198 0.874156501901 Henry Cohn, 2025.
4 199 0.875069199577 Henry Cohn, 2025.
4 200 0.875686480655 Henry Cohn, 2025.
4 201 0.876308845876 Henry Cohn, 2025.
4 202 0.876662092953 Henry Cohn, 2025.
4 203 0.876862422683 Henry Cohn, 2026, needs more optimization.
4 204 0.877356709662 Henry Cohn, 2025.
4 205 0.877534211883 Henry Cohn, 2025.
4 206 0.877831247728 Henry Cohn, 2025.
4 207 0.878017676728 Henry Cohn, 2025.
4 208 0.878215104089 Henry Cohn, 2025.
4 209 0.878616371731 Henry Cohn, 2025.
4 210 0.879213799752 Henry Cohn, 2025.
4 211 0.879586628106 Henry Cohn, 2025.
4 212 0.879665474531 Henry Cohn, 2025.
4 213 0.879834121318 Henry Cohn, 2025.
4 214 0.879945724274 Henry Cohn, 2025.
4 215 0.880272662054 Henry Cohn, 2025.
4 216 0.880905324150 Henry Cohn, 2025.
4 217 0.881535768813 Henry Cohn, 2025.
4 218 0.881833555267 Henry Cohn, 2025.
4 219 0.881957670465 Henry Cohn, 2025.
4 220 0.882547029792 Henry Cohn, 2025.
4 221 0.883034917637 Henry Cohn, 2025.
4 222 0.883456069925 Henry Cohn, 2025.
4 223 0.884138189446 Henry Cohn, 2025.
4 224 0.884684734191 Henry Cohn, 2025.
4 225 0.885143711620 Henry Cohn, 2026, needs more optimization.
4 226 0.885365198857 Henry Cohn, 2025.
4 227 0.885541386047 Henry Cohn, 2025.
4 228 0.885824040293 Henry Cohn, 2025.
4 229 0.886093486636 Henry Cohn, 2025.
4 230 0.886372063295 Henry Cohn, 2025.
4 231 0.886845140552 Henry Cohn, 2025.
4 232 0.887102089163 Henry Cohn, 2025.
4 233 0.887339463629 Henry Cohn, 2025.
4 234 0.887586535331 Henry Cohn, 2025.
4 235 0.887931434008 Henry Cohn, 2025.
4 236 0.888076450831 Henry Cohn, 2025.
4 237 0.888444553045 Henry Cohn, 2025.
4 238 0.888895172867 Henry Cohn, 2025.
4 239 0.889119578653 Henry Cohn, 2026, needs more optimization.
4 240 0.889506258287 Henry Cohn, 2025.
4 241 0.889886657931 Henry Cohn, 2025.
4 242 0.890234249504 Henry Cohn, 2025.
4 243 0.890327494714 Henry Cohn, 2025.
4 244 0.890767792098 Henry Cohn, 2025.
4 245 0.891024994652 Henry Cohn, 2025.
4 246 0.891230987587 Henry Cohn, 2025.
4 247 0.891768677571 Henry Cohn, 2025.
4 248 0.892111703446 Henry Cohn, 2025.
4 249 0.892307117218 Henry Cohn, 2026, needs more optimization.
4 250 0.892631521974 Henry Cohn, 2025.
4 251 0.893094674563 Henry Cohn, 2025.
4 252 0.893341841396 Henry Cohn, 2025.
4 253 0.893646236229 Henry Cohn, 2025.
4 254 0.893921970145 Henry Cohn, 2025.
4 255 0.894009501823 Henry Cohn, 2025.
4 256 0.894575161485 Henry Cohn, 2026, needs more optimization.
4 257 0.894967091737 Henry Cohn, 2026, needs more optimization.
4 258 0.895162078398 Henry Cohn, 2026, needs more optimization.
4 259 0.895560238243 Henry Cohn, 2026, needs more optimization.
4 260 0.895863531818 Henry Cohn, 2025, needs more optimization.
4 261 0.896074641602 Henry Cohn, 2026, needs more optimization.
4 262 0.896224478962 Henry Cohn, 2026, needs more optimization.
4 263 0.896411473848 Henry Cohn, 2026, needs more optimization.
4 264 0.896680909646 Henry Cohn, 2026, needs more optimization.
4 265 0.896868316981 Henry Cohn, 2026, needs more optimization.
4 266 0.897034498719 Henry Cohn, 2026, needs more optimization.
4 267 0.897247294157 Henry Cohn, 2026, needs more optimization.
4 268 0.897379521992 Henry Cohn, 2026, needs more optimization.
4 269 0.897716687703 Henry Cohn, 2026, needs more optimization.
4 270 0.897879064735 Henry Cohn, 2026, needs more optimization.
4 271 0.898149362730 Ilmari Vahteristo, 2026.
4 272 0.898273815183 Henry Cohn, 2025, needs more optimization.
4 273 0.898444364800 Henry Cohn, 2026, needs more optimization.
4 274 0.898527867663 Henry Cohn, 2025, needs more optimization.
4 275 0.898905582819 Henry Cohn, 2026, needs more optimization.
4 276 0.899228765953 Henry Cohn, 2026, needs more optimization.
4 277 0.899355536990 Henry Cohn, 2026, needs more optimization.
4 278 0.899522919658 Henry Cohn, 2026, needs more optimization.
4 279 0.899602410452 Henry Cohn, 2026, needs more optimization.
4 280 0.899645951104 Henry Cohn, 2026, needs more optimization.
4 281 0.900144251353 Henry Cohn, 2025, needs more optimization.
4 282 0.900669748687 Henry Cohn, 2025, needs more optimization.
4 283 0.901133860903 Henry Cohn, 2026, needs more optimization.
4 284 0.901400482679 Ilmari Vahteristo, 2026.
4 285 0.901725475267 Henry Cohn, 2026, needs more optimization.
4 286 0.902187173174 Henry Cohn, 2026, needs more optimization.
4 287 0.902238993011 Ilmari Vahteristo, 2026.
4 288 0.902809372927 Henry Cohn, 2025, needs more optimization.
4 289 0.902960715484 Henry Cohn, 2025, needs more optimization.
4 290 0.903114200287 Henry Cohn, 2026, needs more optimization.
4 291 0.903498175585 Henry Cohn, 2026, needs more optimization.
4 292 0.903643689020 Henry Cohn, 2025, needs more optimization.
4 293 0.903845491920 Henry Cohn, 2026, needs more optimization.
4 294 0.904174048251 Henry Cohn, 2025, needs more optimization.
4 295 0.904242053282 Henry Cohn, 2026, needs more optimization.
4 296 0.904791585539 Henry Cohn, 2026, needs more optimization.
4 297 0.904792565536 Henry Cohn, 2025, needs more optimization.
4 298 0.905081089280 Henry Cohn, 2026, needs more optimization.
4 299 0.905217873794 Henry Cohn, 2026, needs more optimization.
4 300 0.905430124030 Henry Cohn, 2026, needs more optimization.
4 301 0.905749679486 Henry Cohn, 2025, needs more optimization.
4 302 0.905981217126 Henry Cohn, 2026, needs more optimization.
4 303 0.906127796062 Henry Cohn, 2025, needs more optimization.
4 304 0.906270018142 Henry Cohn, 2026, needs more optimization.
4 305 0.906402554620 Henry Cohn, 2025, needs more optimization.
4 306 0.906574109379 Henry Cohn, 2026, needs more optimization.
4 307 0.907315489853 Henry Cohn, 2026, needs more optimization.
4 308 0.907321467879 Henry Cohn, 2026, needs more optimization.
4 309 0.907355948835 Henry Cohn, 2025, needs more optimization.
4 310 0.907358532815 Henry Cohn, 2025, needs more optimization.
4 311 0.907939119141 Henry Cohn, 2025, needs more optimization.
4 312 0.908400731703 Henry Cohn, 2026, needs more optimization.
4 313 0.908532014357 Henry Cohn, 2025, needs more optimization.
4 314 0.908551774846 Henry Cohn, 2025, needs more optimization.
4 315 0.908688049416 Henry Cohn, 2025, needs more optimization.
4 316 0.909046196578 Henry Cohn, 2026, needs more optimization.
4 317 0.909046386562 Henry Cohn, 2026, needs more optimization.
4 318 0.909170050134 Henry Cohn, 2025, needs more optimization.
4 319 0.909208466661 Henry Cohn, 2026, needs more optimization.
4 320 0.909390987337 Henry Cohn, 2026, needs more optimization.
4 321 0.909536185091 Henry Cohn, 2025, needs more optimization.
4 322 0.909674791274 Henry Cohn, 2025, needs more optimization.
4 323 0.909817307305 Henry Cohn, 2026, needs more optimization.
4 324 0.909901672991 Henry Cohn, 2025, needs more optimization.
4 325 0.910096010635 Henry Cohn, 2026, needs more optimization.
4 326 0.910283865043 Henry Cohn, 2025, needs more optimization.
4 327 0.910330672955 Henry Cohn, 2026, needs more optimization.
4 328 0.910660635640 Henry Cohn, 2025, needs more optimization.
4 329 0.910994704935 Henry Cohn, 2026, needs more optimization.
4 330 0.910999882705 Henry Cohn, 2025, needs more optimization.
4 331 0.911221815903 Henry Cohn, 2025, needs more optimization.
4 332 0.911382095911 Henry Cohn, 2026, needs more optimization.
4 333 0.911751408175 Henry Cohn, 2025, needs more optimization.
4 334 0.911800446547 Henry Cohn, 2026, needs more optimization.
4 335 0.912034339982 Henry Cohn, 2026, needs more optimization.
4 336 0.912308609413 Henry Cohn, 2025, needs more optimization.
4 337 0.912392820444 Henry Cohn, 2025, needs more optimization.
4 338 0.912655658852 Henry Cohn, 2026, needs more optimization.
4 339 0.913034799286 Henry Cohn, 2025, needs more optimization.
4 340 0.913204649513 Henry Cohn, 2025, needs more optimization.
4 341 0.913376620602 Henry Cohn, 2025, needs more optimization.
4 342 0.913523258748 Henry Cohn, 2024, needs more optimization.
4 343 0.914067345393 Henry Cohn, 2025, needs more optimization.
4 344 0.914230240004 Henry Cohn, 2025, needs more optimization.
4 345 0.914230519528 Henry Cohn, 2026, needs more optimization.
4 346 0.914438232359 Henry Cohn, 2025, needs more optimization.
4 347 0.914596841729 Henry Cohn, 2025, needs more optimization.
4 348 0.914781818832 Henry Cohn, 2026, needs more optimization.
4 349 0.914804715376 Henry Cohn, 2026, needs more optimization.
4 350 0.914972573951 Henry Cohn, 2025, needs more optimization.
4 351 0.915023495399 Henry Cohn, 2025, needs more optimization.
4 352 0.915307640705 Henry Cohn, 2026, needs more optimization.
4 353 0.915308989155 Henry Cohn, 2026, needs more optimization.
4 354 0.915475633531 Henry Cohn, 2026, needs more optimization.
4 355 0.915634904761 Henry Cohn, 2026, needs more optimization.
4 356 0.915671905923 Henry Cohn, 2025, needs more optimization.
4 357 0.915928280372 Henry Cohn, 2025, needs more optimization.
4 358 0.916202241466 Henry Cohn, 2025, needs more optimization.
4 359 0.916222668672 Henry Cohn, 2025, needs more optimization.
4 360 0.916292806442 Henry Cohn, 2026, needs more optimization.
4 361 0.916301661938 Henry Cohn, 2026, needs more optimization.
4 362 0.916499604247 Henry Cohn, 2026, needs more optimization.
4 363 0.916672248429 Henry Cohn, 2026, needs more optimization.
4 364 0.916812114092 Henry Cohn, 2025, needs more optimization.
4 365 0.916962145964 Henry Cohn, 2025, needs more optimization.
4 366 0.917029402271 Henry Cohn, 2025, needs more optimization.
4 367 0.917162341741 Henry Cohn, 2026, needs more optimization.
4 368 0.917277717682 Henry Cohn, 2025, needs more optimization.
4 369 0.917436486429 Henry Cohn, 2025, needs more optimization.
4 370 0.917439410227 Henry Cohn, 2026, needs more optimization.
4 371 0.917493460397 Henry Cohn, 2026, needs more optimization.
4 372 0.918013926741 Henry Cohn, 2025, needs more optimization.
4 373 0.918344892501 Henry Cohn, 2025, needs more optimization.
4 374 0.918405787049 Henry Cohn, 2026, needs more optimization.
4 375 0.918525851963 Henry Cohn, 2025, needs more optimization.
4 376 0.918529375746 Henry Cohn, 2026, needs more optimization.
4 377 0.918729610703 Henry Cohn, 2026, needs more optimization.
4 378 0.918919301726 Henry Cohn, 2025, needs more optimization.
4 379 0.919068186270 Henry Cohn, 2026, needs more optimization.
4 380 0.919090573869 Henry Cohn, 2025, needs more optimization.
4 381 0.919163200278 Henry Cohn, 2025, needs more optimization.
4 382 0.919320720843 Henry Cohn, 2026, needs more optimization.
4 383 0.919322999212 Henry Cohn, 2026, needs more optimization.
4 384 0.919541420163 Henry Cohn, 2026, needs more optimization.
4 385 0.919548006821 Henry Cohn, 2025, needs more optimization.
4 386 0.919555554896 Henry Cohn, 2026, needs more optimization.
4 387 0.919585651527 Henry Cohn, 2026, needs more optimization.
4 388 0.919734128283 Henry Cohn, 2026, needs more optimization.
4 389 0.919756054809 Henry Cohn, 2026, needs more optimization.
4 390 0.920168261588 Henry Cohn, 2026, needs more optimization.
4 391 0.920444192104 Henry Cohn, 2025, needs more optimization.
4 392 0.920447271773 Henry Cohn, 2026, needs more optimization.
4 393 0.920560967687 Henry Cohn, 2026, needs more optimization.
4 394 0.920564400221 Henry Cohn, 2025, needs more optimization.
4 395 0.920801296768 Henry Cohn, 2025, needs more optimization.
4 397 0.921058203494 Henry Cohn, 2025, needs more optimization.
4 398 0.921351647740 Henry Cohn, 2025, needs more optimization.
4 399 0.921415178392 Henry Cohn, 2025, needs more optimization.
4 400 0.921512874155 Henry Cohn, 2026, needs more optimization.
4 401 0.921560426099 Henry Cohn, 2025, needs more optimization.
4 402 0.921787828480 Henry Cohn, 2026, needs more optimization.
4 403 0.921822136637 Henry Cohn, 2025, needs more optimization.
4 404 0.921896678330 Henry Cohn, 2026, needs more optimization.
4 405 0.921904900277 Henry Cohn, 2025, needs more optimization.
4 406 0.921929943872 Henry Cohn, 2025, needs more optimization.
4 408 0.922090364752 Henry Cohn, 2025, needs more optimization.
4 409 0.923053481556 Henry Cohn, 2026, needs more optimization.
4 410 0.923058192608 Henry Cohn, 2025, needs more optimization.
4 411 0.923059884394 Henry Cohn, 2026, needs more optimization.
4 412 0.923150924629 Henry Cohn, 2026, needs more optimization.
4 413 0.923265302229 Henry Cohn, 2025, needs more optimization.
4 414 0.923265471415 Henry Cohn, 2025, needs more optimization.
4 415 0.923452958450 Henry Cohn, 2026, needs more optimization.
4 416 0.923491299599 Henry Cohn, 2026, needs more optimization.
4 417 0.924180211328 Henry Cohn, 2025, needs more optimization.
4 418 0.924202985128 Henry Cohn, 2025, needs more optimization.
4 419 0.924325560783 Henry Cohn, 2025, needs more optimization.
4 420 0.924349127027 Henry Cohn, 2025, needs more optimization.
4 421 0.924562571586 Henry Cohn, 2025, needs more optimization.
4 422 0.924882682111 Henry Cohn, 2025, needs more optimization.
4 423 0.924973774846 Henry Cohn, 2025, needs more optimization.
4 424 0.925179917088 Henry Cohn, 2026, needs more optimization.
4 425 0.925342369999 Henry Cohn, 2026, needs more optimization.
4 426 0.925371775974 Henry Cohn, 2025, needs more optimization.
4 427 0.925417074839 Henry Cohn, 2025, needs more optimization.
4 428 0.925532846743 Henry Cohn, 2026, needs more optimization.
4 429 0.925657954234 Henry Cohn, 2025, needs more optimization.
4 430 0.925727886792 Henry Cohn, 2026, needs more optimization.
4 431 0.925881192521 Henry Cohn, 2026, needs more optimization.
4 432 0.926039163350 Henry Cohn, 2025, needs more optimization.
4 433 0.926141893047 Henry Cohn, 2026, needs more optimization.
4 434 0.926412475868 Henry Cohn, 2025, needs more optimization.
4 435 0.926570585016 Henry Cohn, 2025, needs more optimization.
4 436 0.926701577204 Henry Cohn, 2026, needs more optimization.
4 438 0.926855073228 Henry Cohn, 2025, needs more optimization.
4 439 0.927093468249 Henry Cohn, 2025, needs more optimization.
4 440 0.927146484882 Henry Cohn, 2026, needs more optimization.
4 441 0.927270883244 Henry Cohn, 2025, needs more optimization.
4 442 0.927285220818 Henry Cohn, 2026, needs more optimization.
4 443 0.927377843541 Henry Cohn, 2025, needs more optimization.
4 444 0.927439079745 Henry Cohn, 2026, needs more optimization.
4 445 0.927496635650 Henry Cohn, 2026, needs more optimization.
4 446 0.927688328376 Henry Cohn, 2025, needs more optimization.
4 447 0.927779601169 Henry Cohn, 2025, needs more optimization.
4 448 0.927913641653 Henry Cohn, 2025, needs more optimization.
4 449 0.928020259559 Henry Cohn, 2025, needs more optimization.
4 450 0.928076278877 Henry Cohn, 2025, needs more optimization.
4 451 0.928097969258 Henry Cohn, 2025, needs more optimization.
4 452 0.928200134709 Henry Cohn, 2025, needs more optimization.
4 453 0.928272948246 Henry Cohn, 2026, needs more optimization.
4 454 0.928373444080 Henry Cohn, 2025, needs more optimization.
4 455 0.928381173710 Henry Cohn, 2025, needs more optimization.
4 456 0.928554698947 Henry Cohn, 2025, needs more optimization.
4 457 0.928559891923 Henry Cohn, 2025, needs more optimization.
4 458 0.928714713007 Henry Cohn, 2025, needs more optimization.
4 459 0.928808529791 Henry Cohn, 2025, needs more optimization.
4 460 0.929058745508 Henry Cohn, 2025, needs more optimization.
4 461 0.929151290904 Henry Cohn, 2025, needs more optimization.
4 462 0.929180744654 Henry Cohn, 2025, needs more optimization.
4 463 0.929192297478 Henry Cohn, 2025, needs more optimization.
4 464 0.929307114423 Henry Cohn, 2026, needs more optimization.
4 465 0.929581795424 Henry Cohn, 2026, needs more optimization.
4 466 0.929681623171 Henry Cohn, 2026, needs more optimization.
4 467 0.929683139361 Henry Cohn, 2025, needs more optimization.
4 468 0.929790230602 Henry Cohn, 2026, needs more optimization.
4 469 0.929886943176 Henry Cohn, 2026, needs more optimization.
4 470 0.930044908339 Henry Cohn, 2025, needs more optimization.
4 471 0.930155433184 Henry Cohn, 2025, needs more optimization.
4 472 0.930304679917 Henry Cohn, 2026, needs more optimization.
4 473 0.930464634928 Henry Cohn, 2026, needs more optimization.
4 474 0.930640382606 Henry Cohn, 2026, needs more optimization.
4 475 0.930687865652 Henry Cohn, 2025, needs more optimization.
4 477 0.930820405012 Henry Cohn, 2025, needs more optimization.
4 478 0.930992801915 Henry Cohn, 2026, needs more optimization.
4 479 0.931005045840 Henry Cohn, 2026, needs more optimization.
4 480 0.931112380865 Henry Cohn, 2025, needs more optimization.
4 481 0.931335892594 Henry Cohn, 2025, needs more optimization.
4 482 0.931382412841 Henry Cohn, 2026, needs more optimization.
4 483 0.931486107590 Henry Cohn, 2026, needs more optimization.
4 484 0.931583863286 Henry Cohn, 2026, needs more optimization.
4 485 0.931598602760 Henry Cohn, 2025, needs more optimization.
4 486 0.931719293668 Henry Cohn, 2026, needs more optimization.
4 487 0.931837199002 Henry Cohn, 2025, needs more optimization.
4 488 0.931876606116 Henry Cohn, 2025, needs more optimization.
4 489 0.931879460145 Henry Cohn, 2025, needs more optimization.
4 490 0.931986511493 Henry Cohn, 2025, needs more optimization.
4 491 0.932129469048 Henry Cohn, 2025, needs more optimization.
4 492 0.932139733980 Henry Cohn, 2026, needs more optimization.
4 493 0.932233182674 Henry Cohn, 2026, needs more optimization.
4 494 0.932236467873 Henry Cohn, 2026, needs more optimization.
4 495 0.932323203465 Henry Cohn, 2025, needs more optimization.
4 496 0.932500272178 Henry Cohn, 2025, needs more optimization.
4 497 0.932512624213 Henry Cohn, 2025, needs more optimization.
4 498 0.932637534156 Henry Cohn, 2026, needs more optimization.
4 499 0.932641716231 Henry Cohn, 2025, needs more optimization.
4 500 0.932793878323 Henry Cohn, 2026, needs more optimization.
4 501 0.932795380893 Henry Cohn, 2025, needs more optimization.
4 502 0.932905617000 Henry Cohn, 2025, needs more optimization.
4 503 0.933005617030 Henry Cohn, 2025, needs more optimization.
4 504 0.933044432549 Henry Cohn, 2026, needs more optimization.
4 505 0.933128723647 Henry Cohn, 2025, needs more optimization.
4 506 0.933175916326 Henry Cohn, 2026, needs more optimization.
4 507 0.933399662810 Henry Cohn, 2026, needs more optimization.
4 508 0.933457715953 Henry Cohn, 2025, needs more optimization.
4 509 0.933553824747 Henry Cohn, 2025, needs more optimization.
4 510 0.933554354656 Henry Cohn, 2025, needs more optimization.
4 511 0.933747497746 Henry Cohn, 2026, needs more optimization.
4 512 0.933804302995 Henry Cohn, 2026, needs more optimization.
4 513 0.933898943863 Henry Cohn, 2026, needs more optimization.
4 514 0.933968668812 Henry Cohn, 2025, needs more optimization.
4 515 0.934045219268 Henry Cohn, 2025, needs more optimization.
4 516 0.934187930613 Henry Cohn, 2026, needs more optimization.
4 517 0.934200348230 Henry Cohn, 2026, needs more optimization.
4 518 0.934459599470 Henry Cohn, 2025, needs more optimization.
4 519 0.934540089409 Henry Cohn, 2025, needs more optimization.
4 520 0.934699248258 Henry Cohn, 2025, needs more optimization.
4 521 0.934710019106 Henry Cohn, 2025, needs more optimization.
4 522 0.934745753310 Henry Cohn, 2025, needs more optimization.
4 523 0.934852797622 Henry Cohn, 2026, needs more optimization.
4 524 0.934944371680 Henry Cohn, 2025, needs more optimization.
4 525 0.935029425094 Henry Cohn, 2026, needs more optimization.
4 526 0.935148024481 Henry Cohn, 2025, needs more optimization.
4 527 0.935256351959 Henry Cohn, 2025, needs more optimization.
4 528 0.935310315348 Henry Cohn, 2025, needs more optimization.
4 529 0.935319514565 Henry Cohn, 2026, needs more optimization.
4 530 0.935497863531 Henry Cohn, 2025, needs more optimization.
4 531 0.935510798794 Henry Cohn, 2025, needs more optimization.
4 532 0.935569232469 Henry Cohn, 2026, needs more optimization.
4 533 0.935676741118 Henry Cohn, 2025, needs more optimization.
4 534 0.935788386292 Henry Cohn, 2026, needs more optimization.
4 535 0.935811939995 Henry Cohn, 2025, needs more optimization.
4 537 0.935910089175 Henry Cohn, 2025, needs more optimization.
4 538 0.936073641293 Henry Cohn, 2025, needs more optimization.
4 539 0.936105500983 Henry Cohn, 2026, needs more optimization.
4 540 0.936187919569 Henry Cohn, 2026, needs more optimization.
4 541 0.936301405234 Henry Cohn, 2025, needs more optimization.
4 542 0.936307463358 Henry Cohn, 2025, needs more optimization.
4 543 0.936417878772 Henry Cohn, 2025, needs more optimization.
4 545 0.936558367404 Henry Cohn, 2025, needs more optimization.
4 546 0.936667874314 Henry Cohn, 2025, needs more optimization.
4 547 0.936744880456 Henry Cohn, 2026, needs more optimization.
4 548 0.936755768894 Henry Cohn, 2026, needs more optimization.
4 549 0.936916079422 Henry Cohn, 2025, needs more optimization.
4 550 0.936922956849 Henry Cohn, 2026, needs more optimization.
4 551 0.937084656947 Henry Cohn, 2026, needs more optimization.
4 552 0.937086856222 Henry Cohn, 2026, needs more optimization.
4 553 0.937240543392 Henry Cohn, 2025, needs more optimization.
4 554 0.937332328028 Henry Cohn, 2025, needs more optimization.
4 555 0.937361688429 Henry Cohn, 2025, needs more optimization.
4 556 0.937380785440 Henry Cohn, 2025, needs more optimization.
4 557 0.937468418241 Henry Cohn, 2025, needs more optimization.
4 558 0.937708798478 Henry Cohn, 2025, needs more optimization.
4 559 0.937710052202 Henry Cohn, 2025, needs more optimization.
4 560 0.937735092692 Henry Cohn, 2026, needs more optimization.
4 561 0.937829919092 Henry Cohn, 2026, needs more optimization.
4 562 0.937832503268 Henry Cohn, 2025, needs more optimization.
4 563 0.937955041395 Henry Cohn, 2025, needs more optimization.
4 564 0.937956581160 Henry Cohn, 2025, needs more optimization.
4 565 0.938152651024 Henry Cohn, 2025, needs more optimization.
4 566 0.938200710767 Henry Cohn, 2025, needs more optimization.
4 567 0.938202567350 Henry Cohn, 2025, needs more optimization.
4 568 0.938330431684 Henry Cohn, 2025, needs more optimization.
4 569 0.938356329917 Henry Cohn, 2026, needs more optimization.
4 570 0.938496721966 Henry Cohn, 2025, needs more optimization.
4 571 0.938513797968 Henry Cohn, 2025, needs more optimization.
4 572 0.938564289842 Henry Cohn, 2025, needs more optimization.
4 573 0.938764076152 Henry Cohn, 2025, needs more optimization.
4 574 0.938926625054 Henry Cohn, 2025, needs more optimization.
4 575 0.938934741529 Henry Cohn, 2025, needs more optimization.
4 576 0.939022786047 Henry Cohn, 2025, needs more optimization.
4 577 0.939023197122 Henry Cohn, 2025, needs more optimization.
4 578 0.939072946058 Henry Cohn, 2025, needs more optimization.
4 579 0.939148002539 Henry Cohn, 2025, needs more optimization.
4 580 0.939201274675 Henry Cohn, 2026, needs more optimization.
4 581 0.939214925124 Henry Cohn, 2026, needs more optimization.
4 582 0.939308245821 Henry Cohn, 2026, needs more optimization.
4 583 0.939358108278 Henry Cohn, 2025, needs more optimization.
4 584 0.939443313373 Henry Cohn, 2025, needs more optimization.
4 585 0.939460812797 Henry Cohn, 2025, needs more optimization.
4 586 0.939571319618 Henry Cohn, 2026, needs more optimization.
4 587 0.939573167768 Henry Cohn, 2026, needs more optimization.
4 588 0.939585867764 Henry Cohn, 2026, needs more optimization.
4 590 0.939702708834 Henry Cohn, 2025, needs more optimization.
4 592 0.939866827831 Henry Cohn, 2026, needs more optimization.
4 593 0.939871636807 Henry Cohn, 2026, needs more optimization.
4 594 0.939873198645 Henry Cohn, 2026, needs more optimization.
4 595 0.939983098032 Henry Cohn, 2026, needs more optimization.
4 596 0.939986602888 Henry Cohn, 2026, needs more optimization.
4 597 0.940099681249 Henry Cohn, 2025, needs more optimization.
4 598 0.940191207503 Henry Cohn, 2025, needs more optimization.
4 600 0.940371740470 Henry Cohn, 2025, needs more optimization.
4 601 0.940462666331 Henry Cohn, 2025, needs more optimization.
4 602 0.940524172905 Henry Cohn, 2025, needs more optimization.
4 603 0.940525601449 Henry Cohn, 2025, needs more optimization.
4 604 0.940582967501 Henry Cohn, 2026, needs more optimization.
4 605 0.940660094668 Henry Cohn, 2025, needs more optimization.
4 606 0.940662163379 Henry Cohn, 2025, needs more optimization.
4 607 0.940742759433 Henry Cohn, 2025, needs more optimization.
4 608 0.940825165665 Henry Cohn, 2026, needs more optimization.
4 609 0.940963167178 Henry Cohn, 2025, needs more optimization.
4 610 0.940986838892 Henry Cohn, 2025, needs more optimization.
4 611 0.941051663092 Henry Cohn, 2025, needs more optimization.
4 612 0.941115211625 Henry Cohn, 2025, needs more optimization.
4 613 0.941175083386 Henry Cohn, 2025, needs more optimization.
4 614 0.941194775682 Henry Cohn, 2026, needs more optimization.
4 615 0.941274274186 Henry Cohn, 2026, needs more optimization.
4 616 0.941285182477 Henry Cohn, 2025, needs more optimization.
4 617 0.941535461906 Henry Cohn, 2025, needs more optimization.
4 618 0.941538011697 Henry Cohn, 2025, needs more optimization.
4 619 0.941542102122 Henry Cohn, 2025, needs more optimization.
4 620 0.941642267240 Henry Cohn, 2025, needs more optimization.
4 621 0.941645219406 Henry Cohn, 2025, needs more optimization.
4 622 0.941698195844 Henry Cohn, 2025, needs more optimization.
4 623 0.941737504146 Henry Cohn, 2026, needs more optimization.
4 624 0.941798551676 Henry Cohn, 2026, needs more optimization.
4 625 0.941981654285 Henry Cohn, 2025, needs more optimization.
4 626 0.942000937392 Henry Cohn, 2025, needs more optimization.
4 627 0.942024040458 Henry Cohn, 2025, needs more optimization.
4 628 0.942134996678 Henry Cohn, 2025, needs more optimization.
4 629 0.942192328200 Henry Cohn, 2025, needs more optimization.
4 631 0.942363907789 Henry Cohn, 2025, needs more optimization.
4 632 0.942374827195 Henry Cohn, 2026, needs more optimization.
4 633 0.942473650646 Henry Cohn, 2025, needs more optimization.
4 634 0.942736605951 Henry Cohn, 2025, needs more optimization.
4 636 0.942737019308 Henry Cohn, 2025, needs more optimization.
4 637 0.942739881086 Henry Cohn, 2025, needs more optimization.
4 638 0.942777496521 Henry Cohn, 2025, needs more optimization.
4 639 0.942840895043 Henry Cohn, 2025, needs more optimization.
4 640 0.942921344577 Henry Cohn, 2026, needs more optimization.
4 641 0.943053199796 Henry Cohn, 2025, needs more optimization.
4 642 0.943076996937 Henry Cohn, 2026, needs more optimization.
4 643 0.943078020099 Henry Cohn, 2025, needs more optimization.
4 644 0.943180934082 Henry Cohn, 2025, needs more optimization.
4 645 0.943263346821 Henry Cohn, 2025, needs more optimization.
4 646 0.943264536655 Henry Cohn, 2025, needs more optimization.
4 647 0.943280433531 Henry Cohn, 2025, needs more optimization.
4 648 0.943291031540 Henry Cohn, 2025, needs more optimization.
4 649 0.943391411174 Henry Cohn, 2026, needs more optimization.
4 650 0.943396727354 Henry Cohn, 2026, needs more optimization.
4 651 0.943398346882 Henry Cohn, 2025, needs more optimization.
4 652 0.943420599120 Henry Cohn, 2026, needs more optimization.
4 653 0.943464499018 Henry Cohn, 2025, needs more optimization.
4 654 0.943482524163 Henry Cohn, 2025, needs more optimization.
4 655 0.943571235187 Henry Cohn, 2025, needs more optimization.
4 656 0.943573032589 Henry Cohn, 2026, needs more optimization.
4 657 0.943574218096 Henry Cohn, 2025, needs more optimization.
4 658 0.943601414683 Henry Cohn, 2025, needs more optimization.
4 659 0.943721696295 Henry Cohn, 2025, needs more optimization.
4 660 0.943757169743 Henry Cohn, 2026, needs more optimization.
4 661 0.943761106881 Henry Cohn, 2026, needs more optimization.
4 662 0.943765195886 Henry Cohn, 2025, needs more optimization.
4 664 0.943843773518 Henry Cohn, 2026, needs more optimization.
4 665 0.943851005572 Henry Cohn, 2025, needs more optimization.
4 666 0.943921780861 Henry Cohn, 2025, needs more optimization.
4 667 0.943923348839 Henry Cohn, 2025, needs more optimization.
4 668 0.943926024634 Henry Cohn, 2025, needs more optimization.
4 669 0.944000307055 Henry Cohn, 2025, needs more optimization.
4 670 0.944106517091 Henry Cohn, 2025, needs more optimization.
4 671 0.944118208019 Henry Cohn, 2025, needs more optimization.
4 672 0.944256472700 Henry Cohn, 2026, needs more optimization.
4 673 0.944357960966 Henry Cohn, 2025, needs more optimization.
4 674 0.944368205369 Henry Cohn, 2025, needs more optimization.
4 675 0.944537997000 Henry Cohn, 2025, needs more optimization.
4 676 0.944653424057 Henry Cohn, 2025, needs more optimization.
4 677 0.944654159692 Henry Cohn, 2026, needs more optimization.
4 679 0.944725392304 Henry Cohn, 2025, needs more optimization.
4 680 0.944745136087 Henry Cohn, 2025, needs more optimization.
4 681 0.944749674631 Henry Cohn, 2026, needs more optimization.
4 682 0.944859053848 Henry Cohn, 2026, needs more optimization.
4 683 0.944864452596 Henry Cohn, 2026, needs more optimization.
4 684 0.944933518727 Henry Cohn, 2025, needs more optimization.
4 685 0.944991182167 Henry Cohn, 2026, needs more optimization.
4 686 0.945085693951 Henry Cohn, 2025, needs more optimization.
4 687 0.945446050038 Henry Cohn, 2026, needs more optimization.
4 688 0.945446825922 Henry Cohn, 2026, needs more optimization.
4 689 0.945721674323 Henry Cohn, 2025, needs more optimization.
4 690 0.945777629919 Henry Cohn, 2026, needs more optimization.
4 691 0.945834751690 Henry Cohn, 2025, needs more optimization.
4 692 0.945892174743 Henry Cohn, 2026, needs more optimization.
4 693 0.945961558591 Henry Cohn, 2025, needs more optimization.
4 694 0.945973683104 Henry Cohn, 2025, needs more optimization.
4 695 0.946062307104 Henry Cohn, 2025, needs more optimization.
4 696 0.946064301813 Henry Cohn, 2026, needs more optimization.
4 697 0.946179220827 Henry Cohn, 2025, needs more optimization.
4 699 0.946181312763 Henry Cohn, 2025, needs more optimization.
4 700 0.946242389787 Henry Cohn, 2026, needs more optimization.
4 701 0.946313706669 Henry Cohn, 2025, needs more optimization.
4 703 0.946361301050 Henry Cohn, 2025, needs more optimization.
4 704 0.946441318944 Henry Cohn, 2026, needs more optimization.
4 705 0.946448765341 Henry Cohn, 2025, needs more optimization.
4 707 0.946622017817 Henry Cohn, 2026, needs more optimization.
4 708 0.946681729852 Henry Cohn, 2026, needs more optimization.
4 709 0.946724955645 Henry Cohn, 2025, needs more optimization.
4 711 0.946797578469 Henry Cohn, 2025, needs more optimization.
4 712 0.946803907594 Henry Cohn, 2025, needs more optimization.
4 713 0.946806771675 Henry Cohn, 2025, needs more optimization.
4 714 0.946809053162 Henry Cohn, 2025, needs more optimization.
4 715 0.946867809071 Henry Cohn, 2026, needs more optimization.
4 716 0.946892530953 Henry Cohn, 2026, needs more optimization.
4 717 0.946944565495 Henry Cohn, 2025, needs more optimization.
4 718 0.946956257897 Henry Cohn, 2025, needs more optimization.
4 719 0.947101600364 Henry Cohn, 2025, needs more optimization.
4 720 0.947108699751 Henry Cohn, 2026, needs more optimization.
4 721 0.947161517163 Henry Cohn, 2025, needs more optimization.
4 722 0.947167435786 Henry Cohn, 2026, needs more optimization.
4 723 0.947182737169 Henry Cohn, 2025, needs more optimization.
4 724 0.947240345492 Henry Cohn, 2026, needs more optimization.
4 726 0.947247520945 Henry Cohn, 2025, needs more optimization.
4 727 0.947393292682 Henry Cohn, 2025, needs more optimization.
4 728 0.947430437257 Henry Cohn, 2026, needs more optimization.
4 729 0.947465166510 Henry Cohn, 2025, needs more optimization.
4 730 0.947471353781 Henry Cohn, 2025, needs more optimization.
4 731 0.947567465655 Henry Cohn, 2025, needs more optimization.
4 732 0.947578648263 Henry Cohn, 2025, needs more optimization.
4 733 0.947580880680 Henry Cohn, 2025, needs more optimization.
4 734 0.947587098177 Henry Cohn, 2025, needs more optimization.
4 736 0.947703911810 Henry Cohn, 2026, needs more optimization.
4 737 0.947873619399 Henry Cohn, 2025, needs more optimization.
4 738 0.947911079645 Henry Cohn, 2025, needs more optimization.
4 739 0.947994127717 Henry Cohn, 2025, needs more optimization.
4 740 0.948007873107 Henry Cohn, 2026, needs more optimization.
4 742 0.948098737459 Henry Cohn, 2026, needs more optimization.
4 744 0.948106489674 Henry Cohn, 2026, needs more optimization.
4 745 0.948209845355 Henry Cohn, 2025, needs more optimization.
4 746 0.948222072640 Henry Cohn, 2025, needs more optimization.
4 747 0.948235644427 Henry Cohn, 2025, needs more optimization.
4 748 0.948396609258 Henry Cohn, 2026, needs more optimization.
4 749 0.948405778670 Henry Cohn, 2026, needs more optimization.
4 750 0.948407063111 Henry Cohn, 2026, needs more optimization.
4 751 0.948410120492 Henry Cohn, 2026, needs more optimization.
4 752 0.948411007174 Henry Cohn, 2026, needs more optimization.
4 753 0.948415181708 Henry Cohn, 2026, needs more optimization.
4 754 0.948598753145 Henry Cohn, 2026, needs more optimization.
4 755 0.948601416034 Henry Cohn, 2026, needs more optimization.
4 756 0.948783172816 Henry Cohn, 2025, needs more optimization.
4 757 0.948784020424 Henry Cohn, 2025, needs more optimization.
4 758 0.948792950573 Henry Cohn, 2025, needs more optimization.
4 759 0.948822279577 Henry Cohn, 2025, needs more optimization.
4 760 0.948840430339 Henry Cohn, 2026, needs more optimization.
4 761 0.948855225174 Henry Cohn, 2025, needs more optimization.
4 762 0.948949691720 Henry Cohn, 2025, needs more optimization.
4 763 0.948951196392 Henry Cohn, 2025, needs more optimization.
4 764 0.948995346035 Henry Cohn, 2025, needs more optimization.
4 765 0.949001397228 Henry Cohn, 2025, needs more optimization.
4 768 0.949199812706 Henry Cohn, 2026, needs more optimization.
4 769 0.949245336819 Henry Cohn, 2025, needs more optimization.
4 770 0.949409316449 Henry Cohn, 2025, needs more optimization.
4 771 0.949411922940 Henry Cohn, 2025, needs more optimization.
4 772 0.949430772935 Henry Cohn, 2026, needs more optimization.
4 773 0.949433529396 Henry Cohn, 2026, needs more optimization.
4 774 0.949484015120 Henry Cohn, 2025, needs more optimization.
4 776 0.949519384499 Henry Cohn, 2026, needs more optimization.
4 780 0.949732425293 Henry Cohn, 2026, needs more optimization.
4 781 0.949987000772 Henry Cohn, 2025, needs more optimization.
4 782 0.949988721320 Henry Cohn, 2025, needs more optimization.
4 788 0.949998985865 Henry Cohn, 2025, needs more optimization.
4 789 0.950008069781 Henry Cohn, 2025, needs more optimization.
4 790 0.950221815630 Henry Cohn, 2026, needs more optimization.
4 792 0.950243741902 Henry Cohn, 2026, needs more optimization.
4 794 0.950452996933 Henry Cohn, 2025, needs more optimization.
4 799 0.950456541411 Henry Cohn, 2025, needs more optimization.
4 802 0.950462877663 Henry Cohn, 2025, needs more optimization.
4 803 0.950465283823 Henry Cohn, 2025, needs more optimization.
4 816 0.950677458913 Henry Cohn, 2025, needs more optimization.
4 817 0.950788447617 Henry Cohn, 2026, needs more optimization.
4 818 0.950788817620 Henry Cohn, 2025, needs more optimization.
4 819 0.950790988511 Henry Cohn, 2026, needs more optimization.
4 840 0.950797547280 Henry Cohn, 2025, needs more optimization.
4 841 0.951651081876 Henry Cohn, 2026, needs more optimization.
4 842 0.951932284894 Henry Cohn, 2026, needs more optimization.
4 843 0.951950022478 Henry Cohn, 2026, needs more optimization.
4 844 0.951961649164 Henry Cohn, 2026, needs more optimization.
4 845 0.952192208755 Henry Cohn, 2025, needs more optimization.
4 847 0.952217603021 Henry Cohn, 2025, needs more optimization.
4 848 0.952218987686 Henry Cohn, 2025, needs more optimization.
4 849 0.952222127536 Henry Cohn, 2025, needs more optimization.
4 850 0.952239784851 Henry Cohn, 2025, needs more optimization.
4 851 0.952280860206 Henry Cohn, 2025, needs more optimization.
4 852 0.952284747198 Henry Cohn, 2026, needs more optimization.
4 853 0.952305685659 Henry Cohn, 2025, needs more optimization.
4 854 0.952451571595 Henry Cohn, 2025, needs more optimization.
4 856 0.952469970909 Henry Cohn, 2025, needs more optimization.
4 857 0.952471686698 Henry Cohn, 2025, needs more optimization.
4 858 0.952695248097 Henry Cohn, 2025, needs more optimization.
4 859 0.952698737895 Henry Cohn, 2026, needs more optimization.
4 860 0.952700137997 Henry Cohn, 2026, needs more optimization.
4 861 0.952763448969 Henry Cohn, 2025, needs more optimization.
4 864 0.952876552024 Henry Cohn, 2026, needs more optimization.
4 866 0.952882242899 Henry Cohn, 2025, needs more optimization.
4 867 0.952902665462 Henry Cohn, 2025, needs more optimization.
4 868 0.952906611806 Henry Cohn, 2025, needs more optimization.
4 869 0.952918558454 Henry Cohn, 2025, needs more optimization.
4 872 0.953067626897 Henry Cohn, 2025, needs more optimization.
4 875 0.953104992009 Henry Cohn, 2025, needs more optimization.
4 876 0.953108610967 Henry Cohn, 2025, needs more optimization.
4 877 0.953110513304 Henry Cohn, 2025, needs more optimization.
4 878 0.953221747445 Henry Cohn, 2025, needs more optimization.
4 880 0.953473362023 Henry Cohn, 2025, needs more optimization.
4 881 0.953498792528 Henry Cohn, 2025, needs more optimization.
4 882 0.953511928838 Henry Cohn, 2026, needs more optimization.
4 883 0.953513789505 Henry Cohn, 2026, needs more optimization.
4 884 0.953525074998 Henry Cohn, 2025, needs more optimization.
4 885 0.953660979356 Henry Cohn, 2025, needs more optimization.
4 886 0.953669586269 Henry Cohn, 2025, needs more optimization.
4 887 0.953695413781 Henry Cohn, 2025, needs more optimization.
4 888 0.953700645565 Henry Cohn, 2026, needs more optimization.
4 889 0.953706262664 Henry Cohn, 2025, needs more optimization.
4 890 0.953717464100 Henry Cohn, 2025, needs more optimization.
4 891 0.953856705201 Henry Cohn, 2025, needs more optimization.
4 893 0.953864479437 Henry Cohn, 2025, needs more optimization.
4 895 0.953876489808 Henry Cohn, 2025, needs more optimization.
4 896 0.953887694041 Henry Cohn, 2026, needs more optimization.
4 897 0.953942963329 Henry Cohn, 2026, needs more optimization.
4 898 0.953951399068 Henry Cohn, 2025, needs more optimization.
4 900 0.954062876830 Henry Cohn, 2026, needs more optimization.
4 902 0.954068349973 Henry Cohn, 2025, needs more optimization.
4 904 0.954139878150 Henry Cohn, 2025, needs more optimization.
4 905 0.954145649734 Henry Cohn, 2025, needs more optimization.
4 906 0.954152636902 Henry Cohn, 2025, needs more optimization.
4 907 0.954160926763 Henry Cohn, 2025, needs more optimization.
4 908 0.954165607366 Henry Cohn, 2025, needs more optimization.
4 909 0.954212784429 Henry Cohn, 2025, needs more optimization.
4 910 0.954234701048 Henry Cohn, 2025, needs more optimization.
4 911 0.954244205857 Henry Cohn, 2025, needs more optimization.
4 912 0.954332283926 Henry Cohn, 2026, needs more optimization.
4 913 0.954332978380 Henry Cohn, 2025, needs more optimization.
4 914 0.954365078066 Henry Cohn, 2025, needs more optimization.
4 915 0.954371201370 Henry Cohn, 2025, needs more optimization.
4 916 0.954372638011 Henry Cohn, 2025, needs more optimization.
4 917 0.954373815292 Henry Cohn, 2025, needs more optimization.
4 918 0.954377733468 Henry Cohn, 2025, needs more optimization.
4 919 0.954491745196 Henry Cohn, 2025, needs more optimization.
4 920 0.954544086173 Henry Cohn, 2026, needs more optimization.
4 921 0.954564180783 Henry Cohn, 2025, needs more optimization.
4 923 0.954634824918 Henry Cohn, 2025, needs more optimization.
4 924 0.954806246462 Henry Cohn, 2025, needs more optimization.
4 925 0.954808607347 Henry Cohn, 2025, needs more optimization.
4 926 0.954811686442 Henry Cohn, 2025, needs more optimization.
4 927 0.954936284612 Henry Cohn, 2025, needs more optimization.
4 928 0.954936964671 Henry Cohn, 2026, needs more optimization.
4 929 0.954965530923 Henry Cohn, 2025, needs more optimization.
4 930 0.954992520001 Henry Cohn, 2025, needs more optimization.
4 931 0.955015118515 Henry Cohn, 2025, needs more optimization.
4 932 0.955021331426 Henry Cohn, 2025, needs more optimization.
4 933 0.955051675674 Henry Cohn, 2025, needs more optimization.
4 934 0.955120742765 Henry Cohn, 2025, needs more optimization.
4 936 0.955258943493 Henry Cohn, 2026, needs more optimization.
4 938 0.955268615415 Henry Cohn, 2025, needs more optimization.
4 940 0.955356743070 Henry Cohn, 2025, needs more optimization.
4 942 0.955390217674 Henry Cohn, 2025, needs more optimization.
4 943 0.955412046992 Henry Cohn, 2025, needs more optimization.
4 944 0.955626784466 Henry Cohn, 2026, needs more optimization.
4 945 0.955693815140 Henry Cohn, 2026, needs more optimization.
4 946 0.955703691696 Henry Cohn, 2026, needs more optimization.
4 947 0.955740079345 Henry Cohn, 2025, needs more optimization.
4 948 0.955814638725 Henry Cohn, 2026, needs more optimization.
4 950 0.955837391408 Henry Cohn, 2025, needs more optimization.
4 951 0.955847659425 Henry Cohn, 2025, needs more optimization.
4 952 0.955901860381 Henry Cohn, 2026, needs more optimization.
4 953 0.955904646548 Henry Cohn, 2026, needs more optimization.
4 954 0.955908026022 Henry Cohn, 2026, needs more optimization.
4 955 0.955914337779 Henry Cohn, 2025, needs more optimization.
4 956 0.955914956613 Henry Cohn, 2026, needs more optimization.
4 957 0.955916742199 Henry Cohn, 2026, needs more optimization.
4 960 0.955934538885 Henry Cohn, 2025, needs more optimization.
4 961 0.956011466695 Henry Cohn, 2026, needs more optimization.
4 962 0.956018479619 Henry Cohn, 2025, needs more optimization.
4 964 0.956100925104 Henry Cohn, 2026, needs more optimization.
4 966 0.956104990579 Henry Cohn, 2026, needs more optimization.
4 968 0.956155573662 Henry Cohn, 2026, needs more optimization.
4 970 0.956173518471 Henry Cohn, 2025, needs more optimization.
4 971 0.956192662084 Henry Cohn, 2025, needs more optimization.
4 972 0.956232654010 Henry Cohn, 2026, needs more optimization.
4 973 0.956331648598 Henry Cohn, 2025, needs more optimization.
4 974 0.956332591997 Henry Cohn, 2025, needs more optimization.
4 975 0.956340300559 Henry Cohn, 2025, needs more optimization.
4 976 0.956436399700 Henry Cohn, 2026, needs more optimization.
4 977 0.956436615854 Henry Cohn, 2025, needs more optimization.
4 978 0.956455330719 Henry Cohn, 2025, needs more optimization.
4 979 0.956490512655 Henry Cohn, 2025, needs more optimization.
4 980 0.956507243147 Henry Cohn, 2025, needs more optimization.
4 981 0.956578822561 Henry Cohn, 2025, needs more optimization.
4 982 0.956584248453 Henry Cohn, 2026, needs more optimization.
4 983 0.956655794511 Henry Cohn, 2025, needs more optimization.
4 984 0.956677294066 Henry Cohn, 2026, needs more optimization.
4 985 0.956685779073 Henry Cohn, 2025, needs more optimization.
4 986 0.956687258610 Henry Cohn, 2025, needs more optimization.
4 987 0.956731139388 Henry Cohn, 2025, needs more optimization.
4 988 0.956859819250 Henry Cohn, 2026, needs more optimization.
4 989 0.956962111341 Henry Cohn, 2025, needs more optimization.
4 990 0.957091191979 Henry Cohn, 2025, needs more optimization.
4 991 0.957174095123 Henry Cohn, 2025, needs more optimization.
4 992 0.957233711366 Henry Cohn, 2026, needs more optimization.
4 994 0.957330704605 Henry Cohn, 2025, needs more optimization.
4 995 0.957468627778 Henry Cohn, 2026, needs more optimization.
4 997 0.957469247295 Henry Cohn, 2025, needs more optimization.
4 998 0.957621777801 Henry Cohn, 2025, needs more optimization.
4 999 0.957624065661 Henry Cohn, 2025, needs more optimization.
4 1000 0.957724044528 Henry Cohn, 2026, needs more optimization.
4 1001 0.957725518200 Henry Cohn, 2025, needs more optimization.
4 1002 0.957879169599 Henry Cohn, 2025, needs more optimization.
4 1003 0.957879722807 Henry Cohn, 2025, needs more optimization.
4 1004 0.957932175239 Henry Cohn, 2026, needs more optimization.
4 1005 0.957933585026 Henry Cohn, 2026, needs more optimization.
4 1006 0.958016244316 Henry Cohn, 2025, needs more optimization.
4 1007 0.958019677521 Henry Cohn, 2025, needs more optimization.
4 1008 0.958025392605 Henry Cohn, 2025, needs more optimization.
4 1009 0.958106506971 Henry Cohn, 2025, needs more optimization.
4 1010 0.958106563311 Henry Cohn, 2026, needs more optimization.
4 1011 0.958226168708 Henry Cohn, 2026, needs more optimization.
4 1012 0.958235111952 Henry Cohn, 2025, needs more optimization.
4 1013 0.958243797980 Henry Cohn, 2025, needs more optimization.
4 1014 0.958252619948 Henry Cohn, 2026, needs more optimization.
4 1015 0.958307571281 Henry Cohn, 2025, needs more optimization.
4 1016 0.958323656469 Henry Cohn, 2026, needs more optimization.
4 1017 0.958433314810 Henry Cohn, 2025, needs more optimization.
4 1018 0.958438818315 Henry Cohn, 2025, needs more optimization.
4 1019 0.958445105410 Henry Cohn, 2026, needs more optimization.
4 1020 0.958491952684 Henry Cohn, 2026, needs more optimization.
4 1021 0.958497806626 Henry Cohn, 2026, needs more optimization.
4 1023 0.958667893556 Henry Cohn, 2025, needs more optimization.
4 1024 0.958676090349 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 0.673830986224 Henry Cohn, 2025.
5 94 0.675154811372 Henry Cohn, 2025.
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 0.688903541719 Henry Cohn, 2025.
5 104 0.689715870633 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
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 0.709336098101 Henry Cohn, 2025.
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 0.715099002544 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
5 125 0.716589774161 Henry Cohn, 2025.
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 0.723208608895 Henry Cohn, 2025.
5 132 0.724187141022 Henry Cohn, 2026, needs more optimization.
5 133 0.725096024568 Henry Cohn, 2026, needs more optimization.
5 134 0.726667487692 Henry Cohn, 2026, needs more optimization.
5 135 0.727819930944 Henry Cohn, 2025.
5 136 0.728641959070 Henry Cohn, 2026.
5 137 0.730011100633 Henry Cohn, 2025.
5 138 0.730143082796 Henry Cohn, 2025.
5 139 0.731031355420 Henry Cohn, 2026, needs more optimization.
5 140 0.731880138963 Henry Cohn, 2025.
5 141 0.732960070489 Henry Cohn, 2026, needs more optimization.
5 142 0.733688627543 Henry Cohn, 2025.
5 143 0.734506087652 Henry Cohn, 2025.
5 144 0.735189318066 Henry Cohn, 2025.
5 145 0.736519094966 Henry Cohn, 2025.
5 146 0.736648368146 Henry Cohn, 2025.
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 0.739527956073 Henry Cohn, 2025.
5 152 0.739824519106 Henry Cohn, 2025.
5 153 0.740779971316 Henry Cohn, 2025.
5 154 0.741354012157 Henry Cohn, 2025.
5 155 0.742161234709 Henry Cohn, 2025.
5 156 0.742808811623 Henry Cohn, 2025.
5 157 0.743339290160 Henry Cohn, 2025.
5 158 0.743500742995 Henry Cohn, 2025.
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 0.752079878060 Henry Cohn, 2025.
5 166 0.752534073395 Henry Cohn, 2025.
5 167 0.753532673949 Henry Cohn, 2025.
5 168 0.754218675211 Henry Cohn, 2025.
5 169 0.755416175364 Henry Cohn, 2025.
5 170 0.755993792807 Henry Cohn, 2025.
5 171 0.756800051039 Henry Cohn, 2025.
5 172 0.757288355849 Henry Cohn, 2025.
5 173 0.759182977238 Henry Cohn, 2025.
5 174 0.759690412033 Henry Cohn, 2025.
5 175 0.760597483271 Henry Cohn, 2025.
5 176 0.761278064091 Henry Cohn, 2025.
5 177 0.762875931769 Henry Cohn, 2025.
5 178 0.763315108223 Henry Cohn, 2025.
5 179 0.764671222232 Henry Cohn, 2025.
5 180 0.764830852765 Henry Cohn, 2025.
5 181 0.764889493147 Henry Cohn, 2026, needs more optimization.
5 182 0.765509073377 Henry Cohn, 2026, needs more optimization.
5 183 0.765786900083 Henry Cohn, 2026, needs more optimization.
5 184 0.766400913097 Henry Cohn, 2026, needs more optimization.
5 185 0.767328447987 Henry Cohn, 2025.
5 186 0.768015283838 Henry Cohn, 2026, needs more optimization.
5 187 0.768477482281 Henry Cohn, 2026, needs more optimization.
5 188 0.769315059750 Henry Cohn, 2026.
5 189 0.769961416902 Henry Cohn, 2026, needs more optimization.
5 190 0.770220241203 Henry Cohn, 2025.
5 191 0.770477151449 Henry Cohn, 2025.
5 192 0.771178995101 Henry Cohn, 2026, needs more optimization.
5 193 0.771640580906 Henry Cohn, 2025.
5 194 0.772357310102 Henry Cohn, 2025.
5 195 0.772914025091 Henry Cohn, 2025.
5 196 0.773820141713 Henry Cohn, 2025.
5 197 0.774290878773 Henry Cohn, 2025.
5 198 0.774958465360 Henry Cohn, 2026, needs more optimization.
5 199 0.775242540360 Henry Cohn, 2025.
5 200 0.775814258853 Henry Cohn, 2025.
5 201 0.776383781495 Henry Cohn, 2026, needs more optimization.
5 202 0.777443383285 Henry Cohn, 2026, needs more optimization.
5 203 0.777969132643 Henry Cohn, 2026, needs more optimization.
5 204 0.778262339953 Henry Cohn, 2025.
5 205 0.779048071982 Henry Cohn, 2025.
5 206 0.779408327452 Henry Cohn, 2026, needs more optimization.
5 207 0.780186249913 Henry Cohn, 2025.
5 208 0.780873741971 Henry Cohn, 2026, needs more optimization.
5 209 0.781333225832 Henry Cohn, 2025.
5 210 0.782460219799 Henry Cohn, 2025.
5 211 0.782855932265 Henry Cohn, 2026, needs more optimization.
5 212 0.783016654957 Henry Cohn, 2025.
5 213 0.783786516576 Henry Cohn, 2025.
5 214 0.784221920412 Henry Cohn, 2025.
5 215 0.784440391336 Henry Cohn, 2025.
5 216 0.785143218786 Henry Cohn, 2026, needs more optimization.
5 217 0.785510050827 Henry Cohn, 2025.
5 218 0.785996484357 Henry Cohn, 2025.
5 219 0.786890579920 Henry Cohn, 2026, needs more optimization.
5 220 0.787295059910 Henry Cohn, 2025.
5 221 0.787561403335 Henry Cohn, 2025.
5 222 0.788126323248 Henry Cohn, 2025.
5 223 0.788437486442 Henry Cohn, 2025.
5 224 0.788866206268 Henry Cohn, 2025.
5 225 0.789325624436 Henry Cohn, 2025.
5 226 0.789501827423 Henry Cohn, 2026, needs more optimization.
5 227 0.790566449848 Henry Cohn, 2025.
5 228 0.790672654054 Henry Cohn, 2026, needs more optimization.
5 229 0.790950228764 Henry Cohn, 2025.
5 230 0.791641402438 Henry Cohn, 2026, needs more optimization.
5 231 0.791859278921 Henry Cohn, 2025.
5 232 0.792500892930 Henry Cohn, 2025.
5 233 0.792671214420 Henry Cohn, 2026, needs more optimization.
5 234 0.792936161090 Henry Cohn, 2026, needs more optimization.
5 235 0.793680055721 Henry Cohn, 2025.
5 236 0.794236325882 Henry Cohn, 2025.
5 237 0.794670674646 Henry Cohn, 2025.
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 0.796930028362 Henry Cohn, 2025.
5 243 0.797123580924 Henry Cohn, 2026, needs more optimization.
5 244 0.797604028749 Henry Cohn, 2026, needs more optimization.
5 245 0.797916847251 Henry Cohn, 2025.
5 246 0.798283603534 Henry Cohn, 2025.
5 247 0.798790606421 Henry Cohn, 2025.
5 248 0.799294089857 Henry Cohn, 2025.
5 249 0.799665163470 Henry Cohn, 2025.
5 250 0.799687724511 Henry Cohn, 2026, needs more optimization.
5 251 0.799695494157 Henry Cohn, 2026, needs more optimization.
5 252 0.800042141214 Henry Cohn, 2026, needs more optimization.
5 253 0.800361794284 Henry Cohn, 2026, needs more optimization.
5 254 0.800542384474 Henry Cohn, 2026, needs more optimization.
5 255 0.801468669593 Henry Cohn, 2026, needs more optimization.
5 256 0.801475125011 Henry Cohn, 2026, needs more optimization.
5 257 0.802206877452 Henry Cohn, 2026, needs more optimization.
5 258 0.802656826349 Henry Cohn, 2025, needs more optimization.
5 259 0.802675225550 Henry Cohn, 2025, needs more optimization.
5 260 0.802955606789 Henry Cohn, 2026, needs more optimization.
5 261 0.803531206141 Henry Cohn, 2026, needs more optimization.
5 262 0.803924735750 Henry Cohn, 2026, needs more optimization.
5 263 0.804141588076 Henry Cohn, 2026, needs more optimization.
5 264 0.804511457554 Henry Cohn, 2026, needs more optimization.
5 265 0.804525832482 Henry Cohn, 2026, needs more optimization.
5 266 0.805070511691 Henry Cohn, 2025, needs more optimization.
5 267 0.805182447272 Henry Cohn, 2026, needs more optimization.
5 268 0.805447930744 Henry Cohn, 2026, needs more optimization.
5 269 0.805694705601 Henry Cohn, 2026, needs more optimization.
5 270 0.805892214741 Henry Cohn, 2026, needs more optimization.
5 271 0.806104593335 Henry Cohn, 2026, needs more optimization.
5 272 0.806492034146 Henry Cohn, 2025, needs more optimization.
5 274 0.806559079295 Henry Cohn, 2026, needs more optimization.
5 275 0.806633113314 Henry Cohn, 2026, needs more optimization.
5 276 0.806750111069 Henry Cohn, 2026, needs more optimization.
5 277 0.806878203435 Henry Cohn, 2026, needs more optimization.
5 279 0.807069479288 Henry Cohn, 2026, needs more optimization.
5 280 0.807210314038 Henry Cohn, 2026, needs more optimization.
5 281 0.807260409149 Henry Cohn, 2026, needs more optimization.
5 282 0.807790416393 Henry Cohn, 2026, needs more optimization.
5 283 0.807990452871 Henry Cohn, 2026, needs more optimization.
5 284 0.808502441915 Henry Cohn, 2025, needs more optimization.
5 285 0.809222044082 Henry Cohn, 2025, needs more optimization.
5 286 0.809311967369 Henry Cohn, 2026, needs more optimization.
5 287 0.809859358344 Henry Cohn, 2026, needs more optimization.
5 288 0.810387182281 Henry Cohn, 2026, needs more optimization.
5 289 0.810515942365 Henry Cohn, 2026, needs more optimization.
5 290 0.811849330647 Henry Cohn, 2026, needs more optimization.
5 291 0.812038638659 Henry Cohn, 2025, needs more optimization.
5 292 0.812315403741 Henry Cohn, 2026, needs more optimization.
5 293 0.812784716715 Henry Cohn, 2026, needs more optimization.
5 294 0.813162150808 Henry Cohn, 2026, needs more optimization.
5 295 0.813794458355 Henry Cohn, 2026, needs more optimization.
5 296 0.814121903369 Henry Cohn, 2026, needs more optimization.
5 297 0.815118059518 Henry Cohn, 2026, needs more optimization.
5 298 0.815629330255 Henry Cohn, 2026, needs more optimization.
5 299 0.816118912242 Henry Cohn, 2026, needs more optimization.
5 300 0.816515571492 Henry Cohn, 2025, needs more optimization.
5 301 0.816884029652 Henry Cohn, 2025, needs more optimization.
5 302 0.817416382715 Henry Cohn, 2026, needs more optimization.
5 303 0.817678249405 Henry Cohn, 2025, needs more optimization.
5 304 0.818236802717 Henry Cohn, 2026, needs more optimization.
5 305 0.818530915024 Henry Cohn, 2025, needs more optimization.
5 306 0.818846725648 Henry Cohn, 2026, needs more optimization.
5 307 0.819649993393 Ilmari Vahteristo, 2026.
5 308 0.819704042350 Henry Cohn, 2025, needs more optimization.
5 309 0.820136258550 Henry Cohn, 2025, needs more optimization.
5 310 0.820291870315 Henry Cohn, 2025, needs more optimization.
5 311 0.820683934305 Henry Cohn, 2025, needs more optimization.
5 312 0.820907477416 Henry Cohn, 2025, needs more optimization.
5 313 0.821238678583 Henry Cohn, 2025, needs more optimization.
5 314 0.821842718616 Henry Cohn, 2025, needs more optimization.
5 315 0.822166006099 Henry Cohn, 2025, needs more optimization.
5 316 0.822348273561 Henry Cohn, 2026, needs more optimization.
5 317 0.822600119096 Henry Cohn, 2025, needs more optimization.
5 318 0.822851367310 Henry Cohn, 2025, needs more optimization.
5 319 0.823386083659 Henry Cohn, 2026, needs more optimization.
5 321 0.823945293516 Henry Cohn, 2025, needs more optimization.
5 322 0.824227974650 Henry Cohn, 2026, needs more optimization.
5 323 0.824521620521 Henry Cohn, 2025, needs more optimization.
5 324 0.824672784814 Ilmari Vahteristo, 2026.
5 325 0.825136817529 Henry Cohn, 2026, needs more optimization.
5 326 0.825465801700 Henry Cohn, 2025, needs more optimization.
5 327 0.825636523896 Henry Cohn, 2026, needs more optimization.
5 328 0.826102388552 Henry Cohn, 2025, needs more optimization.
5 329 0.826424481057 Ilmari Vahteristo, 2026.
5 331 0.826573216614 Ilmari Vahteristo, 2026.
5 332 0.827012207972 Ilmari Vahteristo, 2026.
5 333 0.827486994092 Ilmari Vahteristo, 2026.
5 334 0.827773996545 Ilmari Vahteristo, 2026.
5 335 0.828006262238 Henry Cohn, 2026, needs more optimization.
5 336 0.828034033820 Ilmari Vahteristo, 2026.
5 337 0.828501751462 Ilmari Vahteristo, 2026.
5 338 0.828788070280 Henry Cohn, 2026, needs more optimization.
5 339 0.828788082318 Ilmari Vahteristo, 2026.
5 340 0.829152368222 Henry Cohn, 2025, needs more optimization.
5 341 0.829388117676 Henry Cohn, 2026, needs more optimization.
5 342 0.829749117524 Henry Cohn, 2025, needs more optimization.
5 343 0.829988638760 Ilmari Vahteristo, 2026.
5 344 0.830288948112 Henry Cohn, 2025, needs more optimization.
5 345 0.830334873964 Ilmari Vahteristo, 2026.
5 346 0.830743543200 Henry Cohn, 2025, needs more optimization.
5 347 0.830944830997 Ilmari Vahteristo, 2026.
5 348 0.831093213465 Ilmari Vahteristo, 2026.
5 349 0.831549947592 Henry Cohn, 2026, needs more optimization.
5 350 0.831603555680 Henry Cohn, 2026, needs more optimization.
5 351 0.831919598187 Henry Cohn, 2025, needs more optimization.
5 352 0.831978050097 Ilmari Vahteristo, 2026.
5 353 0.832359675560 Ilmari Vahteristo, 2026.
5 354 0.832781308439 Ilmari Vahteristo, 2026.
5 355 0.832820133321 Ilmari Vahteristo, 2026.
5 356 0.833098647880 Ilmari Vahteristo, 2026.
5 357 0.833368449930 Henry Cohn, 2025, needs more optimization.
5 358 0.833452870525 Henry Cohn, 2025, needs more optimization.
5 359 0.833777259172 Ilmari Vahteristo, 2026.
5 360 0.833869567239 Henry Cohn, 2026, needs more optimization.
5 361 0.834182975616 Henry Cohn, 2025, needs more optimization.
5 362 0.834274529233 Henry Cohn, 2026, needs more optimization.
5 363 0.834618950083 Henry Cohn, 2025, needs more optimization.
5 364 0.834837068276 Henry Cohn, 2026, needs more optimization.
5 365 0.835048430244 Henry Cohn, 2026, needs more optimization.
5 366 0.835387548410 Henry Cohn, 2025, needs more optimization.
5 367 0.835389435183 Henry Cohn, 2025, needs more optimization.
5 368 0.835712494152 Henry Cohn, 2026, needs more optimization.
5 369 0.835765894972 Henry Cohn, 2025, needs more optimization.
5 370 0.836140292070 Henry Cohn, 2026, needs more optimization.
5 371 0.836473545501 Henry Cohn, 2025, needs more optimization.
5 372 0.836679323230 Henry Cohn, 2026, needs more optimization.
5 373 0.836702413007 Henry Cohn, 2026, needs more optimization.
5 374 0.836999067577 Henry Cohn, 2026, needs more optimization.
5 375 0.837271070757 Henry Cohn, 2025, needs more optimization.
5 376 0.837539201868 Henry Cohn, 2025, needs more optimization.
5 377 0.837708951550 Henry Cohn, 2025, needs more optimization.
5 378 0.838003296452 Henry Cohn, 2025, needs more optimization.
5 379 0.838083866651 Henry Cohn, 2026, needs more optimization.
5 380 0.838327924680 Henry Cohn, 2025, needs more optimization.
5 381 0.838354217251 Henry Cohn, 2025, needs more optimization.
5 382 0.838798152226 Henry Cohn, 2025, needs more optimization.
5 383 0.838881488627 Henry Cohn, 2025, needs more optimization.
5 384 0.839339620040 Henry Cohn, 2025, needs more optimization.
5 385 0.839355829121 Henry Cohn, 2025, needs more optimization.
5 386 0.839622713054 Henry Cohn, 2026, needs more optimization.
5 387 0.839804191321 Henry Cohn, 2026, needs more optimization.
5 388 0.839991024596 Henry Cohn, 2025, needs more optimization.
5 389 0.840516182174 Henry Cohn, 2026, needs more optimization.
5 390 0.840803815311 Henry Cohn, 2025, needs more optimization.
5 391 0.840904105112 Henry Cohn, 2026, needs more optimization.
5 392 0.840920101150 Henry Cohn, 2026, needs more optimization.
5 393 0.841234032091 Henry Cohn, 2025, needs more optimization.
5 394 0.841517571002 Henry Cohn, 2025, needs more optimization.
5 395 0.841518430864 Henry Cohn, 2025, needs more optimization.
5 396 0.841721666351 Henry Cohn, 2026, needs more optimization.
5 397 0.841929833352 Henry Cohn, 2026, needs more optimization.
5 398 0.842019642437 Henry Cohn, 2025, needs more optimization.
5 399 0.842351224361 Henry Cohn, 2025, needs more optimization.
5 400 0.842667381746 Henry Cohn, 2026, needs more optimization.
5 401 0.842755099804 Henry Cohn, 2025, needs more optimization.
5 402 0.843048678997 Henry Cohn, 2026, needs more optimization.
5 403 0.843178483011 Henry Cohn, 2025, needs more optimization.
5 404 0.843233612969 Henry Cohn, 2026, needs more optimization.
5 405 0.843596031205 Henry Cohn, 2025, needs more optimization.
5 406 0.843634615469 Henry Cohn, 2025, needs more optimization.
5 407 0.843834979070 Henry Cohn, 2025, needs more optimization.
5 408 0.843903654365 Henry Cohn, 2026, needs more optimization.
5 409 0.843990630575 Henry Cohn, 2025, needs more optimization.
5 410 0.844138429797 Henry Cohn, 2025, needs more optimization.
5 411 0.844505725469 Henry Cohn, 2026, needs more optimization.
5 412 0.844674709808 Henry Cohn, 2025, needs more optimization.
5 413 0.844824973155 Henry Cohn, 2025, needs more optimization.
5 414 0.844870169871 Henry Cohn, 2025, needs more optimization.
5 415 0.845396059797 Henry Cohn, 2025, needs more optimization.
5 416 0.845502920468 Henry Cohn, 2025, needs more optimization.
5 417 0.845632826733 Henry Cohn, 2025, needs more optimization.
5 418 0.845740891849 Henry Cohn, 2026, needs more optimization.
5 419 0.845818752271 Henry Cohn, 2025, needs more optimization.
5 420 0.845999170102 Henry Cohn, 2026, needs more optimization.
5 421 0.846210387692 Henry Cohn, 2026, needs more optimization.
5 422 0.846488117361 Henry Cohn, 2025, needs more optimization.
5 423 0.846740415916 Henry Cohn, 2025, needs more optimization.
5 424 0.846828782623 Henry Cohn, 2026, needs more optimization.
5 425 0.847111917510 Henry Cohn, 2026, needs more optimization.
5 426 0.847141264817 Henry Cohn, 2025, needs more optimization.
5 427 0.847356510265 Henry Cohn, 2026, needs more optimization.
5 428 0.847782849632 Henry Cohn, 2026, needs more optimization.
5 429 0.847871831387 Henry Cohn, 2026, needs more optimization.
5 430 0.848148846253 Henry Cohn, 2025, needs more optimization.
5 431 0.848182648352 Henry Cohn, 2026, needs more optimization.
5 432 0.848428081817 Henry Cohn, 2025, needs more optimization.
5 433 0.848473227014 Henry Cohn, 2025, needs more optimization.
5 434 0.848750844911 Henry Cohn, 2026, needs more optimization.
5 435 0.848935967498 Henry Cohn, 2025, needs more optimization.
5 436 0.849091840672 Henry Cohn, 2025, needs more optimization.
5 437 0.849166823783 Henry Cohn, 2025, needs more optimization.
5 438 0.849457353237 Henry Cohn, 2026, needs more optimization.
5 439 0.849665555849 Henry Cohn, 2026, needs more optimization.
5 440 0.849761491108 Henry Cohn, 2026, needs more optimization.
5 441 0.849905344307 Henry Cohn, 2026, needs more optimization.
5 442 0.850005854540 Henry Cohn, 2026, needs more optimization.
5 443 0.850173997001 Henry Cohn, 2026, needs more optimization.
5 444 0.850591420205 Henry Cohn, 2025, needs more optimization.
5 445 0.850688858705 Henry Cohn, 2025, needs more optimization.
5 446 0.850872757151 Henry Cohn, 2026, needs more optimization.
5 447 0.851046882825 Henry Cohn, 2025, needs more optimization.
5 448 0.851136609114 Henry Cohn, 2026, needs more optimization.
5 449 0.851144183240 Henry Cohn, 2025, needs more optimization.
5 450 0.851519869513 Henry Cohn, 2025, needs more optimization.
5 451 0.851797504621 Henry Cohn, 2025, needs more optimization.
5 452 0.851801627681 Henry Cohn, 2025, needs more optimization.
5 453 0.852169963403 Henry Cohn, 2026, needs more optimization.
5 454 0.852178960242 Henry Cohn, 2026, needs more optimization.
5 455 0.852341044858 Henry Cohn, 2026, needs more optimization.
5 456 0.852509268186 Henry Cohn, 2026, needs more optimization.
5 457 0.852749067895 Henry Cohn, 2025, needs more optimization.
5 458 0.852757857919 Henry Cohn, 2025, needs more optimization.
5 459 0.852826843904 Henry Cohn, 2026, needs more optimization.
5 460 0.853097261023 Henry Cohn, 2026, needs more optimization.
5 461 0.853282800509 Henry Cohn, 2026, needs more optimization.
5 462 0.853613227584 Henry Cohn, 2026, needs more optimization.
5 463 0.853616344570 Henry Cohn, 2025, needs more optimization.
5 464 0.853696327126 Henry Cohn, 2026, needs more optimization.
5 465 0.853910231679 Henry Cohn, 2025, needs more optimization.
5 466 0.854125175508 Henry Cohn, 2025, needs more optimization.
5 467 0.854126192783 Henry Cohn, 2026, needs more optimization.
5 468 0.854465241932 Henry Cohn, 2025, needs more optimization.
5 469 0.854481278069 Henry Cohn, 2026, needs more optimization.
5 470 0.854683349001 Henry Cohn, 2025, needs more optimization.
5 471 0.854796588645 Henry Cohn, 2026, needs more optimization.
5 472 0.854963819384 Henry Cohn, 2025, needs more optimization.
5 473 0.855271668132 Henry Cohn, 2025, needs more optimization.
5 474 0.855274943930 Henry Cohn, 2025, needs more optimization.
5 475 0.855315364840 Henry Cohn, 2025, needs more optimization.
5 476 0.855484878935 Henry Cohn, 2026, needs more optimization.
5 477 0.855695759041 Henry Cohn, 2025, needs more optimization.
5 478 0.855841719507 Henry Cohn, 2026, needs more optimization.
5 479 0.856359033178 Henry Cohn, 2026, needs more optimization.
5 481 0.856438290668 Henry Cohn, 2025, needs more optimization.
5 482 0.856479136994 Henry Cohn, 2025, needs more optimization.
5 483 0.856712971651 Henry Cohn, 2025, needs more optimization.
5 484 0.856722994352 Henry Cohn, 2025, needs more optimization.
5 485 0.856820007940 Henry Cohn, 2025, needs more optimization.
5 486 0.857094821423 Henry Cohn, 2025, needs more optimization.
5 487 0.857117989588 Henry Cohn, 2025, needs more optimization.
5 488 0.857287179940 Henry Cohn, 2025, needs more optimization.
5 489 0.857435857392 Henry Cohn, 2025, needs more optimization.
5 490 0.857565211369 Henry Cohn, 2025, needs more optimization.
5 491 0.857620435328 Henry Cohn, 2025, needs more optimization.
5 492 0.857846614823 Henry Cohn, 2025, needs more optimization.
5 493 0.857887587311 Henry Cohn, 2026, needs more optimization.
5 494 0.857985545441 Henry Cohn, 2025, needs more optimization.
5 495 0.858367120376 Henry Cohn, 2025, needs more optimization.
5 496 0.858507150778 Henry Cohn, 2025, needs more optimization.
5 497 0.858685307857 Henry Cohn, 2025, needs more optimization.
5 498 0.858833192245 Henry Cohn, 2025, needs more optimization.
5 499 0.858944591166 Henry Cohn, 2026, needs more optimization.
5 500 0.859136977171 Henry Cohn, 2025, needs more optimization.
5 501 0.859512033864 Henry Cohn, 2025, needs more optimization.
5 502 0.859555607488 Henry Cohn, 2026, needs more optimization.
5 503 0.859590934115 Henry Cohn, 2025, needs more optimization.
5 504 0.859701419249 Henry Cohn, 2026, needs more optimization.
5 505 0.859778505009 Henry Cohn, 2025, needs more optimization.
5 506 0.859876844867 Henry Cohn, 2025, needs more optimization.
5 507 0.860054961546 Henry Cohn, 2026, needs more optimization.
5 508 0.860267863182 Henry Cohn, 2026, needs more optimization.
5 509 0.860322505942 Henry Cohn, 2025, needs more optimization.
5 510 0.860628775031 Henry Cohn, 2025, needs more optimization.
5 511 0.860697231201 Henry Cohn, 2025, needs more optimization.
5 512 0.860725260477 Henry Cohn, 2025, needs more optimization.
5 513 0.860797749661 Henry Cohn, 2026, needs more optimization.
5 515 0.861143775119 Henry Cohn, 2026, needs more optimization.
5 516 0.861368957008 Henry Cohn, 2025, needs more optimization.
5 517 0.861388637378 Henry Cohn, 2026, needs more optimization.
5 518 0.861543720608 Henry Cohn, 2025, needs more optimization.
5 519 0.861749444634 Henry Cohn, 2026, needs more optimization.
5 520 0.861749994508 Henry Cohn, 2026, needs more optimization.
5 521 0.861795267361 Henry Cohn, 2025, needs more optimization.
5 522 0.862091307594 Henry Cohn, 2025, needs more optimization.
5 523 0.862318412803 Henry Cohn, 2025, needs more optimization.
5 524 0.862466887973 Henry Cohn, 2026, needs more optimization.
5 525 0.862470664059 Henry Cohn, 2025, needs more optimization.
5 526 0.862683702407 Henry Cohn, 2025, needs more optimization.
5 527 0.862707887103 Henry Cohn, 2026, needs more optimization.
5 528 0.862884014457 Henry Cohn, 2026, needs more optimization.
5 529 0.863035952578 Henry Cohn, 2025, needs more optimization.
5 530 0.863104542022 Henry Cohn, 2026, needs more optimization.
5 531 0.863240337579 Henry Cohn, 2025, needs more optimization.
5 532 0.863458712182 Henry Cohn, 2026, needs more optimization.
5 533 0.863618313032 Henry Cohn, 2026, needs more optimization.
5 534 0.863843381931 Henry Cohn, 2025, needs more optimization.
5 535 0.863880240397 Henry Cohn, 2025, needs more optimization.
5 536 0.863923777463 Henry Cohn, 2025, needs more optimization.
5 537 0.864152691676 Henry Cohn, 2026, needs more optimization.
5 538 0.864154701351 Henry Cohn, 2025, needs more optimization.
5 540 0.864395058631 Henry Cohn, 2025, needs more optimization.
5 542 0.864745296806 Henry Cohn, 2025, needs more optimization.
5 543 0.864969144430 Henry Cohn, 2026, needs more optimization.
5 544 0.864997867521 Henry Cohn, 2025, needs more optimization.
5 545 0.865069847868 Henry Cohn, 2025, needs more optimization.
5 546 0.865281323991 Henry Cohn, 2026, needs more optimization.
5 547 0.865434209594 Henry Cohn, 2026, needs more optimization.
5 548 0.865438315541 Henry Cohn, 2026, needs more optimization.
5 549 0.865712585376 Henry Cohn, 2025, needs more optimization.
5 550 0.865824560652 Henry Cohn, 2026, needs more optimization.
5 551 0.865842695323 Henry Cohn, 2026, needs more optimization.
5 552 0.865879307122 Henry Cohn, 2025, needs more optimization.
5 553 0.866159324412 Henry Cohn, 2025, needs more optimization.
5 554 0.866200338542 Henry Cohn, 2025, needs more optimization.
5 555 0.866352525315 Henry Cohn, 2025, needs more optimization.
5 556 0.866362800622 Henry Cohn, 2025, needs more optimization.
5 557 0.866758622688 Henry Cohn, 2026, needs more optimization.
5 558 0.866872959031 Henry Cohn, 2025, needs more optimization.
5 559 0.866900685443 Henry Cohn, 2025, needs more optimization.
5 560 0.867099425536 Henry Cohn, 2025, needs more optimization.
5 561 0.867325322385 Henry Cohn, 2025, needs more optimization.
5 562 0.867343447361 Henry Cohn, 2025, needs more optimization.
5 563 0.867436150282 Henry Cohn, 2025, needs more optimization.
5 564 0.867447737084 Henry Cohn, 2026, needs more optimization.
5 565 0.867452395939 Henry Cohn, 2025, needs more optimization.
5 566 0.867653917205 Henry Cohn, 2025, needs more optimization.
5 567 0.867784283396 Henry Cohn, 2026, needs more optimization.
5 568 0.867887760645 Henry Cohn, 2025, needs more optimization.
5 569 0.868077290034 Henry Cohn, 2025, needs more optimization.
5 570 0.868216680382 Henry Cohn, 2025, needs more optimization.
5 572 0.868451973652 Henry Cohn, 2026, needs more optimization.
5 573 0.868654373375 Henry Cohn, 2025, needs more optimization.
5 574 0.868673755205 Henry Cohn, 2025, needs more optimization.
5 575 0.868676712166 Henry Cohn, 2026, needs more optimization.
5 577 0.868935335122 Henry Cohn, 2025, needs more optimization.
5 578 0.868981819142 Henry Cohn, 2025, needs more optimization.
5 579 0.869153575403 Henry Cohn, 2026, needs more optimization.
5 580 0.869345631288 Henry Cohn, 2025, needs more optimization.
5 581 0.869468305984 Henry Cohn, 2025, needs more optimization.
5 582 0.869569569795 Henry Cohn, 2025, needs more optimization.
5 583 0.869749722833 Henry Cohn, 2026, needs more optimization.
5 584 0.869920874945 Henry Cohn, 2026, needs more optimization.
5 585 0.869929165808 Henry Cohn, 2026, needs more optimization.
5 586 0.870175585547 Henry Cohn, 2025, needs more optimization.
5 587 0.870179294621 Henry Cohn, 2025, needs more optimization.
5 588 0.870186408492 Henry Cohn, 2026, needs more optimization.
5 589 0.870249803628 Henry Cohn, 2025, needs more optimization.
5 590 0.870385377115 Henry Cohn, 2025, needs more optimization.
5 591 0.870414929971 Henry Cohn, 2025, needs more optimization.
5 592 0.870655172327 Henry Cohn, 2026, needs more optimization.
5 593 0.870691681545 Henry Cohn, 2026, needs more optimization.
5 594 0.870810238973 Henry Cohn, 2026, needs more optimization.
5 595 0.871066955540 Henry Cohn, 2025, needs more optimization.
5 596 0.871070914052 Henry Cohn, 2026, needs more optimization.
5 597 0.871105033160 Henry Cohn, 2025, needs more optimization.
5 598 0.871326407700 Henry Cohn, 2025, needs more optimization.
5 599 0.871327354638 Henry Cohn, 2026, needs more optimization.
5 600 0.871382362457 Henry Cohn, 2026, needs more optimization.
5 601 0.871604091828 Henry Cohn, 2026, needs more optimization.
5 602 0.871606438312 Henry Cohn, 2025, needs more optimization.
5 603 0.871665796035 Henry Cohn, 2026, needs more optimization.
5 604 0.871805838747 Henry Cohn, 2026, needs more optimization.
5 605 0.871824322660 Henry Cohn, 2025, needs more optimization.
5 606 0.871902403634 Henry Cohn, 2026, needs more optimization.
5 607 0.872081555797 Henry Cohn, 2026, needs more optimization.
5 608 0.872084141228 Henry Cohn, 2026, needs more optimization.
5 609 0.872517588599 Henry Cohn, 2026, needs more optimization.
5 610 0.872521651154 Henry Cohn, 2026, needs more optimization.
5 611 0.872670113057 Henry Cohn, 2025, needs more optimization.
5 612 0.872701370708 Henry Cohn, 2026, needs more optimization.
5 613 0.872895228619 Henry Cohn, 2026, needs more optimization.
5 614 0.872896331494 Henry Cohn, 2026, needs more optimization.
5 615 0.873090713168 Henry Cohn, 2025, needs more optimization.
5 616 0.873103833019 Henry Cohn, 2026, needs more optimization.
5 617 0.873301059105 Henry Cohn, 2025, needs more optimization.
5 618 0.873380978365 Henry Cohn, 2025, needs more optimization.
5 619 0.873472760121 Henry Cohn, 2026, needs more optimization.
5 620 0.873605610177 Henry Cohn, 2026, needs more optimization.
5 621 0.873622039759 Henry Cohn, 2025, needs more optimization.
5 622 0.873753446890 Henry Cohn, 2025, needs more optimization.
5 623 0.873905770256 Henry Cohn, 2025, needs more optimization.
5 624 0.873949410115 Henry Cohn, 2026, needs more optimization.
5 625 0.874124521820 Henry Cohn, 2026, needs more optimization.
5 626 0.874138805817 Henry Cohn, 2025, needs more optimization.
5 627 0.874162709567 Henry Cohn, 2025, needs more optimization.
5 628 0.874359782501 Henry Cohn, 2026, needs more optimization.
5 629 0.874485297919 Henry Cohn, 2025, needs more optimization.
5 630 0.874703509407 Henry Cohn, 2025, needs more optimization.
5 631 0.874836646897 Henry Cohn, 2026, needs more optimization.
5 633 0.874969572156 Henry Cohn, 2025, needs more optimization.
5 634 0.874987432232 Henry Cohn, 2026, needs more optimization.
5 635 0.875121083724 Henry Cohn, 2026, needs more optimization.
5 636 0.875300468091 Henry Cohn, 2025, needs more optimization.
5 637 0.875307252400 Henry Cohn, 2025, needs more optimization.
5 638 0.875387823448 Henry Cohn, 2025, needs more optimization.
5 639 0.875463236969 Henry Cohn, 2025, needs more optimization.
5 640 0.875640540653 Henry Cohn, 2026, needs more optimization.
5 641 0.875645428560 Henry Cohn, 2026, needs more optimization.
5 642 0.875664298640 Henry Cohn, 2025, needs more optimization.
5 643 0.875835676045 Henry Cohn, 2025, needs more optimization.
5 644 0.876028785170 Henry Cohn, 2026, needs more optimization.
5 645 0.876115945893 Henry Cohn, 2026, needs more optimization.
5 646 0.876190173583 Henry Cohn, 2026, needs more optimization.
5 647 0.876317790109 Henry Cohn, 2026, needs more optimization.
5 648 0.876321229584 Henry Cohn, 2025, needs more optimization.
5 649 0.876512730152 Henry Cohn, 2026, needs more optimization.
5 650 0.876534189853 Henry Cohn, 2025, needs more optimization.
5 651 0.876643344064 Henry Cohn, 2026, needs more optimization.
5 652 0.876649196799 Henry Cohn, 2025, needs more optimization.
5 653 0.876891012640 Henry Cohn, 2025, needs more optimization.
5 654 0.877000319265 Henry Cohn, 2025, needs more optimization.
5 655 0.877194944627 Henry Cohn, 2025, needs more optimization.
5 656 0.877250936425 Henry Cohn, 2026, needs more optimization.
5 657 0.877335064927 Henry Cohn, 2026, needs more optimization.
5 659 0.877422215326 Henry Cohn, 2025, needs more optimization.
5 660 0.877460598524 Henry Cohn, 2026, needs more optimization.
5 661 0.877492961756 Henry Cohn, 2025, needs more optimization.
5 662 0.877622878303 Henry Cohn, 2025, needs more optimization.
5 663 0.877665604940 Henry Cohn, 2025, needs more optimization.
5 664 0.877808986150 Henry Cohn, 2025, needs more optimization.
5 665 0.877818204583 Henry Cohn, 2025, needs more optimization.
5 666 0.877882963051 Henry Cohn, 2025, needs more optimization.
5 667 0.878015154801 Henry Cohn, 2025, needs more optimization.
5 668 0.878121319924 Henry Cohn, 2026, needs more optimization.
5 669 0.878257366556 Henry Cohn, 2026, needs more optimization.
5 670 0.878394096821 Henry Cohn, 2025, needs more optimization.
5 671 0.878396868361 Henry Cohn, 2026, needs more optimization.
5 672 0.878555950413 Henry Cohn, 2026, needs more optimization.
5 673 0.878568357345 Henry Cohn, 2025, needs more optimization.
5 674 0.878677355021 Henry Cohn, 2025, needs more optimization.
5 675 0.878691240621 Henry Cohn, 2026, needs more optimization.
5 676 0.878895335529 Henry Cohn, 2025, needs more optimization.
5 677 0.879051400128 Henry Cohn, 2026, needs more optimization.
5 678 0.879056198237 Henry Cohn, 2025, needs more optimization.
5 680 0.879254843264 Henry Cohn, 2025, needs more optimization.
5 681 0.879266797921 Henry Cohn, 2025, needs more optimization.
5 683 0.879420942902 Henry Cohn, 2026, needs more optimization.
5 685 0.879604768234 Henry Cohn, 2025, needs more optimization.
5 686 0.879615298504 Henry Cohn, 2025, needs more optimization.
5 687 0.879927224792 Henry Cohn, 2025, needs more optimization.
5 688 0.879940879306 Henry Cohn, 2025, needs more optimization.
5 689 0.880050272700 Henry Cohn, 2025, needs more optimization.
5 690 0.880076920142 Henry Cohn, 2026, needs more optimization.
5 691 0.880186913631 Henry Cohn, 2025, needs more optimization.
5 692 0.880342004990 Henry Cohn, 2026, needs more optimization.
5 693 0.880342482614 Henry Cohn, 2026, needs more optimization.
5 694 0.880440443447 Henry Cohn, 2025, needs more optimization.
5 695 0.880560210580 Henry Cohn, 2025, needs more optimization.
5 696 0.880565807461 Henry Cohn, 2026, needs more optimization.
5 697 0.880726173156 Henry Cohn, 2026, needs more optimization.
5 698 0.880751251728 Henry Cohn, 2026, needs more optimization.
5 699 0.880831552541 Henry Cohn, 2025, needs more optimization.
5 700 0.880840937215 Henry Cohn, 2026, needs more optimization.
5 701 0.881073608246 Henry Cohn, 2026, needs more optimization.
5 702 0.881075411709 Henry Cohn, 2026, needs more optimization.
5 703 0.881076952719 Henry Cohn, 2026, needs more optimization.
5 704 0.881254031900 Henry Cohn, 2026, needs more optimization.
5 705 0.881266162475 Henry Cohn, 2025, needs more optimization.
5 706 0.881503126136 Henry Cohn, 2026, needs more optimization.
5 707 0.881504079243 Henry Cohn, 2026, needs more optimization.
5 708 0.881611839007 Henry Cohn, 2026, needs more optimization.
5 709 0.881738346869 Henry Cohn, 2026, needs more optimization.
5 710 0.881746195595 Henry Cohn, 2025, needs more optimization.
5 711 0.881850335459 Henry Cohn, 2025, needs more optimization.
5 712 0.881972602373 Henry Cohn, 2026, needs more optimization.
5 713 0.882012668941 Henry Cohn, 2025, needs more optimization.
5 714 0.882161638275 Henry Cohn, 2025, needs more optimization.
5 715 0.882184668744 Henry Cohn, 2026, needs more optimization.
5 716 0.882320732625 Henry Cohn, 2025, needs more optimization.
5 717 0.882323465849 Henry Cohn, 2026, needs more optimization.
5 718 0.882450334297 Henry Cohn, 2026, needs more optimization.
5 719 0.882451993509 Henry Cohn, 2026, needs more optimization.
5 720 0.882579799033 Henry Cohn, 2026, needs more optimization.
5 721 0.882850229503 Henry Cohn, 2025, needs more optimization.
5 722 0.882852390341 Henry Cohn, 2026, needs more optimization.
5 723 0.882955687290 Henry Cohn, 2025, needs more optimization.
5 724 0.882977268110 Henry Cohn, 2026, needs more optimization.
5 725 0.882978206211 Henry Cohn, 2026, needs more optimization.
5 726 0.883106952536 Henry Cohn, 2025, needs more optimization.
5 727 0.883131612758 Henry Cohn, 2025, needs more optimization.
5 728 0.883292687410 Henry Cohn, 2026, needs more optimization.
5 729 0.883327308778 Henry Cohn, 2025, needs more optimization.
5 730 0.883442618904 Henry Cohn, 2026, needs more optimization.
5 731 0.883524469603 Henry Cohn, 2026, needs more optimization.
5 732 0.883524699608 Henry Cohn, 2025, needs more optimization.
5 733 0.883673967839 Henry Cohn, 2025, needs more optimization.
5 734 0.883712670984 Henry Cohn, 2025, needs more optimization.
5 735 0.883861020714 Henry Cohn, 2026, needs more optimization.
5 736 0.883894566369 Henry Cohn, 2026, needs more optimization.
5 737 0.883899759689 Henry Cohn, 2025, needs more optimization.
5 738 0.883986347823 Henry Cohn, 2025, needs more optimization.
5 739 0.884167589206 Henry Cohn, 2025, needs more optimization.
5 740 0.884196725787 Henry Cohn, 2026, needs more optimization.
5 741 0.884317424162 Henry Cohn, 2026, needs more optimization.
5 742 0.884402016745 Henry Cohn, 2026, needs more optimization.
5 743 0.884526608919 Henry Cohn, 2025, needs more optimization.
5 744 0.884643952628 Henry Cohn, 2026, needs more optimization.
5 745 0.884681580162 Henry Cohn, 2026, needs more optimization.
5 746 0.884796361056 Henry Cohn, 2025, needs more optimization.
5 747 0.884903075377 Henry Cohn, 2025, needs more optimization.
5 748 0.885005159387 Henry Cohn, 2025, needs more optimization.
5 749 0.885008274623 Henry Cohn, 2026, needs more optimization.
5 750 0.885067837931 Henry Cohn, 2025, needs more optimization.
5 751 0.885133168731 Henry Cohn, 2025, needs more optimization.
5 752 0.885244724931 Henry Cohn, 2025, needs more optimization.
5 753 0.885246223059 Henry Cohn, 2026, needs more optimization.
5 754 0.885355810051 Henry Cohn, 2025, needs more optimization.
5 755 0.885389819977 Henry Cohn, 2025, needs more optimization.
5 756 0.885486686725 Henry Cohn, 2026, needs more optimization.
5 757 0.885576627751 Henry Cohn, 2025, needs more optimization.
5 758 0.885608708664 Henry Cohn, 2026, needs more optimization.
5 759 0.885788496516 Henry Cohn, 2025, needs more optimization.
5 760 0.885791735831 Henry Cohn, 2025, needs more optimization.
5 761 0.885915712593 Henry Cohn, 2025, needs more optimization.
5 762 0.885947686981 Henry Cohn, 2025, needs more optimization.
5 763 0.886054211065 Henry Cohn, 2026, needs more optimization.
5 764 0.886068745964 Henry Cohn, 2026, needs more optimization.
5 765 0.886195389172 Henry Cohn, 2025, needs more optimization.
5 766 0.886239507362 Henry Cohn, 2025, needs more optimization.
5 767 0.886286097191 Henry Cohn, 2025, needs more optimization.
5 768 0.886313548380 Henry Cohn, 2026, needs more optimization.
5 769 0.886333828851 Henry Cohn, 2025, needs more optimization.
5 771 0.886566932341 Henry Cohn, 2025, needs more optimization.
5 772 0.886580171023 Henry Cohn, 2026, needs more optimization.
5 773 0.886811509004 Henry Cohn, 2025, needs more optimization.
5 774 0.886818199717 Henry Cohn, 2026, needs more optimization.
5 775 0.886857339438 Henry Cohn, 2025, needs more optimization.
5 776 0.886976946131 Henry Cohn, 2026, needs more optimization.
5 777 0.886986115500 Henry Cohn, 2025, needs more optimization.
5 778 0.887166152141 Henry Cohn, 2025, needs more optimization.
5 779 0.887173485788 Henry Cohn, 2025, needs more optimization.
5 780 0.887282002983 Henry Cohn, 2026, needs more optimization.
5 781 0.887293711372 Henry Cohn, 2026, needs more optimization.
5 782 0.887328810543 Henry Cohn, 2025, needs more optimization.
5 783 0.887387168253 Henry Cohn, 2026, needs more optimization.
5 784 0.887486537415 Henry Cohn, 2026, needs more optimization.
5 785 0.887487426156 Henry Cohn, 2025, needs more optimization.
5 786 0.887548227422 Henry Cohn, 2025, needs more optimization.
5 787 0.887727286658 Henry Cohn, 2025, needs more optimization.
5 788 0.887728284656 Henry Cohn, 2026, needs more optimization.
5 789 0.887822163350 Henry Cohn, 2026, needs more optimization.
5 790 0.887929616199 Henry Cohn, 2025, needs more optimization.
5 791 0.887936822195 Henry Cohn, 2025, needs more optimization.
5 792 0.888004025348 Henry Cohn, 2026, needs more optimization.
5 793 0.888116581586 Henry Cohn, 2025, needs more optimization.
5 794 0.888134980619 Henry Cohn, 2026, needs more optimization.
5 795 0.888214561367 Henry Cohn, 2026, needs more optimization.
5 796 0.888241437301 Henry Cohn, 2026, needs more optimization.
5 797 0.888445319206 Henry Cohn, 2025, needs more optimization.
5 798 0.888463671895 Henry Cohn, 2026, needs more optimization.
5 799 0.888486462856 Henry Cohn, 2025, needs more optimization.
5 800 0.888530875178 Henry Cohn, 2026, needs more optimization.
5 801 0.888651958404 Henry Cohn, 2025, needs more optimization.
5 802 0.888655481864 Henry Cohn, 2025, needs more optimization.
5 803 0.888896550093 Henry Cohn, 2025, needs more optimization.
5 804 0.888903636362 Henry Cohn, 2026, needs more optimization.
5 805 0.888947331540 Henry Cohn, 2026, needs more optimization.
5 806 0.888961995804 Henry Cohn, 2025, needs more optimization.
5 807 0.889157983995 Henry Cohn, 2025, needs more optimization.
5 808 0.889232054009 Henry Cohn, 2026, needs more optimization.
5 809 0.889293843886 Henry Cohn, 2025, needs more optimization.
5 810 0.889368730713 Henry Cohn, 2026, needs more optimization.
5 811 0.889450629631 Henry Cohn, 2026, needs more optimization.
5 812 0.889465251480 Henry Cohn, 2026, needs more optimization.
5 813 0.889601237234 Henry Cohn, 2025, needs more optimization.
5 814 0.889708667362 Henry Cohn, 2025, needs more optimization.
5 815 0.889709777622 Henry Cohn, 2026, needs more optimization.
5 816 0.889735671604 Henry Cohn, 2026, needs more optimization.
5 817 0.889771290214 Henry Cohn, 2025, needs more optimization.
5 818 0.889883195543 Henry Cohn, 2026, needs more optimization.
5 819 0.889885890089 Henry Cohn, 2025, needs more optimization.
5 820 0.889896735801 Henry Cohn, 2026, needs more optimization.
5 821 0.890125339019 Henry Cohn, 2025, needs more optimization.
5 822 0.890125982949 Henry Cohn, 2026, needs more optimization.
5 823 0.890285307138 Henry Cohn, 2025, needs more optimization.
5 824 0.890287123138 Henry Cohn, 2026, needs more optimization.
5 825 0.890421726452 Henry Cohn, 2026, needs more optimization.
5 826 0.890422086940 Henry Cohn, 2026, needs more optimization.
5 827 0.890443189481 Henry Cohn, 2025, needs more optimization.
5 828 0.890565574880 Henry Cohn, 2026, needs more optimization.
5 829 0.890617714667 Henry Cohn, 2025, needs more optimization.
5 830 0.890713303532 Henry Cohn, 2026, needs more optimization.
5 831 0.890729720533 Henry Cohn, 2026, needs more optimization.
5 832 0.890754211876 Henry Cohn, 2026, needs more optimization.
5 833 0.890775695838 Henry Cohn, 2025, needs more optimization.
5 834 0.890801076780 Henry Cohn, 2025, needs more optimization.
5 836 0.891033531559 Henry Cohn, 2026, needs more optimization.
5 837 0.891260899176 Henry Cohn, 2025, needs more optimization.
5 838 0.891262029631 Henry Cohn, 2026, needs more optimization.
5 839 0.891295870406 Henry Cohn, 2025, needs more optimization.
5 840 0.891307991324 Henry Cohn, 2026, needs more optimization.
5 841 0.891426470359 Henry Cohn, 2025, needs more optimization.
5 842 0.891453340278 Henry Cohn, 2025, needs more optimization.
5 843 0.891563208434 Henry Cohn, 2025, needs more optimization.
5 844 0.891565320583 Henry Cohn, 2026, needs more optimization.
5 845 0.891706512207 Henry Cohn, 2025, needs more optimization.
5 846 0.891719866224 Henry Cohn, 2026, needs more optimization.
5 847 0.891744709015 Henry Cohn, 2025, needs more optimization.
5 848 0.891879939732 Henry Cohn, 2026, needs more optimization.
5 849 0.891893926884 Henry Cohn, 2025, needs more optimization.
5 850 0.891961059961 Henry Cohn, 2026, needs more optimization.
5 851 0.891972040917 Henry Cohn, 2025, needs more optimization.
5 852 0.892114758060 Henry Cohn, 2025, needs more optimization.
5 853 0.892116266712 Henry Cohn, 2025, needs more optimization.
5 854 0.892208187773 Henry Cohn, 2025, needs more optimization.
5 855 0.892312453139 Henry Cohn, 2025, needs more optimization.
5 856 0.892364658170 Henry Cohn, 2026, needs more optimization.
5 857 0.892374108700 Henry Cohn, 2025, needs more optimization.
5 858 0.892429171477 Henry Cohn, 2026, needs more optimization.
5 860 0.892629264993 Henry Cohn, 2026, needs more optimization.
5 861 0.892631606669 Henry Cohn, 2026, needs more optimization.
5 862 0.892636630150 Henry Cohn, 2025, needs more optimization.
5 863 0.892802953508 Henry Cohn, 2025, needs more optimization.
5 864 0.892813781513 Henry Cohn, 2026, needs more optimization.
5 865 0.892904803395 Henry Cohn, 2026, needs more optimization.
5 866 0.892947410984 Henry Cohn, 2025, needs more optimization.
5 867 0.893069164751 Henry Cohn, 2025, needs more optimization.
5 869 0.893092115983 Henry Cohn, 2025, needs more optimization.
5 870 0.893250126298 Henry Cohn, 2026, needs more optimization.
5 871 0.893285775424 Henry Cohn, 2025, needs more optimization.
5 872 0.893349843187 Henry Cohn, 2026, needs more optimization.
5 873 0.893401125154 Henry Cohn, 2025, needs more optimization.
5 874 0.893405519716 Henry Cohn, 2026, needs more optimization.
5 875 0.893537264211 Henry Cohn, 2026, needs more optimization.
5 876 0.893548204171 Henry Cohn, 2026, needs more optimization.
5 877 0.893675348805 Henry Cohn, 2025, needs more optimization.
5 878 0.893675401364 Henry Cohn, 2026, needs more optimization.
5 879 0.893830168591 Henry Cohn, 2025, needs more optimization.
5 880 0.893831729413 Henry Cohn, 2025, needs more optimization.
5 881 0.893865663145 Henry Cohn, 2025, needs more optimization.
5 882 0.893870916377 Henry Cohn, 2026, needs more optimization.
5 883 0.893951538397 Henry Cohn, 2025, needs more optimization.
5 884 0.894089862035 Henry Cohn, 2025, needs more optimization.
5 885 0.894104455283 Henry Cohn, 2025, needs more optimization.
5 886 0.894274102485 Henry Cohn, 2025, needs more optimization.
5 887 0.894276380550 Henry Cohn, 2026, needs more optimization.
5 888 0.894376187680 Henry Cohn, 2026, needs more optimization.
5 889 0.894397153171 Henry Cohn, 2025, needs more optimization.
5 890 0.894515998427 Henry Cohn, 2026, needs more optimization.
5 891 0.894532550295 Henry Cohn, 2025, needs more optimization.
5 892 0.894550995136 Henry Cohn, 2026, needs more optimization.
5 893 0.894620493080 Henry Cohn, 2025, needs more optimization.
5 894 0.894666957215 Henry Cohn, 2025, needs more optimization.
5 895 0.894667517151 Henry Cohn, 2025, needs more optimization.
5 896 0.894750896742 Henry Cohn, 2025, needs more optimization.
5 897 0.894838699596 Henry Cohn, 2025, needs more optimization.
5 898 0.894839527562 Henry Cohn, 2025, needs more optimization.
5 899 0.894961728514 Henry Cohn, 2025, needs more optimization.
5 900 0.894963952553 Henry Cohn, 2026, needs more optimization.
5 901 0.895053970280 Henry Cohn, 2026, needs more optimization.
5 902 0.895056901178 Henry Cohn, 2025, needs more optimization.
5 903 0.895266108241 Henry Cohn, 2025, needs more optimization.
5 904 0.895275689100 Henry Cohn, 2025, needs more optimization.
5 905 0.895302564593 Henry Cohn, 2025, needs more optimization.
5 906 0.895398566320 Henry Cohn, 2025, needs more optimization.
5 907 0.895399183332 Henry Cohn, 2025, needs more optimization.
5 908 0.895486681607 Henry Cohn, 2026, needs more optimization.
5 909 0.895529684165 Henry Cohn, 2025, needs more optimization.
5 910 0.895643993781 Henry Cohn, 2025, needs more optimization.
5 912 0.895721235146 Henry Cohn, 2026, needs more optimization.
5 913 0.895831413756 Henry Cohn, 2026, needs more optimization.
5 914 0.895866634964 Henry Cohn, 2026, needs more optimization.
5 915 0.895867784677 Henry Cohn, 2026, needs more optimization.
5 916 0.896008207188 Henry Cohn, 2026, needs more optimization.
5 917 0.896010138422 Henry Cohn, 2026, needs more optimization.
5 918 0.896128589466 Henry Cohn, 2026, needs more optimization.
5 919 0.896157599104 Henry Cohn, 2025, needs more optimization.
5 920 0.896279397003 Henry Cohn, 2026, needs more optimization.
5 921 0.896298563295 Henry Cohn, 2025, needs more optimization.
5 922 0.896300489015 Henry Cohn, 2025, needs more optimization.
5 923 0.896387283905 Henry Cohn, 2026, needs more optimization.
5 924 0.896388483329 Henry Cohn, 2026, needs more optimization.
5 925 0.896427119985 Henry Cohn, 2026, needs more optimization.
5 926 0.896488554964 Henry Cohn, 2026, needs more optimization.
5 927 0.896566089205 Henry Cohn, 2026, needs more optimization.
5 928 0.896570399324 Henry Cohn, 2026, needs more optimization.
5 929 0.896664763022 Henry Cohn, 2025, needs more optimization.
5 931 0.896785863752 Henry Cohn, 2026, needs more optimization.
5 932 0.896898653164 Henry Cohn, 2026, needs more optimization.
5 933 0.896903780677 Henry Cohn, 2025, needs more optimization.
5 934 0.897005323952 Henry Cohn, 2026, needs more optimization.
5 935 0.897007731039 Henry Cohn, 2025, needs more optimization.
5 936 0.897038468539 Henry Cohn, 2026, needs more optimization.
5 937 0.897157934409 Henry Cohn, 2025, needs more optimization.
5 938 0.897159993258 Henry Cohn, 2025, needs more optimization.
5 939 0.897264928383 Henry Cohn, 2025, needs more optimization.
5 940 0.897301498985 Henry Cohn, 2026, needs more optimization.
5 941 0.897424645659 Henry Cohn, 2026, needs more optimization.
5 942 0.897429445726 Henry Cohn, 2025, needs more optimization.
5 943 0.897435822418 Henry Cohn, 2025, needs more optimization.
5 944 0.897512142346 Henry Cohn, 2026, needs more optimization.
5 945 0.897673470977 Henry Cohn, 2026, needs more optimization.
5 946 0.897715672570 Henry Cohn, 2025, needs more optimization.
5 947 0.897801351017 Henry Cohn, 2026, needs more optimization.
5 948 0.897802739305 Henry Cohn, 2026, needs more optimization.
5 949 0.897828002885 Henry Cohn, 2025, needs more optimization.
5 950 0.897931543882 Henry Cohn, 2026, needs more optimization.
5 952 0.897962728304 Henry Cohn, 2026, needs more optimization.
5 953 0.898026166430 Henry Cohn, 2026, needs more optimization.
5 954 0.898043026347 Henry Cohn, 2025, needs more optimization.
5 955 0.898064550461 Henry Cohn, 2025, needs more optimization.
5 956 0.898075128638 Henry Cohn, 2025, needs more optimization.
5 957 0.898241407327 Henry Cohn, 2025, needs more optimization.
5 958 0.898250870216 Henry Cohn, 2025, needs more optimization.
5 959 0.898260631410 Henry Cohn, 2025, needs more optimization.
5 960 0.898312398441 Henry Cohn, 2026, needs more optimization.
5 961 0.898393471322 Henry Cohn, 2026, needs more optimization.
5 962 0.898408422618 Henry Cohn, 2026, needs more optimization.
5 963 0.898422521081 Henry Cohn, 2025, needs more optimization.
5 964 0.898521213325 Henry Cohn, 2026, needs more optimization.
5 965 0.898534843820 Henry Cohn, 2025, needs more optimization.
5 966 0.898735260894 Henry Cohn, 2026, needs more optimization.
5 967 0.898736744826 Henry Cohn, 2025, needs more optimization.
5 968 0.898831647675 Henry Cohn, 2026, needs more optimization.
5 969 0.898834405539 Henry Cohn, 2025, needs more optimization.
5 970 0.898858612689 Henry Cohn, 2025, needs more optimization.
5 971 0.898934578212 Henry Cohn, 2026, needs more optimization.
5 972 0.898939223336 Henry Cohn, 2025, needs more optimization.
5 973 0.899008765823 Henry Cohn, 2026, needs more optimization.
5 974 0.899116428966 Henry Cohn, 2025, needs more optimization.
5 975 0.899121313598 Henry Cohn, 2025, needs more optimization.
5 976 0.899130526227 Henry Cohn, 2025, needs more optimization.
5 977 0.899260041990 Henry Cohn, 2025, needs more optimization.
5 978 0.899359638664 Henry Cohn, 2026, needs more optimization.
5 979 0.899371062173 Henry Cohn, 2026, needs more optimization.
5 980 0.899385690646 Henry Cohn, 2026, needs more optimization.
5 981 0.899409604665 Henry Cohn, 2026, needs more optimization.
5 982 0.899489717508 Henry Cohn, 2025, needs more optimization.
5 983 0.899611274544 Henry Cohn, 2026, needs more optimization.
5 984 0.899630531156 Henry Cohn, 2026, needs more optimization.
5 985 0.899632280944 Henry Cohn, 2026, needs more optimization.
5 986 0.899708088763 Henry Cohn, 2025, needs more optimization.
5 987 0.899728049908 Henry Cohn, 2026, needs more optimization.
5 988 0.899890869229 Henry Cohn, 2026, needs more optimization.
5 989 0.899895541128 Henry Cohn, 2025, needs more optimization.
5 990 0.899896298443 Henry Cohn, 2026, needs more optimization.
5 991 0.899929613953 Henry Cohn, 2025, needs more optimization.
5 992 0.899964158387 Henry Cohn, 2026, needs more optimization.
5 993 0.900083161501 Henry Cohn, 2025, needs more optimization.
5 994 0.900136138090 Henry Cohn, 2026, needs more optimization.
5 995 0.900264310026 Henry Cohn, 2025, needs more optimization.
5 996 0.900271407903 Henry Cohn, 2026, needs more optimization.
5 997 0.900353938698 Henry Cohn, 2026, needs more optimization.
5 999 0.900431347128 Henry Cohn, 2025, needs more optimization.
5 1000 0.900448613272 Henry Cohn, 2026, needs more optimization.
5 1001 0.900513764048 Henry Cohn, 2025, needs more optimization.
5 1002 0.900550914266 Henry Cohn, 2026, needs more optimization.
5 1003 0.900572695383 Henry Cohn, 2026, needs more optimization.
5 1004 0.900586582336 Henry Cohn, 2026, needs more optimization.
5 1005 0.900829365091 Henry Cohn, 2025, needs more optimization.
5 1006 0.900830319894 Henry Cohn, 2026, needs more optimization.
5 1007 0.900854009714 Henry Cohn, 2025, needs more optimization.
5 1008 0.900860790028 Henry Cohn, 2026, needs more optimization.
5 1009 0.900977984132 Henry Cohn, 2025, needs more optimization.
5 1010 0.900983910276 Henry Cohn, 2025, needs more optimization.
5 1011 0.900985935596 Henry Cohn, 2025, needs more optimization.
5 1012 0.901010944206 Henry Cohn, 2026, needs more optimization.
5 1013 0.901098896278 Henry Cohn, 2025, needs more optimization.
5 1014 0.901120381058 Henry Cohn, 2025, needs more optimization.
5 1015 0.901122877982 Henry Cohn, 2025, needs more optimization.
5 1016 0.901144980530 Henry Cohn, 2026, needs more optimization.
5 1017 0.901213595613 Henry Cohn, 2025, needs more optimization.
5 1018 0.901225020400 Henry Cohn, 2026, needs more optimization.
5 1019 0.901325787568 Henry Cohn, 2025, needs more optimization.
5 1020 0.901329213303 Henry Cohn, 2026, needs more optimization.
5 1021 0.901442156851 Henry Cohn, 2025, needs more optimization.
5 1022 0.901561636441 Henry Cohn, 2026, needs more optimization.
5 1023 0.901639556614 Henry Cohn, 2025, needs more optimization.
5 1024 0.901697490054 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 0.441277260126 Henry Cohn, 2023.
24⁢x3+16⁢x2−14⁢x+1
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 0.486119746833 Henry Cohn, 2023.
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 0.525662331586 Henry Cohn, 2026.
6 76 0.526754953537 Henry Cohn, 2025.
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 0.539006300696 Henry Cohn, 2025.
6 82 0.541487958459 Henry Cohn, 2025.
6 83 0.543866459696 Henry Cohn, 2025.
6 84 0.546018230582 Henry Cohn, 2025.
6 85 0.546038397748 Henry Cohn, 2026.
6 86 0.550011129820 Henry Cohn, 2025.
6 87 0.551714767476 Henry Cohn, 2023.
6 88 0.552456735670 Henry Cohn, 2025.
6 89 0.555561660912 Henry Cohn, 2025, needs more optimization.
6 91 0.557603429720 Henry Cohn, 2024.
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 0.571167178278 Henry Cohn, 2025.
6 99 0.573881665753 Henry Cohn, 2023.
6 100 0.574916276575 Henry Cohn, 2024.
6 101 0.578331393550 Henry Cohn, 2023.
6 102 0.580736682189 Henry Cohn, 2023, needs more optimization.
6 103 0.583220131624 Henry Cohn, 2024.
6 106 0.583371498649 Henry Cohn, 2026, needs more optimization.
6 107 0.583372432432 Henry Cohn, 2026.
6 108 0.584811059741 Henry Cohn, 2026, needs more optimization.
6 109 0.585348750770 Henry Cohn, 2026.
6 110 0.585638229827 Henry Cohn, 2025.
6 111 0.585638229827 Henry Cohn, 2026, needs more optimization.
6 112 0.585693130025 Henry Cohn, 2026, needs more optimization.
6 113 0.586622932873 Henry Cohn, 2025.
6 114 0.588109690133 Henry Cohn, 2023.
6 115 0.596006832892 Henry Cohn, 2025, needs more optimization.
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, needs more optimization.
6 120 0.599174837096 Henry Cohn, 2026.
6 121 0.604468330433 Henry Cohn, 2026, needs more optimization.
6 122 0.606689340567 Henry Cohn, 2025, needs more optimization.
6 123 0.607115797651 Henry Cohn, 2025.
6 124 0.607974063056 Henry Cohn, 2025, needs more optimization.
6 125 0.607974063065 Henry Cohn, 2024, needs more optimization.
6 126 0.610431849202 Henry Cohn, 2024.
6 127 0.616514741171 Henry Cohn, 2026, needs more optimization.
6 128 0.619107420038 Henry Cohn, 2025.
6 129 0.620224367829 Henry Cohn, 2025, needs more optimization.
6 130 0.623555051946 Henry Cohn, 2026, needs more optimization.
6 132 0.624698642975 Henry Cohn, 2026, needs more optimization.
6 133 0.626200672027 Henry Cohn, 2026, needs more optimization.
6 134 0.628628892212 Henry Cohn, 2026, needs more optimization.
6 135 0.630887583786 Henry Cohn, 2025.
6 136 0.631874287806 Henry Cohn, 2025, needs more optimization.
6 137 0.633402294823 Henry Cohn, 2025.
6 138 0.634638694265 Henry Cohn, 2025, needs more optimization.
6 139 0.636181037362 Henry Cohn, 2026, needs more optimization.
6 140 0.637463152694 Henry Cohn, 2025, needs more optimization.
6 141 0.639558404219 Henry Cohn, 2026, needs more optimization.
6 142 0.640095486086 Henry Cohn, 2025, needs more optimization.
6 143 0.641708987693 Henry Cohn, 2026, needs more optimization.
6 144 0.642541256726 Henry Cohn, 2025, needs more optimization.
6 145 0.643784843229 Henry Cohn, 2026, needs more optimization.
6 146 0.644879889014 Henry Cohn, 2026, needs more optimization.
6 147 0.645794121776 Henry Cohn, 2026, needs more optimization.
6 148 0.646754557568 Henry Cohn, 2026, needs more optimization.
6 149 0.648326882327 Henry Cohn, 2026, needs more optimization.
6 150 0.649319669619 Henry Cohn, 2024, needs more optimization.
6 151 0.649994962578 Henry Cohn, 2024, needs more optimization.
6 152 0.651431539348 Henry Cohn, 2026, needs more optimization.
6 153 0.652218453846 Henry Cohn, 2025, needs more optimization.
6 154 0.652618605342 Henry Cohn, 2026, needs more optimization.
6 155 0.652720275231 Henry Cohn, 2026, needs more optimization.
6 156 0.653436836366 Henry Cohn, 2026, needs more optimization.
6 157 0.653954713337 Henry Cohn, 2026, needs more optimization.
6 158 0.654692727430 Henry Cohn, 2026, needs more optimization.
6 159 0.654941559051 Henry Cohn, 2026, needs more optimization.
6 160 0.655687784052 Henry Cohn, 2026, needs more optimization.
6 161 0.656363153942 Henry Cohn, 2026, needs more optimization.
6 162 0.657162096688 Henry Cohn, 2026, needs more optimization.
6 163 0.658346391837 Henry Cohn, 2026, needs more optimization.
6 164 0.658863806927 Henry Cohn, 2026, needs more optimization.
6 165 0.659473510348 Henry Cohn, 2026, needs more optimization.
6 166 0.660002721404 Henry Cohn, 2026, needs more optimization.
6 168 0.660633002772 Henry Cohn, 2026, needs more optimization.
6 169 0.662226543177 Henry Cohn, 2026, needs more optimization.
6 170 0.662781525750 Henry Cohn, 2026, needs more optimization.
6 171 0.664082173790 Henry Cohn, 2026, needs more optimization.
6 172 0.664209295970 Henry Cohn, 2026, needs more optimization.
6 173 0.664892704155 Henry Cohn, 2026, needs more optimization.
6 174 0.666059243435 Henry Cohn, 2026, needs more optimization.
6 175 0.667057154212 Henry Cohn, 2026, needs more optimization.
6 176 0.667600208838 Henry Cohn, 2026, needs more optimization.
6 177 0.670160562984 Henry Cohn, 2026, needs more optimization.
6 178 0.670208134368 Henry Cohn, 2026, needs more optimization.
6 179 0.671285507580 Henry Cohn, 2026, needs more optimization.
6 180 0.672101200863 Henry Cohn, 2026, needs more optimization.
6 181 0.672751145795 Henry Cohn, 2026, needs more optimization.
6 182 0.673469717171 Henry Cohn, 2025, needs more optimization.
6 183 0.673602836320 Henry Cohn, 2026, needs more optimization.
6 184 0.674007349083 Henry Cohn, 2025, needs more optimization.
6 185 0.674430599223 Henry Cohn, 2026, needs more optimization.
6 186 0.674824503468 Henry Cohn, 2026, needs more optimization.
6 187 0.676048363572 Henry Cohn, 2026, needs more optimization.
6 188 0.676645080423 Henry Cohn, 2026, needs more optimization.
6 189 0.677357783496 Henry Cohn, 2026, needs more optimization.
6 190 0.678644225950 Henry Cohn, 2026, needs more optimization.
6 191 0.678995862775 Henry Cohn, 2025, needs more optimization.
6 192 0.679822426017 Henry Cohn, 2026, needs more optimization.
6 193 0.680337121448 Henry Cohn, 2026, needs more optimization.
6 194 0.680909361810 Henry Cohn, 2026, needs more optimization.
6 195 0.681532644969 Henry Cohn, 2026, needs more optimization.
6 196 0.682159746632 Henry Cohn, 2026, needs more optimization.
6 197 0.682795908536 Henry Cohn, 2026, needs more optimization.
6 198 0.683080534618 Henry Cohn, 2026, needs more optimization.
6 199 0.683982784805 Henry Cohn, 2026, needs more optimization.
6 200 0.684465018928 Henry Cohn, 2025, needs more optimization.
6 201 0.685097993319 Henry Cohn, 2025, needs more optimization.
6 202 0.685180223481 Henry Cohn, 2026, needs more optimization.
6 203 0.685546185510 Henry Cohn, 2026, needs more optimization.
6 204 0.686651445462 Henry Cohn, 2026, needs more optimization.
6 205 0.686878507699 Henry Cohn, 2026, needs more optimization.
6 206 0.687366549612 Henry Cohn, 2025, needs more optimization.
6 207 0.688405102276 Henry Cohn, 2026, needs more optimization.
6 208 0.688912084157 Henry Cohn, 2026, needs more optimization.
6 209 0.689622322916 Henry Cohn, 2025, needs more optimization.
6 210 0.690029211034 Henry Cohn, 2026, needs more optimization.
6 211 0.690744229128 Henry Cohn, 2026, needs more optimization.
6 212 0.691274191101 Henry Cohn, 2026, needs more optimization.
6 213 0.691995031842 Henry Cohn, 2026, needs more optimization.
6 214 0.692460410213 Henry Cohn, 2026, needs more optimization.
6 215 0.692862394754 Henry Cohn, 2026, needs more optimization.
6 216 0.694779483236 Henry Cohn, 2026, needs more optimization.
6 217 0.696803156787 Henry Cohn, 2026, needs more optimization.
6 218 0.697795157096 Henry Cohn, 2024, needs more optimization.
6 219 0.697976887301 Henry Cohn, 2024, needs more optimization.
6 220 0.698816894891 Henry Cohn, 2024, needs more optimization.
6 221 0.699055638081 Henry Cohn, 2026, needs more optimization.
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 0.704412544995 Henry Cohn, 2026, needs more optimization.
6 245 0.704421457784 Henry Cohn, 2026, needs more optimization.
6 246 0.704428604983 Henry Cohn, 2026, needs more optimization.
6 247 0.704461281269 Henry Cohn, 2026, needs more optimization.
6 248 0.704676584226 Henry Cohn, 2026, needs more optimization.
6 249 0.704738838079 Henry Cohn, 2026, needs more optimization.
6 250 0.705106536843 Henry Cohn, 2025, needs more optimization.
6 251 0.705124811872 Henry Cohn, 2025, needs more optimization.
6 252 0.705192701697 Henry Cohn, 2026, needs more optimization.
6 253 0.705794258515 Henry Cohn, 2025, needs more optimization.
6 255 0.705843588318 Henry Cohn, 2026, needs more optimization.
6 256 0.706169235108 Henry Cohn, 2026, needs more optimization.
6 257 0.706302165620 Henry Cohn, 2026, needs more optimization.
6 258 0.706833900567 Henry Cohn, 2026, needs more optimization.
6 259 0.707211776493 Henry Cohn, 2025, needs more optimization.
6 260 0.707292210716 Henry Cohn, 2026, needs more optimization.
6 261 0.710446151192 Henry Cohn, 2025, needs more optimization.
6 262 0.710476652782 Henry Cohn, 2025, needs more optimization.
6 263 0.710583270955 Henry Cohn, 2026, needs more optimization.
6 264 0.710716541775 Henry Cohn, 2026, needs more optimization.
6 265 0.712521350579 Henry Cohn, 2025, needs more optimization.
6 266 0.712844955170 Henry Cohn, 2026, needs more optimization.
6 267 0.714931955932 Henry Cohn, 2026, needs more optimization.
6 268 0.715225849019 Henry Cohn, 2026, needs more optimization.
6 269 0.715313706808 Henry Cohn, 2026, needs more optimization.
6 270 0.716445862172 Henry Cohn, 2026, needs more optimization.
6 271 0.716615767417 Henry Cohn, 2026, needs more optimization.
6 272 0.717692497225 Henry Cohn, 2026, needs more optimization.
6 274 0.717964292229 Henry Cohn, 2025, needs more optimization.
6 275 0.718472982001 Henry Cohn, 2026, needs more optimization.
6 276 0.719245854451 Henry Cohn, 2026, needs more optimization.
6 277 0.720813612645 Henry Cohn, 2026, needs more optimization.
6 278 0.720823227172 Henry Cohn, 2026, needs more optimization.
6 279 0.721401126539 Henry Cohn, 2026, needs more optimization.
6 280 0.722581820279 Henry Cohn, 2026, needs more optimization.
6 281 0.722624158914 Henry Cohn, 2026, needs more optimization.
6 282 0.723518454655 Henry Cohn, 2025, needs more optimization.
6 283 0.723929075276 Henry Cohn, 2026, needs more optimization.
6 284 0.724648389144 Henry Cohn, 2025, needs more optimization.
6 285 0.724986871185 Henry Cohn, 2026, needs more optimization.
6 286 0.725124817630 Henry Cohn, 2026, needs more optimization.
6 287 0.725353916757 Henry Cohn, 2026, needs more optimization.
6 288 0.726261034203 Henry Cohn, 2026, needs more optimization.
6 289 0.726669077996 Henry Cohn, 2026, needs more optimization.
6 290 0.726809945253 Henry Cohn, 2026, needs more optimization.
6 291 0.728162829923 Henry Cohn, 2025, needs more optimization.
6 292 0.728174504449 Henry Cohn, 2025, needs more optimization.
6 293 0.728704272607 Henry Cohn, 2025, needs more optimization.
6 294 0.729030926219 Henry Cohn, 2025, needs more optimization.
6 295 0.729437652313 Henry Cohn, 2025, needs more optimization.
6 296 0.730290502935 Henry Cohn, 2025, needs more optimization.
6 297 0.731076300664 Henry Cohn, 2025, needs more optimization.
6 298 0.731139671600 Henry Cohn, 2026, needs more optimization.
6 299 0.731510074994 Henry Cohn, 2026, needs more optimization.
6 300 0.732112845366 Henry Cohn, 2025, needs more optimization.
6 301 0.732416678518 Henry Cohn, 2025, needs more optimization.
6 302 0.733154597342 Henry Cohn, 2025, needs more optimization.
6 303 0.733265144419 Henry Cohn, 2025, needs more optimization.
6 304 0.733474326159 Henry Cohn, 2025, needs more optimization.
6 305 0.733794655030 Henry Cohn, 2025, needs more optimization.
6 306 0.733866177993 Henry Cohn, 2025, needs more optimization.
6 307 0.734390329949 Henry Cohn, 2025, needs more optimization.
6 308 0.735148466320 Henry Cohn, 2025, needs more optimization.
6 309 0.735661892248 Henry Cohn, 2025, needs more optimization.
6 310 0.736073358656 Henry Cohn, 2025, needs more optimization.
6 311 0.736181169237 Henry Cohn, 2026, needs more optimization.
6 312 0.736700074960 Henry Cohn, 2025, needs more optimization.
6 313 0.737357322296 Henry Cohn, 2025, needs more optimization.
6 314 0.737761728767 Henry Cohn, 2025, needs more optimization.
6 315 0.737831637343 Henry Cohn, 2025, needs more optimization.
6 316 0.738209850784 Henry Cohn, 2026, needs more optimization.
6 317 0.738613322480 Henry Cohn, 2025, needs more optimization.
6 318 0.739530231283 Henry Cohn, 2025, needs more optimization.
6 319 0.740040267366 Henry Cohn, 2026, needs more optimization.
6 320 0.740195855213 Henry Cohn, 2025, needs more optimization.
6 321 0.740402273601 Henry Cohn, 2026, needs more optimization.
6 322 0.740872947420 Henry Cohn, 2026, needs more optimization.
6 323 0.741323429328 Henry Cohn, 2025, needs more optimization.
6 324 0.741700909002 Henry Cohn, 2025, needs more optimization.
6 325 0.742218586647 Henry Cohn, 2026, needs more optimization.
6 326 0.742456930608 Henry Cohn, 2025, needs more optimization.
6 327 0.742951316911 Henry Cohn, 2025, needs more optimization.
6 328 0.743206035143 Henry Cohn, 2026, needs more optimization.
6 329 0.743917206939 Henry Cohn, 2025, needs more optimization.
6 330 0.744395552873 Henry Cohn, 2026, needs more optimization.
6 331 0.744800502360 Henry Cohn, 2025, needs more optimization.
6 332 0.745075935606 Henry Cohn, 2025, needs more optimization.
6 333 0.745467810779 Henry Cohn, 2025, needs more optimization.
6 334 0.745876428076 Henry Cohn, 2025, needs more optimization.
6 335 0.746518221120 Henry Cohn, 2026, needs more optimization.
6 336 0.746526630978 Henry Cohn, 2026, needs more optimization.
6 342 0.746790391073 Henry Cohn, 2023, needs more optimization.
6 343 0.748841050044 Henry Cohn, 2025, needs more optimization.
6 344 0.749056432048 Henry Cohn, 2026, needs more optimization.
6 345 0.749265236147 Henry Cohn, 2026, needs more optimization.
6 346 0.749564741696 Henry Cohn, 2025, needs more optimization.
6 347 0.749797304227 Henry Cohn, 2026, needs more optimization.
6 348 0.750331506180 Henry Cohn, 2025, needs more optimization.
6 349 0.750503191071 Henry Cohn, 2025, needs more optimization.
6 350 0.750780551529 Henry Cohn, 2026, needs more optimization.
6 351 0.750837736399 Henry Cohn, 2025, needs more optimization.
6 352 0.751253722010 Henry Cohn, 2025, needs more optimization.
6 353 0.751714863962 Henry Cohn, 2025, needs more optimization.
6 354 0.751805047730 Henry Cohn, 2025, needs more optimization.
6 355 0.751934926381 Henry Cohn, 2025, needs more optimization.
6 356 0.752284354827 Henry Cohn, 2025, needs more optimization.
6 357 0.752897715808 Henry Cohn, 2026, needs more optimization.
6 358 0.752944135015 Henry Cohn, 2025, needs more optimization.
6 359 0.753290360804 Henry Cohn, 2025, needs more optimization.
6 360 0.753398391402 Henry Cohn, 2025, needs more optimization.
6 361 0.753737071365 Henry Cohn, 2025, needs more optimization.
6 362 0.754060455855 Henry Cohn, 2025, needs more optimization.
6 363 0.754391381517 Henry Cohn, 2025, needs more optimization.
6 364 0.754666347797 Henry Cohn, 2025, needs more optimization.
6 365 0.754818502152 Henry Cohn, 2025, needs more optimization.
6 366 0.755036821765 Henry Cohn, 2026, needs more optimization.
6 367 0.755458232833 Henry Cohn, 2025, needs more optimization.
6 368 0.755618078029 Henry Cohn, 2026, needs more optimization.
6 369 0.756134137839 Henry Cohn, 2025, needs more optimization.
6 370 0.756492187511 Henry Cohn, 2025, needs more optimization.
6 371 0.756625060003 Henry Cohn, 2025, needs more optimization.
6 372 0.756759262628 Henry Cohn, 2025, needs more optimization.
6 373 0.757132722236 Henry Cohn, 2025, needs more optimization.
6 374 0.757313417240 Henry Cohn, 2026, needs more optimization.
6 375 0.757922987508 Henry Cohn, 2025, needs more optimization.
6 376 0.757993367495 Henry Cohn, 2025, needs more optimization.
6 377 0.758664541092 Henry Cohn, 2025, needs more optimization.
6 378 0.758717144387 Henry Cohn, 2025, needs more optimization.
6 379 0.758939583890 Ilmari Vahteristo, 2026.
6 380 0.759289338453 Henry Cohn, 2025, needs more optimization.
6 381 0.759421496990 Henry Cohn, 2026, needs more optimization.
6 382 0.759588110302 Henry Cohn, 2025, needs more optimization.
6 383 0.759892829859 Henry Cohn, 2025, needs more optimization.
6 384 0.759900544934 Henry Cohn, 2026, needs more optimization.
6 385 0.760347676343 Henry Cohn, 2025, needs more optimization.
6 386 0.760469383839 Henry Cohn, 2025, needs more optimization.
6 387 0.760835708448 Henry Cohn, 2025, needs more optimization.
6 388 0.761176884264 Henry Cohn, 2025, needs more optimization.
6 389 0.761392923324 Henry Cohn, 2025, needs more optimization.
6 390 0.761779583649 Henry Cohn, 2025, needs more optimization.
6 391 0.761801350661 Henry Cohn, 2025, needs more optimization.
6 392 0.762156311332 Henry Cohn, 2026, needs more optimization.
6 393 0.762160511164 Henry Cohn, 2025, needs more optimization.
6 394 0.762467144423 Henry Cohn, 2025, needs more optimization.
6 395 0.762824595902 Henry Cohn, 2026, needs more optimization.
6 396 0.763226986795 Henry Cohn, 2025, needs more optimization.
6 397 0.763265417521 Henry Cohn, 2025, needs more optimization.
6 398 0.763667586383 Henry Cohn, 2025, needs more optimization.
6 399 0.763778015015 Henry Cohn, 2025, needs more optimization.
6 400 0.764313410189 Henry Cohn, 2025, needs more optimization.
6 401 0.764321098938 Henry Cohn, 2025, needs more optimization.
6 402 0.764359402081 Henry Cohn, 2026, needs more optimization.
6 403 0.764572152690 Henry Cohn, 2025, needs more optimization.
6 404 0.764948720712 Henry Cohn, 2025, needs more optimization.
6 405 0.765119391862 Henry Cohn, 2025, needs more optimization.
6 406 0.765531096457 Henry Cohn, 2026, needs more optimization.
6 407 0.765562373015 Henry Cohn, 2025, needs more optimization.
6 408 0.765843084808 Henry Cohn, 2025, needs more optimization.
6 409 0.765847573501 Henry Cohn, 2025, needs more optimization.
6 410 0.766034682898 Henry Cohn, 2026, needs more optimization.
6 411 0.766428857285 Henry Cohn, 2026, needs more optimization.
6 412 0.766619840406 Henry Cohn, 2025, needs more optimization.
6 413 0.766783053501 Henry Cohn, 2025, needs more optimization.
6 414 0.767103548283 Henry Cohn, 2026, needs more optimization.
6 415 0.767558038199 Henry Cohn, 2025, needs more optimization.
6 416 0.767822571162 Henry Cohn, 2025, needs more optimization.
6 417 0.768110015375 Ilmari Vahteristo, 2026.
6 418 0.768325691504 Henry Cohn, 2025, needs more optimization.
6 419 0.768667400220 Ilmari Vahteristo, 2026.
6 420 0.768700416304 Henry Cohn, 2026, needs more optimization.
6 421 0.768870069376 Henry Cohn, 2025, needs more optimization.
6 422 0.769140912986 Henry Cohn, 2026, needs more optimization.
6 423 0.769380268362 Henry Cohn, 2026, needs more optimization.
6 424 0.769735933377 Henry Cohn, 2026, needs more optimization.
6 425 0.769905701850 Henry Cohn, 2026, needs more optimization.
6 426 0.770200252343 Ilmari Vahteristo, 2026.
6 427 0.770470798880 Henry Cohn, 2025, needs more optimization.
6 428 0.770653463637 Ilmari Vahteristo, 2026.
6 429 0.770681981055 Henry Cohn, 2025, needs more optimization.
6 430 0.770908838569 Henry Cohn, 2026, needs more optimization.
6 431 0.770929384281 Henry Cohn, 2025, needs more optimization.
6 432 0.771241013622 Henry Cohn, 2026, needs more optimization.
6 433 0.771382581330 Henry Cohn, 2025, needs more optimization.
6 434 0.771535594990 Henry Cohn, 2025, needs more optimization.
6 435 0.771885822672 Henry Cohn, 2025, needs more optimization.
6 436 0.771893175548 Henry Cohn, 2025, needs more optimization.
6 437 0.772029819935 Henry Cohn, 2025, needs more optimization.
6 438 0.772265509671 Henry Cohn, 2025, needs more optimization.
6 439 0.772523939817 Henry Cohn, 2025, needs more optimization.
6 440 0.772663149453 Henry Cohn, 2025, needs more optimization.
6 441 0.772955200339 Henry Cohn, 2025, needs more optimization.
6 442 0.773109581137 Henry Cohn, 2026, needs more optimization.
6 443 0.773310557624 Henry Cohn, 2025, needs more optimization.
6 444 0.773776826434 Henry Cohn, 2025, needs more optimization.
6 445 0.773983280335 Henry Cohn, 2025, needs more optimization.
6 446 0.774219246104 Henry Cohn, 2025, needs more optimization.
6 447 0.774236279177 Henry Cohn, 2025, needs more optimization.
6 448 0.774534657349 Henry Cohn, 2026, needs more optimization.
6 449 0.774731477728 Henry Cohn, 2025, needs more optimization.
6 450 0.775058351359 Henry Cohn, 2026, needs more optimization.
6 451 0.775063237723 Henry Cohn, 2026, needs more optimization.
6 452 0.775246412303 Henry Cohn, 2025, needs more optimization.
6 453 0.775432127164 Henry Cohn, 2026, needs more optimization.
6 454 0.775505106768 Henry Cohn, 2025, needs more optimization.
6 455 0.775855579167 Henry Cohn, 2026, needs more optimization.
6 456 0.776068757202 Henry Cohn, 2025, needs more optimization.
6 457 0.776321955413 Henry Cohn, 2025, needs more optimization.
6 458 0.776539559719 Henry Cohn, 2025, needs more optimization.
6 459 0.776803861429 Henry Cohn, 2026, needs more optimization.
6 460 0.776807101274 Henry Cohn, 2025, needs more optimization.
6 461 0.776809166143 Henry Cohn, 2025, needs more optimization.
6 462 0.777196189852 Henry Cohn, 2026, needs more optimization.
6 463 0.777434326346 Henry Cohn, 2025, needs more optimization.
6 464 0.777508700669 Henry Cohn, 2025, needs more optimization.
6 465 0.777692189029 Henry Cohn, 2026, needs more optimization.
6 466 0.777954893493 Henry Cohn, 2026, needs more optimization.
6 467 0.778148493090 Henry Cohn, 2026, needs more optimization.
6 468 0.778287393273 Henry Cohn, 2025, needs more optimization.
6 469 0.778345056785 Henry Cohn, 2026, needs more optimization.
6 470 0.779001228385 Henry Cohn, 2025, needs more optimization.
6 471 0.779024956635 Henry Cohn, 2025, needs more optimization.
6 472 0.779181329561 Henry Cohn, 2025, needs more optimization.
6 473 0.779488936123 Henry Cohn, 2025, needs more optimization.
6 474 0.779739517357 Henry Cohn, 2026, needs more optimization.
6 475 0.779753504424 Henry Cohn, 2025, needs more optimization.
6 476 0.779768569425 Henry Cohn, 2025, needs more optimization.
6 477 0.780128871313 Henry Cohn, 2025, needs more optimization.
6 478 0.780205950103 Henry Cohn, 2025, needs more optimization.
6 479 0.780501205782 Henry Cohn, 2025, needs more optimization.
6 480 0.780553951214 Henry Cohn, 2025, needs more optimization.
6 481 0.780794006151 Henry Cohn, 2026, needs more optimization.
6 482 0.780977289950 Henry Cohn, 2025, needs more optimization.
6 483 0.781178259455 Henry Cohn, 2026, needs more optimization.
6 484 0.781464673023 Henry Cohn, 2026, needs more optimization.
6 485 0.781607451896 Henry Cohn, 2025, needs more optimization.
6 486 0.781666833507 Henry Cohn, 2026, needs more optimization.
6 487 0.782092404018 Henry Cohn, 2025, needs more optimization.
6 488 0.782189214112 Henry Cohn, 2026, needs more optimization.
6 489 0.782411616128 Henry Cohn, 2026, needs more optimization.
6 490 0.782463158072 Henry Cohn, 2025, needs more optimization.
6 491 0.782767005066 Henry Cohn, 2026, needs more optimization.
6 492 0.782865245898 Henry Cohn, 2025, needs more optimization.
6 493 0.783018604741 Henry Cohn, 2026, needs more optimization.
6 494 0.783328089629 Henry Cohn, 2025, needs more optimization.
6 495 0.783396974283 Henry Cohn, 2025, needs more optimization.
6 496 0.783465207879 Henry Cohn, 2026, needs more optimization.
6 497 0.783759592457 Henry Cohn, 2026, needs more optimization.
6 498 0.783946677385 Henry Cohn, 2025, needs more optimization.
6 499 0.783955309086 Henry Cohn, 2025, needs more optimization.
6 500 0.784225819721 Henry Cohn, 2025, needs more optimization.
6 501 0.784506246453 Henry Cohn, 2025, needs more optimization.
6 502 0.784696939909 Henry Cohn, 2025, needs more optimization.
6 503 0.784879873306 Henry Cohn, 2025, needs more optimization.
6 504 0.785043563985 Henry Cohn, 2026, needs more optimization.
6 505 0.785179710994 Henry Cohn, 2026, needs more optimization.
6 506 0.785431882752 Henry Cohn, 2025, needs more optimization.
6 507 0.785540748252 Henry Cohn, 2026, needs more optimization.
6 508 0.785799771003 Henry Cohn, 2026, needs more optimization.
6 509 0.785963085809 Henry Cohn, 2025, needs more optimization.
6 510 0.786078564642 Henry Cohn, 2025, needs more optimization.
6 511 0.786344662388 Henry Cohn, 2025, needs more optimization.
6 512 0.786379684678 Henry Cohn, 2026, needs more optimization.
6 513 0.786463332303 Henry Cohn, 2026, needs more optimization.
6 514 0.786699853689 Henry Cohn, 2026, needs more optimization.
6 515 0.786913884715 Henry Cohn, 2025, needs more optimization.
6 516 0.787047171505 Henry Cohn, 2026, needs more optimization.
6 517 0.787230377399 Henry Cohn, 2026, needs more optimization.
6 518 0.787272798145 Henry Cohn, 2025, needs more optimization.
6 519 0.787318272676 Henry Cohn, 2025, needs more optimization.
6 520 0.787617124479 Henry Cohn, 2025, needs more optimization.
6 521 0.787734926114 Henry Cohn, 2025, needs more optimization.
6 522 0.788137976651 Henry Cohn, 2025, needs more optimization.
6 523 0.788156267395 Henry Cohn, 2025, needs more optimization.
6 524 0.788441800907 Henry Cohn, 2026, needs more optimization.
6 525 0.788608388669 Henry Cohn, 2025, needs more optimization.
6 526 0.788709148657 Henry Cohn, 2025, needs more optimization.
6 527 0.788874161694 Henry Cohn, 2026, needs more optimization.
6 528 0.788926543638 Henry Cohn, 2026, needs more optimization.
6 529 0.789134700458 Henry Cohn, 2025, needs more optimization.
6 530 0.789414807102 Henry Cohn, 2025, needs more optimization.
6 531 0.789428246829 Henry Cohn, 2026, needs more optimization.
6 532 0.789787457345 Henry Cohn, 2026, needs more optimization.
6 533 0.789792757309 Henry Cohn, 2025, needs more optimization.
6 534 0.789817192244 Henry Cohn, 2025, needs more optimization.
6 535 0.790045702885 Henry Cohn, 2025, needs more optimization.
6 536 0.790080666571 Henry Cohn, 2025, needs more optimization.
6 537 0.790456481764 Henry Cohn, 2026, needs more optimization.
6 538 0.790512511145 Henry Cohn, 2026, needs more optimization.
6 539 0.790575573190 Henry Cohn, 2025, needs more optimization.
6 540 0.790802834220 Henry Cohn, 2026, needs more optimization.
6 541 0.790905992923 Henry Cohn, 2026, needs more optimization.
6 542 0.790912425048 Henry Cohn, 2025, needs more optimization.
6 543 0.791109702429 Henry Cohn, 2025, needs more optimization.
6 544 0.791482114125 Henry Cohn, 2026, needs more optimization.
6 545 0.791558205412 Henry Cohn, 2026, needs more optimization.
6 546 0.791799721623 Henry Cohn, 2025, needs more optimization.
6 547 0.791817853845 Henry Cohn, 2025, needs more optimization.
6 548 0.792007169007 Henry Cohn, 2026, needs more optimization.
6 549 0.792120458535 Henry Cohn, 2025, needs more optimization.
6 550 0.792413480597 Henry Cohn, 2026, needs more optimization.
6 551 0.792571287759 Henry Cohn, 2025, needs more optimization.
6 552 0.792575911224 Henry Cohn, 2026, needs more optimization.
6 553 0.792720237063 Henry Cohn, 2025, needs more optimization.
6 554 0.792991123280 Henry Cohn, 2025, needs more optimization.
6 555 0.793030377786 Henry Cohn, 2025, needs more optimization.
6 556 0.793345560359 Henry Cohn, 2025, needs more optimization.
6 557 0.793375623664 Henry Cohn, 2025, needs more optimization.
6 558 0.793392931595 Henry Cohn, 2026, needs more optimization.
6 559 0.793540032966 Henry Cohn, 2026, needs more optimization.
6 560 0.793970939934 Henry Cohn, 2026, needs more optimization.
6 561 0.793997720863 Henry Cohn, 2025, needs more optimization.
6 562 0.793999096351 Henry Cohn, 2025, needs more optimization.
6 563 0.794253599934 Henry Cohn, 2025, needs more optimization.
6 564 0.794345967712 Henry Cohn, 2025, needs more optimization.
6 565 0.794514240296 Henry Cohn, 2025, needs more optimization.
6 566 0.794720999866 Henry Cohn, 2025, needs more optimization.
6 567 0.794822227717 Henry Cohn, 2026, needs more optimization.
6 568 0.795027686258 Henry Cohn, 2026, needs more optimization.
6 569 0.795033176405 Henry Cohn, 2026, needs more optimization.
6 570 0.795265951322 Henry Cohn, 2026, needs more optimization.
6 571 0.795288705125 Henry Cohn, 2025, needs more optimization.
6 572 0.795516409345 Henry Cohn, 2025, needs more optimization.
6 573 0.795829156946 Henry Cohn, 2025, needs more optimization.
6 574 0.795900175913 Henry Cohn, 2025, needs more optimization.
6 575 0.795904568008 Henry Cohn, 2025, needs more optimization.
6 576 0.796101080809 Henry Cohn, 2025, needs more optimization.
6 577 0.796256548729 Henry Cohn, 2025, needs more optimization.
6 578 0.796571670123 Henry Cohn, 2025, needs more optimization.
6 579 0.796576792514 Henry Cohn, 2026, needs more optimization.
6 580 0.796751653475 Henry Cohn, 2025, needs more optimization.
6 581 0.796786785592 Henry Cohn, 2026, needs more optimization.
6 582 0.797057202471 Henry Cohn, 2025, needs more optimization.
6 583 0.797104811578 Henry Cohn, 2025, needs more optimization.
6 584 0.797356665470 Henry Cohn, 2026, needs more optimization.
6 585 0.797384718954 Henry Cohn, 2025, needs more optimization.
6 586 0.797385241881 Henry Cohn, 2026, needs more optimization.
6 587 0.797603948018 Henry Cohn, 2025, needs more optimization.
6 588 0.797789322431 Henry Cohn, 2026, needs more optimization.
6 589 0.797840114335 Henry Cohn, 2026, needs more optimization.
6 590 0.798162548924 Henry Cohn, 2026, needs more optimization.
6 591 0.798166091649 Henry Cohn, 2025, needs more optimization.
6 592 0.798376791335 Henry Cohn, 2025, needs more optimization.
6 593 0.798472384327 Henry Cohn, 2025, needs more optimization.
6 594 0.798669532087 Henry Cohn, 2026, needs more optimization.
6 595 0.798805187978 Henry Cohn, 2025, needs more optimization.
6 596 0.799063819653 Henry Cohn, 2026, needs more optimization.
6 597 0.799214553851 Henry Cohn, 2025, needs more optimization.
6 598 0.799240654751 Henry Cohn, 2026, needs more optimization.
6 599 0.799406794187 Henry Cohn, 2025, needs more optimization.
6 600 0.799541345677 Henry Cohn, 2026, needs more optimization.
6 601 0.799696542620 Henry Cohn, 2025, needs more optimization.
6 602 0.799818854650 Henry Cohn, 2026, needs more optimization.
6 603 0.799927083241 Henry Cohn, 2025, needs more optimization.
6 604 0.800237726072 Henry Cohn, 2025, needs more optimization.
6 605 0.800238223191 Henry Cohn, 2025, needs more optimization.
6 606 0.800239423949 Henry Cohn, 2025, needs more optimization.
6 607 0.800492441363 Henry Cohn, 2025, needs more optimization.
6 608 0.800495024091 Henry Cohn, 2026, needs more optimization.
6 609 0.800688709880 Henry Cohn, 2025, needs more optimization.
6 610 0.801072650459 Henry Cohn, 2025, needs more optimization.
6 611 0.801085375103 Henry Cohn, 2026, needs more optimization.
6 612 0.801133000500 Henry Cohn, 2025, needs more optimization.
6 613 0.801192982451 Henry Cohn, 2025, needs more optimization.
6 614 0.801486649069 Henry Cohn, 2026, needs more optimization.
6 615 0.801487334924 Henry Cohn, 2025, needs more optimization.
6 616 0.801657461132 Henry Cohn, 2026, needs more optimization.
6 617 0.801682559413 Henry Cohn, 2026, needs more optimization.
6 618 0.801908204381 Henry Cohn, 2026, needs more optimization.
6 619 0.801914036391 Henry Cohn, 2026, needs more optimization.
6 620 0.802028436564 Henry Cohn, 2026, needs more optimization.
6 621 0.802209048142 Henry Cohn, 2026, needs more optimization.
6 622 0.802454074297 Henry Cohn, 2025, needs more optimization.
6 623 0.802568688111 Henry Cohn, 2025, needs more optimization.
6 624 0.802580355221 Henry Cohn, 2026, needs more optimization.
6 625 0.802875169852 Henry Cohn, 2025, needs more optimization.
6 626 0.802899751488 Henry Cohn, 2026, needs more optimization.
6 627 0.802921218541 Henry Cohn, 2025, needs more optimization.
6 628 0.803035532929 Henry Cohn, 2026, needs more optimization.
6 629 0.803299590474 Henry Cohn, 2026, needs more optimization.
6 630 0.803301323863 Henry Cohn, 2026, needs more optimization.
6 631 0.803487382574 Henry Cohn, 2025, needs more optimization.
6 632 0.803728175116 Henry Cohn, 2026, needs more optimization.
6 633 0.803849473735 Henry Cohn, 2026, needs more optimization.
6 634 0.804007465348 Henry Cohn, 2026, needs more optimization.
6 635 0.804025542024 Henry Cohn, 2025, needs more optimization.
6 636 0.804180065316 Henry Cohn, 2026, needs more optimization.
6 637 0.804238749445 Henry Cohn, 2026, needs more optimization.
6 638 0.804384859272 Henry Cohn, 2025, needs more optimization.
6 639 0.804386938080 Henry Cohn, 2026, needs more optimization.
6 640 0.804616355202 Henry Cohn, 2025, needs more optimization.
6 641 0.804666298456 Henry Cohn, 2025, needs more optimization.
6 642 0.804672578592 Henry Cohn, 2025, needs more optimization.
6 643 0.804842333605 Henry Cohn, 2026, needs more optimization.
6 644 0.805068138518 Henry Cohn, 2026, needs more optimization.
6 645 0.805285069869 Henry Cohn, 2025, needs more optimization.
6 646 0.805384911647 Henry Cohn, 2025, needs more optimization.
6 647 0.805448187462 Henry Cohn, 2025, needs more optimization.
6 648 0.805456820919 Henry Cohn, 2025, needs more optimization.
6 649 0.805642092642 Henry Cohn, 2025, needs more optimization.
6 650 0.805658850314 Henry Cohn, 2025, needs more optimization.
6 651 0.805913789108 Henry Cohn, 2026, needs more optimization.
6 652 0.805952437252 Henry Cohn, 2026, needs more optimization.
6 653 0.806116288247 Henry Cohn, 2026, needs more optimization.
6 654 0.806370880524 Henry Cohn, 2025, needs more optimization.
6 655 0.806375912850 Henry Cohn, 2025, needs more optimization.
6 656 0.806422253369 Henry Cohn, 2026, needs more optimization.
6 657 0.806640579298 Henry Cohn, 2025, needs more optimization.
6 658 0.806679762038 Henry Cohn, 2025, needs more optimization.
6 659 0.806730375136 Henry Cohn, 2025, needs more optimization.
6 660 0.806757030490 Henry Cohn, 2025, needs more optimization.
6 661 0.806983357269 Henry Cohn, 2025, needs more optimization.
6 662 0.807247874962 Henry Cohn, 2025, needs more optimization.
6 663 0.807373630299 Henry Cohn, 2026, needs more optimization.
6 664 0.807378892261 Henry Cohn, 2026, needs more optimization.
6 665 0.807624736629 Henry Cohn, 2026, needs more optimization.
6 666 0.807660969307 Henry Cohn, 2026, needs more optimization.
6 667 0.807795326218 Henry Cohn, 2025, needs more optimization.
6 668 0.807828789748 Henry Cohn, 2025, needs more optimization.
6 669 0.807833607483 Henry Cohn, 2025, needs more optimization.
6 670 0.807898038068 Henry Cohn, 2026, needs more optimization.
6 671 0.808077665747 Henry Cohn, 2026, needs more optimization.
6 672 0.808175676168 Henry Cohn, 2026, needs more optimization.
6 673 0.808414765330 Henry Cohn, 2025, needs more optimization.
6 674 0.808465382532 Henry Cohn, 2026, needs more optimization.
6 676 0.808770309220 Henry Cohn, 2026, needs more optimization.
6 677 0.808946782452 Henry Cohn, 2025, needs more optimization.
6 678 0.809095726889 Henry Cohn, 2026, needs more optimization.
6 679 0.809105555259 Henry Cohn, 2025, needs more optimization.
6 680 0.809285168486 Henry Cohn, 2025, needs more optimization.
6 681 0.809550813598 Henry Cohn, 2025, needs more optimization.
6 682 0.809556610555 Henry Cohn, 2026, needs more optimization.
6 683 0.809593568170 Henry Cohn, 2025, needs more optimization.
6 684 0.809809729757 Henry Cohn, 2026, needs more optimization.
6 685 0.809815681557 Henry Cohn, 2025, needs more optimization.
6 686 0.809957609025 Henry Cohn, 2026, needs more optimization.
6 687 0.809987501148 Henry Cohn, 2026, needs more optimization.
6 688 0.810216131855 Henry Cohn, 2025, needs more optimization.
6 689 0.810286164813 Henry Cohn, 2025, needs more optimization.
6 690 0.810404495670 Henry Cohn, 2025, needs more optimization.
6 691 0.810680318644 Henry Cohn, 2025, needs more optimization.
6 692 0.810691458399 Henry Cohn, 2026, needs more optimization.
6 693 0.810692518870 Henry Cohn, 2026, needs more optimization.
6 694 0.810883889506 Henry Cohn, 2025, needs more optimization.
6 695 0.810952995250 Henry Cohn, 2025, needs more optimization.
6 696 0.811134509113 Henry Cohn, 2026, needs more optimization.
6 697 0.811178575942 Henry Cohn, 2026, needs more optimization.
6 698 0.811436541795 Henry Cohn, 2025, needs more optimization.
6 699 0.811556195073 Henry Cohn, 2025, needs more optimization.
6 700 0.811692885419 Henry Cohn, 2026, needs more optimization.
6 701 0.811698518362 Henry Cohn, 2026, needs more optimization.
6 702 0.811787077923 Henry Cohn, 2025, needs more optimization.
6 703 0.811896779748 Henry Cohn, 2026, needs more optimization.
6 704 0.811933453698 Henry Cohn, 2026, needs more optimization.
6 705 0.812056196050 Henry Cohn, 2026, needs more optimization.
6 706 0.812335450951 Henry Cohn, 2025, needs more optimization.
6 707 0.812337723232 Henry Cohn, 2025, needs more optimization.
6 708 0.812521323092 Henry Cohn, 2025, needs more optimization.
6 709 0.812709123718 Henry Cohn, 2026, needs more optimization.
6 710 0.812869067662 Henry Cohn, 2026, needs more optimization.
6 711 0.812870939378 Henry Cohn, 2025, needs more optimization.
6 712 0.812909766290 Henry Cohn, 2026, needs more optimization.
6 713 0.813168514782 Henry Cohn, 2025, needs more optimization.
6 714 0.813189998744 Henry Cohn, 2026, needs more optimization.
6 715 0.813306799649 Henry Cohn, 2025, needs more optimization.
6 716 0.813312306830 Henry Cohn, 2025, needs more optimization.
6 717 0.813340180925 Henry Cohn, 2025, needs more optimization.
6 718 0.813645012868 Henry Cohn, 2026, needs more optimization.
6 719 0.813647808802 Henry Cohn, 2025, needs more optimization.
6 720 0.813677877521 Henry Cohn, 2026, needs more optimization.
6 721 0.813962266975 Henry Cohn, 2025, needs more optimization.
6 722 0.814008585494 Henry Cohn, 2025, needs more optimization.
6 723 0.814032728403 Henry Cohn, 2026, needs more optimization.
6 724 0.814066976477 Henry Cohn, 2026, needs more optimization.
6 725 0.814205535670 Henry Cohn, 2026, needs more optimization.
6 726 0.814326606162 Henry Cohn, 2026, needs more optimization.
6 727 0.814502502478 Henry Cohn, 2026, needs more optimization.
6 728 0.814503288797 Henry Cohn, 2025, needs more optimization.
6 729 0.814570219480 Henry Cohn, 2026, needs more optimization.
6 730 0.814691836372 Henry Cohn, 2026, needs more optimization.
6 731 0.814856583331 Henry Cohn, 2026, needs more optimization.
6 732 0.814941616114 Henry Cohn, 2026, needs more optimization.
6 733 0.815064953607 Henry Cohn, 2025, needs more optimization.
6 734 0.815076327349 Henry Cohn, 2025, needs more optimization.
6 735 0.815129595166 Henry Cohn, 2025, needs more optimization.
6 736 0.815223603952 Henry Cohn, 2025, needs more optimization.
6 737 0.815682268478 Henry Cohn, 2026, needs more optimization.
6 738 0.815693468417 Henry Cohn, 2026, needs more optimization.
6 739 0.815709376578 Henry Cohn, 2025, needs more optimization.
6 740 0.815877414246 Henry Cohn, 2026, needs more optimization.
6 741 0.815898132570 Henry Cohn, 2025, needs more optimization.
6 742 0.816035860658 Henry Cohn, 2025, needs more optimization.
6 743 0.816066086302 Henry Cohn, 2025, needs more optimization.
6 744 0.816072924951 Henry Cohn, 2026, needs more optimization.
6 745 0.816297758800 Henry Cohn, 2025, needs more optimization.
6 746 0.816305246119 Henry Cohn, 2026, needs more optimization.
6 747 0.816590719307 Henry Cohn, 2026, needs more optimization.
6 748 0.816629818356 Henry Cohn, 2025, needs more optimization.
6 749 0.816636310815 Henry Cohn, 2025, needs more optimization.
6 750 0.816834403280 Henry Cohn, 2026, needs more optimization.
6 751 0.816988092892 Henry Cohn, 2026, needs more optimization.
6 752 0.817000737748 Henry Cohn, 2026, needs more optimization.
6 753 0.817252063848 Henry Cohn, 2025, needs more optimization.
6 754 0.817260199019 Henry Cohn, 2025, needs more optimization.
6 755 0.817289678208 Henry Cohn, 2026, needs more optimization.
6 756 0.817435527872 Henry Cohn, 2026, needs more optimization.
6 757 0.817476590341 Henry Cohn, 2025, needs more optimization.
6 758 0.817495067424 Henry Cohn, 2026, needs more optimization.
6 759 0.817679682538 Henry Cohn, 2025, needs more optimization.
6 760 0.817728595799 Henry Cohn, 2026, needs more optimization.
6 761 0.817738637151 Henry Cohn, 2026, needs more optimization.
6 762 0.818009280002 Henry Cohn, 2025, needs more optimization.
6 763 0.818126943364 Henry Cohn, 2026, needs more optimization.
6 764 0.818293022730 Henry Cohn, 2026, needs more optimization.
6 765 0.818387391667 Henry Cohn, 2025, needs more optimization.
6 766 0.818390100651 Henry Cohn, 2025, needs more optimization.
6 767 0.818394454662 Henry Cohn, 2025, needs more optimization.
6 768 0.818596596606 Henry Cohn, 2025, needs more optimization.
6 769 0.818775965803 Henry Cohn, 2025, needs more optimization.
6 770 0.818805061007 Henry Cohn, 2026, needs more optimization.
6 771 0.818923267989 Henry Cohn, 2026, needs more optimization.
6 772 0.818932450167 Henry Cohn, 2026, needs more optimization.
6 773 0.818970769208 Henry Cohn, 2025, needs more optimization.
6 775 0.819130040801 Henry Cohn, 2026, needs more optimization.
6 776 0.819373850853 Henry Cohn, 2026, needs more optimization.
6 777 0.819410314136 Henry Cohn, 2025, needs more optimization.
6 778 0.819549833203 Henry Cohn, 2025, needs more optimization.
6 779 0.819551772387 Henry Cohn, 2026, needs more optimization.
6 780 0.819703678444 Henry Cohn, 2026, needs more optimization.
6 781 0.819710578070 Henry Cohn, 2026, needs more optimization.
6 782 0.819732926480 Henry Cohn, 2026, needs more optimization.
6 783 0.819933707254 Henry Cohn, 2025, needs more optimization.
6 784 0.819960428163 Henry Cohn, 2026, needs more optimization.
6 785 0.820143659869 Henry Cohn, 2025, needs more optimization.
6 786 0.820162706123 Henry Cohn, 2026, needs more optimization.
6 787 0.820192193425 Henry Cohn, 2026, needs more optimization.
6 788 0.820407823502 Henry Cohn, 2026, needs more optimization.
6 789 0.820418485236 Henry Cohn, 2025, needs more optimization.
6 790 0.820541743786 Henry Cohn, 2026, needs more optimization.
6 791 0.820646161966 Henry Cohn, 2026, needs more optimization.
6 792 0.820801628820 Henry Cohn, 2026, needs more optimization.
6 793 0.820847663795 Henry Cohn, 2025, needs more optimization.
6 794 0.820992944116 Henry Cohn, 2026, needs more optimization.
6 795 0.820998941353 Henry Cohn, 2025, needs more optimization.
6 796 0.821019788207 Henry Cohn, 2025, needs more optimization.
6 797 0.821162357325 Henry Cohn, 2026, needs more optimization.
6 798 0.821168742970 Henry Cohn, 2026, needs more optimization.
6 799 0.821271329935 Henry Cohn, 2025, needs more optimization.
6 800 0.821599446854 Henry Cohn, 2025, needs more optimization.
6 801 0.821655585342 Henry Cohn, 2025, needs more optimization.
6 802 0.821671715423 Henry Cohn, 2025, needs more optimization.
6 803 0.821753358327 Henry Cohn, 2026, needs more optimization.
6 804 0.821760010760 Henry Cohn, 2026, needs more optimization.
6 805 0.821921704628 Henry Cohn, 2025, needs more optimization.
6 806 0.821925354397 Henry Cohn, 2025, needs more optimization.
6 807 0.822127138753 Henry Cohn, 2025, needs more optimization.
6 808 0.822136942702 Henry Cohn, 2026, needs more optimization.
6 809 0.822274739568 Henry Cohn, 2025, needs more optimization.
6 810 0.822299924242 Henry Cohn, 2025, needs more optimization.
6 811 0.822381953139 Henry Cohn, 2025, needs more optimization.
6 812 0.822493820161 Henry Cohn, 2026, needs more optimization.
6 813 0.822714297203 Henry Cohn, 2025, needs more optimization.
6 814 0.822719272780 Henry Cohn, 2025, needs more optimization.
6 815 0.822810732997 Henry Cohn, 2025, needs more optimization.
6 816 0.822862618507 Henry Cohn, 2026, needs more optimization.
6 817 0.823003742491 Henry Cohn, 2025, needs more optimization.
6 820 0.823199035966 Henry Cohn, 2026, needs more optimization.
6 821 0.823458312032 Henry Cohn, 2025, needs more optimization.
6 824 0.823661404172 Henry Cohn, 2025, needs more optimization.
6 825 0.823727831164 Henry Cohn, 2025, needs more optimization.
6 826 0.823995407863 Henry Cohn, 2025, needs more optimization.
6 827 0.823998838954 Henry Cohn, 2025, needs more optimization.
6 828 0.824000600074 Henry Cohn, 2026, needs more optimization.
6 829 0.824087347346 Henry Cohn, 2026, needs more optimization.
6 830 0.824248007756 Henry Cohn, 2026, needs more optimization.
6 831 0.824253060781 Henry Cohn, 2025, needs more optimization.
6 832 0.824405563460 Henry Cohn, 2026, needs more optimization.
6 833 0.824413825655 Henry Cohn, 2025, needs more optimization.
6 834 0.824560460920 Henry Cohn, 2025, needs more optimization.
6 835 0.824562867216 Henry Cohn, 2025, needs more optimization.
6 836 0.824565043044 Henry Cohn, 2025, needs more optimization.
6 837 0.824857490202 Henry Cohn, 2025, needs more optimization.
6 838 0.824860456156 Henry Cohn, 2026, needs more optimization.
6 839 0.824886179725 Henry Cohn, 2026, needs more optimization.
6 840 0.824920182114 Henry Cohn, 2025, needs more optimization.
6 841 0.825001746346 Henry Cohn, 2025, needs more optimization.
6 842 0.825319421071 Henry Cohn, 2025, needs more optimization.
6 843 0.825320807229 Henry Cohn, 2025, needs more optimization.
6 844 0.825332142790 Henry Cohn, 2026, needs more optimization.
6 845 0.825431145892 Henry Cohn, 2025, needs more optimization.
6 846 0.825566867495 Henry Cohn, 2025, needs more optimization.
6 847 0.825579490995 Henry Cohn, 2025, needs more optimization.
6 848 0.825586029457 Henry Cohn, 2026, needs more optimization.
6 849 0.825841722374 Henry Cohn, 2025, needs more optimization.
6 850 0.825860506676 Henry Cohn, 2025, needs more optimization.
6 851 0.825868206288 Henry Cohn, 2026, needs more optimization.
6 852 0.826024374941 Henry Cohn, 2026, needs more optimization.
6 853 0.826141690504 Henry Cohn, 2025, needs more optimization.
6 854 0.826367084565 Henry Cohn, 2026, needs more optimization.
6 855 0.826400472648 Henry Cohn, 2025, needs more optimization.
6 856 0.826415296291 Henry Cohn, 2026, needs more optimization.
6 857 0.826652046639 Henry Cohn, 2025, needs more optimization.
6 858 0.826659628926 Henry Cohn, 2025, needs more optimization.
6 859 0.826687113923 Henry Cohn, 2026, needs more optimization.
6 860 0.826841472698 Henry Cohn, 2026, needs more optimization.
6 861 0.826932469101 Henry Cohn, 2026, needs more optimization.
6 862 0.826936875274 Henry Cohn, 2025, needs more optimization.
6 863 0.827096118447 Henry Cohn, 2025, needs more optimization.
6 864 0.827100003459 Henry Cohn, 2026, needs more optimization.
6 865 0.827296940286 Henry Cohn, 2026, needs more optimization.
6 867 0.827303375728 Henry Cohn, 2025, needs more optimization.
6 868 0.827394189128 Henry Cohn, 2026, needs more optimization.
6 869 0.827401797850 Henry Cohn, 2026, needs more optimization.
6 870 0.827591086516 Henry Cohn, 2026, needs more optimization.
6 871 0.827597158369 Henry Cohn, 2025, needs more optimization.
6 872 0.827728271232 Henry Cohn, 2026, needs more optimization.
6 873 0.827729680529 Henry Cohn, 2026, needs more optimization.
6 874 0.827730794125 Henry Cohn, 2025, needs more optimization.
6 875 0.827737392377 Henry Cohn, 2025, needs more optimization.
6 876 0.827801485706 Henry Cohn, 2026, needs more optimization.
6 877 0.827866203405 Henry Cohn, 2026, needs more optimization.
6 878 0.828013879401 Henry Cohn, 2025, needs more optimization.
6 880 0.828018048100 Henry Cohn, 2026, needs more optimization.
6 881 0.828046955944 Henry Cohn, 2025, needs more optimization.
6 882 0.828050309265 Henry Cohn, 2026, needs more optimization.
6 883 0.828099087083 Henry Cohn, 2025, needs more optimization.
6 884 0.828212504038 Henry Cohn, 2026, needs more optimization.
6 885 0.828338428446 Henry Cohn, 2026, needs more optimization.
6 886 0.828367158085 Henry Cohn, 2026, needs more optimization.
6 887 0.828500110788 Henry Cohn, 2025, needs more optimization.
6 888 0.828533748457 Henry Cohn, 2026, needs more optimization.
6 890 0.828644258996 Henry Cohn, 2025, needs more optimization.
6 891 0.828695697577 Henry Cohn, 2025, needs more optimization.
6 892 0.828880658446 Henry Cohn, 2026, needs more optimization.
6 894 0.828882968640 Henry Cohn, 2026, needs more optimization.
6 895 0.828942339148 Henry Cohn, 2026, needs more optimization.
6 896 0.828942922823 Henry Cohn, 2025, needs more optimization.
6 897 0.829140202323 Henry Cohn, 2025, needs more optimization.
6 898 0.829142880376 Henry Cohn, 2025, needs more optimization.
6 899 0.829153915719 Henry Cohn, 2025, needs more optimization.
6 900 0.829310619521 Henry Cohn, 2026, needs more optimization.
6 901 0.829419331220 Henry Cohn, 2026, needs more optimization.
6 902 0.829427787011 Henry Cohn, 2025, needs more optimization.
6 904 0.829628240514 Henry Cohn, 2026, needs more optimization.
6 905 0.829701077326 Henry Cohn, 2025, needs more optimization.
6 906 0.829812045947 Henry Cohn, 2025, needs more optimization.
6 907 0.829817198209 Henry Cohn, 2025, needs more optimization.
6 908 0.829818655010 Henry Cohn, 2025, needs more optimization.
6 909 0.830020033127 Henry Cohn, 2026, needs more optimization.
6 910 0.830022358121 Henry Cohn, 2026, needs more optimization.
6 911 0.830065610631 Henry Cohn, 2025, needs more optimization.
6 912 0.830113517537 Henry Cohn, 2026, needs more optimization.
6 913 0.830239845292 Henry Cohn, 2026, needs more optimization.
6 914 0.830242519417 Henry Cohn, 2025, needs more optimization.
6 916 0.830521683842 Henry Cohn, 2026, needs more optimization.
6 917 0.830522878283 Henry Cohn, 2025, needs more optimization.
6 918 0.830527013915 Henry Cohn, 2025, needs more optimization.
6 919 0.830527776902 Henry Cohn, 2025, needs more optimization.
6 920 0.830717981265 Henry Cohn, 2026, needs more optimization.
6 921 0.830738180489 Henry Cohn, 2025, needs more optimization.
6 922 0.830829231774 Henry Cohn, 2025, needs more optimization.
6 923 0.830840743540 Henry Cohn, 2025, needs more optimization.
6 924 0.830903672293 Henry Cohn, 2026, needs more optimization.
6 925 0.830906862451 Henry Cohn, 2025, needs more optimization.
6 926 0.830908268155 Henry Cohn, 2025, needs more optimization.
6 928 0.831284349465 Henry Cohn, 2025, needs more optimization.
6 929 0.831287055099 Henry Cohn, 2025, needs more optimization.
6 930 0.831326342580 Henry Cohn, 2025, needs more optimization.
6 932 0.831470102843 Henry Cohn, 2026, needs more optimization.
6 934 0.831471568058 Henry Cohn, 2025, needs more optimization.
6 936 0.831503858491 Henry Cohn, 2026, needs more optimization.
6 937 0.831654977354 Henry Cohn, 2025, needs more optimization.
6 938 0.831657240242 Henry Cohn, 2025, needs more optimization.
6 939 0.831778720014 Henry Cohn, 2026, needs more optimization.
6 940 0.831799691532 Henry Cohn, 2026, needs more optimization.
6 941 0.831803415016 Henry Cohn, 2025, needs more optimization.
6 942 0.831858895761 Henry Cohn, 2026, needs more optimization.
6 944 0.831997404175 Henry Cohn, 2026, needs more optimization.
6 945 0.831997660390 Henry Cohn, 2026, needs more optimization.
6 946 0.831998896870 Henry Cohn, 2026, needs more optimization.
6 947 0.832020842073 Henry Cohn, 2026, needs more optimization.
6 948 0.832138138234 Henry Cohn, 2025, needs more optimization.
6 950 0.832159838275 Henry Cohn, 2025, needs more optimization.
6 951 0.832288455846 Henry Cohn, 2026, needs more optimization.
6 952 0.832294478981 Henry Cohn, 2026, needs more optimization.
6 953 0.832310934537 Henry Cohn, 2026, needs more optimization.
6 954 0.832417866581 Henry Cohn, 2025, needs more optimization.
6 956 0.832433305929 Henry Cohn, 2026, needs more optimization.
6 957 0.832443618756 Henry Cohn, 2025, needs more optimization.
6 958 0.832590542539 Henry Cohn, 2026, needs more optimization.
6 959 0.832608439140 Henry Cohn, 2025, needs more optimization.
6 960 0.832608515714 Henry Cohn, 2025, needs more optimization.
6 961 0.832622827750 Henry Cohn, 2026, needs more optimization.
6 964 0.832772805190 Henry Cohn, 2026, needs more optimization.
6 965 0.832786351085 Henry Cohn, 2025, needs more optimization.
6 966 0.832897436776 Henry Cohn, 2026, needs more optimization.
6 967 0.832901388916 Henry Cohn, 2025, needs more optimization.
6 968 0.832904729760 Henry Cohn, 2026, needs more optimization.
6 969 0.832918121401 Henry Cohn, 2025, 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
6 991 0.835257411625 Henry Cohn, 2026, needs more optimization.
6 992 0.836344602402 Henry Cohn, 2026, needs more optimization.
6 993 0.836365663324 Henry Cohn, 2025, needs more optimization.
6 994 0.836412974463 Henry Cohn, 2026, needs more optimization.
6 995 0.836413523076 Henry Cohn, 2025, needs more optimization.
6 996 0.836586134983 Henry Cohn, 2025, needs more optimization.
6 997 0.836735501990 Henry Cohn, 2026, needs more optimization.
6 998 0.836761508200 Henry Cohn, 2026, needs more optimization.
6 999 0.836916042999 Henry Cohn, 2025, needs more optimization.
6 1000 0.836920990870 Henry Cohn, 2026, needs more optimization.
6 1001 0.836925063933 Henry Cohn, 2026, needs more optimization.
6 1002 0.836954720379 Henry Cohn, 2025, needs more optimization.
6 1004 0.837120788733 Henry Cohn, 2025, needs more optimization.
6 1005 0.837377370064 Henry Cohn, 2026, needs more optimization.
6 1006 0.837381434825 Henry Cohn, 2026, needs more optimization.
6 1007 0.837391864929 Henry Cohn, 2025, needs more optimization.
6 1008 0.837393643211 Henry Cohn, 2026, needs more optimization.
6 1009 0.837522537170 Henry Cohn, 2025, needs more optimization.
6 1010 0.837636537050 Henry Cohn, 2025, needs more optimization.
6 1012 0.837675282618 Henry Cohn, 2026, needs more optimization.
6 1013 0.837809183769 Henry Cohn, 2025, needs more optimization.
6 1014 0.837817927547 Henry Cohn, 2025, needs more optimization.
6 1015 0.837940910005 Henry Cohn, 2025, needs more optimization.
6 1016 0.837946894777 Henry Cohn, 2025, needs more optimization.
6 1017 0.837962553501 Henry Cohn, 2026, needs more optimization.
6 1018 0.838156036821 Henry Cohn, 2026, needs more optimization.
6 1019 0.838161452587 Henry Cohn, 2025, needs more optimization.
6 1020 0.838339854919 Henry Cohn, 2025, needs more optimization.
6 1021 0.838343021300 Henry Cohn, 2026, needs more optimization.
6 1022 0.838432480085 Henry Cohn, 2025, needs more optimization.
6 1023 0.838513425608 Henry Cohn, 2025, needs more optimization.
6 1024 0.838621267399 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 0.333312302687 Henry Cohn, 2025.
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 0.414766349117 Henry Cohn, 2025.
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 0.428235713853 Henry Cohn, 2025.
7 69 0.428531302684 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 0.453278412444 Henry Cohn, 2024.
7 80 0.453887992064 Henry Cohn, 2024.
7 81 0.459667826759 Henry Cohn, 2025.
7 82 0.461219223470 Henry Cohn, 2025.
7 83 0.461669205843 Henry Cohn, 2024.
7 84 0.465073032663 Henry Cohn, 2025.
7 86 0.466580867327 Henry Cohn, 2025, needs more optimization.
7 87 0.469578821552 Henry Cohn, 2024.
7 88 0.473067267884 Henry Cohn, 2024.
7 89 0.474988257844 Henry Cohn, 2024.
7 90 0.475294477919 Henry Cohn, 2024.
7 91 0.479167604557 Henry Cohn, 2026, needs more optimization.
7 92 0.480306853225 Henry Cohn, 2025, needs more optimization.
7 93 0.482408792669 Henry Cohn, 2026, needs more optimization.
7 94 0.483507258083 Henry Cohn, 2025.
7 96 0.486808303779 Henry Cohn, 2025.
7 97 0.487296284314 Henry Cohn, 2025.
7 98 0.489141129031 Henry Cohn, 2026, needs more optimization.
7 99 0.494793494531 Henry Cohn, 2026, needs more optimization.
7 101 0.496533689719 Henry Cohn, 2026, needs more optimization.
7 102 0.496935829987 Henry Cohn, 2026, needs more optimization.
7 103 0.498541861705 Henry Cohn, 2026, needs more optimization.
7 106 0.499144603452 Henry Cohn, 2026, needs more optimization.
7 107 0.499592044297 Henry Cohn, 2026, needs more optimization.
7 108 0.499944082669 Henry Cohn, 2026, needs more optimization.
7 109 0.499990542788 Henry Cohn, 2026, needs more optimization.
7 110 0.499999099965 Henry Cohn, 2026, needs more optimization.
7 111 0.499999997332 Henry Cohn, 2026, needs more optimization.
7 112 0.499999997662 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 0.509963471599 Henry Cohn, 2025.
7 128 0.513867786048 Henry Cohn, 2026, needs more optimization.
7 129 0.518845743940 Henry Cohn, 2026, needs more optimization.
7 132 0.519151939817 Henry Cohn, 2026, needs more optimization.
7 134 0.519151940547 Henry Cohn, 2026, needs more optimization.
7 136 0.519153914325 Henry Cohn, 2026, needs more optimization.
7 137 0.519751518195 Henry Cohn, 2024.
7 138 0.527218738805 Henry Cohn, 2025.
7 139 0.531617221195 Henry Cohn, 2026, needs more optimization.
7 140 0.531617339410 Henry Cohn, 2026, needs more optimization.
7 141 0.531620399948 Henry Cohn, 2026, needs more optimization.
7 142 0.531667393940 Henry Cohn, 2025, needs more optimization.
7 144 0.531670507818 Henry Cohn, 2026, needs more optimization.
7 145 0.532801092831 Henry Cohn, 2026, needs more optimization.
7 146 0.532883690322 Henry Cohn, 2025.
7 147 0.533479772596 Henry Cohn, 2024.
7 148 0.534155136567 Henry Cohn, 2026.
7 150 0.546228544380 Henry Cohn, 2026, needs more optimization.
7 151 0.546228627740 Henry Cohn, 2026, needs more optimization.
7 152 0.546229237935 Henry Cohn, 2026, needs more optimization.
7 154 0.546281372154 Henry Cohn, 2026, needs more optimization.
7 155 0.548973616291 Henry Cohn, 2026, needs more optimization.
7 156 0.552241694823 Henry Cohn, 2026, needs more optimization.
7 157 0.557025332397 Henry Cohn, 2026, needs more optimization.
7 158 0.559769084391 Henry Cohn, 2026, needs more optimization.
7 160 0.560495664198 Henry Cohn, 2026, needs more optimization.
7 161 0.560502494060 Henry Cohn, 2026, needs more optimization.
7 163 0.561767689319 Henry Cohn, 2026, needs more optimization.
7 164 0.563372868920 Henry Cohn, 2025, needs more optimization.
7 165 0.563378384553 Henry Cohn, 2025, needs more optimization.
7 168 0.563381948463 Henry Cohn, 2025, needs more optimization.
7 169 0.563588109639 Henry Cohn, 2026, needs more optimization.
7 170 0.563592107095 Henry Cohn, 2026, needs more optimization.
7 171 0.570278986786 Henry Cohn, 2026, needs more optimization.
7 175 0.570446757462 Henry Cohn, 2026, needs more optimization.
7 177 0.570455825668 Henry Cohn, 2026, needs more optimization.
7 178 0.570455990678 Henry Cohn, 2026, needs more optimization.
7 180 0.570549324134 Henry Cohn, 2026, needs more optimization.
7 181 0.573146880911 Henry Cohn, 2025, 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 0.587541965804 Ilmari Vahteristo, 2026.
7 184 0.590395029876 Henry Cohn, 2024, needs more optimization.
7 185 0.592031258395 Henry Cohn, 2024, needs more optimization.
7 186 0.592610444725 Henry Cohn, 2026, needs more optimization.
7 188 0.593610059910 Henry Cohn, 2026, needs more optimization.
7 190 0.594826599979 Henry Cohn, 2025, needs more optimization.
7 191 0.594827112265 Henry Cohn, 2025, needs more optimization.
7 192 0.596061486654 Henry Cohn, 2026, needs more optimization.
7 193 0.596071968555 Henry Cohn, 2026, needs more optimization.
7 194 0.599360499965 Henry Cohn, 2024, needs more optimization.
7 195 0.601540224587 Henry Cohn, 2024, needs more optimization.
7 196 0.601793608585 Henry Cohn, 2024, needs more optimization.
7 197 0.603597835671 Henry Cohn, 2026, needs more optimization.
7 198 0.604006403946 Henry Cohn, 2025, needs more optimization.
7 199 0.605261083349 Henry Cohn, 2024, needs more optimization.
7 200 0.605866105540 Henry Cohn, 2024, needs more optimization.
7 201 0.607444492181 Henry Cohn, 2026, needs more optimization.
7 202 0.607791427450 Henry Cohn, 2026, needs more optimization.
7 203 0.608324827470 Henry Cohn, 2025, needs more optimization.
7 204 0.609417002285 Henry Cohn, 2024, needs more optimization.
7 205 0.611260863785 Henry Cohn, 2024, needs more optimization.
7 206 0.611945534082 Henry Cohn, 2024, needs more optimization.
7 207 0.612727397745 Henry Cohn, 2024, needs more optimization.
7 208 0.613448534998 Henry Cohn, 2024, needs more optimization.
7 209 0.614590794819 Henry Cohn, 2024, needs more optimization.
7 210 0.614894346303 Henry Cohn, 2024, needs more optimization.
7 211 0.616021679004 Henry Cohn, 2024, needs more optimization.
7 212 0.616329554386 Henry Cohn, 2026, needs more optimization.
7 213 0.617073701156 Henry Cohn, 2024, needs more optimization.
7 214 0.618442660293 Henry Cohn, 2026, needs more optimization.
7 215 0.619130840652 Henry Cohn, 2026, needs more optimization.
7 216 0.619599983206 Henry Cohn, 2024, needs more optimization.
7 217 0.620540826883 Henry Cohn, 2026, needs more optimization.
7 218 0.621368072363 Henry Cohn, 2024, needs more optimization.
7 219 0.621900185806 Henry Cohn, 2026, needs more optimization.
7 220 0.622604993923 Henry Cohn, 2024, needs more optimization.
7 221 0.624023095035 Henry Cohn, 2024, needs more optimization.
7 222 0.624410753011 Henry Cohn, 2026, needs more optimization.
7 223 0.624822505678 Henry Cohn, 2026, needs more optimization.
7 224 0.625206654600 Henry Cohn, 2026, needs more optimization.
7 225 0.625872966956 Henry Cohn, 2024, needs more optimization.
7 226 0.627180587577 Henry Cohn, 2026, needs more optimization.
7 227 0.627364742643 Henry Cohn, 2026, needs more optimization.
7 228 0.628144528595 Henry Cohn, 2026, needs more optimization.
7 229 0.629183026831 Henry Cohn, 2026, needs more optimization.
7 230 0.630264678870 Henry Cohn, 2024, needs more optimization.
7 231 0.630549078404 Henry Cohn, 2024, needs more optimization.
7 232 0.631248222170 Henry Cohn, 2024, needs more optimization.
7 233 0.631901836958 Henry Cohn, 2024, needs more optimization.
7 234 0.632643043718 Henry Cohn, 2024, needs more optimization.
7 235 0.633043566268 Henry Cohn, 2026, needs more optimization.
7 236 0.633943127321 Henry Cohn, 2024, needs more optimization.
7 237 0.634261704526 Henry Cohn, 2026, needs more optimization.
7 238 0.634781311206 Henry Cohn, 2024, needs more optimization.
7 239 0.635356766795 Henry Cohn, 2024, needs more optimization.
7 240 0.635677240819 Henry Cohn, 2024, needs more optimization.
7 241 0.636614389125 Henry Cohn, 2024, needs more optimization.
7 242 0.636965575506 Henry Cohn, 2024, needs more optimization.
7 243 0.637513507990 Henry Cohn, 2024, needs more optimization.
7 244 0.638074677610 Henry Cohn, 2024, needs more optimization.
7 245 0.638592844169 Henry Cohn, 2025, needs more optimization.
7 246 0.638771563838 Henry Cohn, 2025, needs more optimization.
7 247 0.639347723126 Henry Cohn, 2025, needs more optimization.
7 248 0.640032835036 Henry Cohn, 2024, needs more optimization.
7 249 0.640408857728 Henry Cohn, 2025, needs more optimization.
7 250 0.640982436344 Henry Cohn, 2025, needs more optimization.
7 251 0.641158392745 Henry Cohn, 2026, needs more optimization.
7 252 0.641653401103 Henry Cohn, 2026, needs more optimization.
7 253 0.641879425965 Henry Cohn, 2025, needs more optimization.
7 254 0.642941709635 Henry Cohn, 2026, needs more optimization.
7 255 0.643269607048 Henry Cohn, 2025, needs more optimization.
7 256 0.643614466517 Henry Cohn, 2025, needs more optimization.
7 257 0.644347933308 Henry Cohn, 2026, needs more optimization.
7 258 0.644908976495 Henry Cohn, 2026, needs more optimization.
7 259 0.645222821952 Henry Cohn, 2026, needs more optimization.
7 260 0.645645895739 Henry Cohn, 2026, needs more optimization.
7 261 0.645847145637 Henry Cohn, 2026, needs more optimization.
7 262 0.646146152305 Henry Cohn, 2026, needs more optimization.
7 263 0.647124066463 Henry Cohn, 2026, needs more optimization.
7 264 0.647393555376 Henry Cohn, 2026, needs more optimization.
7 265 0.648281926512 Henry Cohn, 2026, needs more optimization.
7 266 0.648454561163 Henry Cohn, 2026, needs more optimization.
7 267 0.648884959686 Henry Cohn, 2026, needs more optimization.
7 268 0.649484032054 Henry Cohn, 2025, needs more optimization.
7 269 0.649637461961 Henry Cohn, 2026, needs more optimization.
7 270 0.650037311217 Henry Cohn, 2026, needs more optimization.
7 271 0.650210530176 Henry Cohn, 2026, needs more optimization.
7 272 0.650872965179 Henry Cohn, 2025, needs more optimization.
7 273 0.651436196216 Henry Cohn, 2026, needs more optimization.
7 274 0.651535200058 Henry Cohn, 2026, needs more optimization.
7 275 0.651758524713 Henry Cohn, 2026, needs more optimization.
7 276 0.652816200390 Henry Cohn, 2025, needs more optimization.
7 277 0.652937956970 Henry Cohn, 2026, needs more optimization.
7 278 0.653567114525 Henry Cohn, 2026, needs more optimization.
7 279 0.654130199784 Henry Cohn, 2026, needs more optimization.
7 280 0.654181712325 Henry Cohn, 2026, needs more optimization.
7 281 0.654947513766 Henry Cohn, 2026, needs more optimization.
7 282 0.655071481483 Henry Cohn, 2025, needs more optimization.
7 283 0.655694421143 Henry Cohn, 2026, needs more optimization.
7 284 0.655939395423 Henry Cohn, 2026, needs more optimization.
7 285 0.656544346448 Henry Cohn, 2026, needs more optimization.
7 286 0.657024138855 Henry Cohn, 2026, needs more optimization.
7 287 0.657332541225 Henry Cohn, 2026, needs more optimization.
7 288 0.657574191509 Henry Cohn, 2026, needs more optimization.
7 289 0.658060848385 Henry Cohn, 2026, needs more optimization.
7 290 0.658671892385 Henry Cohn, 2026, needs more optimization.
7 291 0.659127213481 Henry Cohn, 2026, needs more optimization.
7 292 0.659401922113 Henry Cohn, 2026, needs more optimization.
7 293 0.659727765304 Henry Cohn, 2026, needs more optimization.
7 294 0.660045005661 Henry Cohn, 2026, needs more optimization.
7 295 0.661026050450 Henry Cohn, 2026, needs more optimization.
7 296 0.661083622910 Henry Cohn, 2026, needs more optimization.
7 297 0.661248245899 Henry Cohn, 2025, needs more optimization.
7 298 0.661780957395 Henry Cohn, 2026, needs more optimization.
7 299 0.662450024429 Henry Cohn, 2026, needs more optimization.
7 300 0.662682038294 Henry Cohn, 2026, needs more optimization.
7 301 0.663480479645 Henry Cohn, 2025, needs more optimization.
7 302 0.663759454150 Henry Cohn, 2025, needs more optimization.
7 303 0.663998669282 Henry Cohn, 2026, needs more optimization.
7 304 0.664599851270 Henry Cohn, 2026, needs more optimization.
7 305 0.664628042274 Henry Cohn, 2025, needs more optimization.
7 306 0.664738733263 Henry Cohn, 2026, needs more optimization.
7 307 0.665702963255 Henry Cohn, 2025, needs more optimization.
7 308 0.666037244322 Henry Cohn, 2025, needs more optimization.
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 0.675386736306 Henry Cohn, 2026, needs more optimization.
7 360 0.675672261492 Henry Cohn, 2026, needs more optimization.
7 361 0.675712378451 Henry Cohn, 2026, needs more optimization.
7 362 0.675811135637 Henry Cohn, 2026, needs more optimization.
7 363 0.675811653557 Henry Cohn, 2026, needs more optimization.
7 365 0.675946641714 Henry Cohn, 2026, needs more optimization.
7 366 0.676117098486 Henry Cohn, 2026, needs more optimization.
7 367 0.676399959676 Henry Cohn, 2026, needs more optimization.
7 368 0.676415352949 Henry Cohn, 2026, needs more optimization.
7 369 0.676479305561 Henry Cohn, 2026, needs more optimization.
7 371 0.676745531011 Henry Cohn, 2026, needs more optimization.
7 372 0.676762790902 Henry Cohn, 2026, needs more optimization.
7 373 0.676833567738 Henry Cohn, 2026, needs more optimization.
7 376 0.677059596678 Henry Cohn, 2026, needs more optimization.
7 377 0.677114554454 Henry Cohn, 2026, needs more optimization.
7 378 0.677121673978 Henry Cohn, 2026, needs more optimization.
7 379 0.677122721268 Henry Cohn, 2026, needs more optimization.
7 380 0.677165380534 Henry Cohn, 2026, needs more optimization.
7 381 0.677446098721 Henry Cohn, 2026, needs more optimization.
7 382 0.677466298004 Henry Cohn, 2026, needs more optimization.
7 383 0.678022967422 Henry Cohn, 2026, needs more optimization.
7 384 0.679172662319 Henry Cohn, 2026, needs more optimization.
7 385 0.679178805122 Henry Cohn, 2026, needs more optimization.
7 386 0.679753598396 Henry Cohn, 2026, needs more optimization.
7 388 0.680358102666 Henry Cohn, 2026, needs more optimization.
7 389 0.680994589993 Henry Cohn, 2026, needs more optimization.
7 390 0.681057709175 Henry Cohn, 2026, needs more optimization.
7 391 0.681263351807 Henry Cohn, 2026, needs more optimization.
7 392 0.681696095783 Henry Cohn, 2026, needs more optimization.
7 394 0.681765586423 Henry Cohn, 2026, needs more optimization.
7 395 0.681798498173 Henry Cohn, 2026, needs more optimization.
7 396 0.682990272288 Henry Cohn, 2026, needs more optimization.
7 397 0.682997247619 Henry Cohn, 2026, needs more optimization.
7 398 0.683036748947 Henry Cohn, 2026, needs more optimization.
7 399 0.683110520018 Henry Cohn, 2026, needs more optimization.
7 400 0.683129736371 Henry Cohn, 2026, needs more optimization.
7 401 0.683185948128 Henry Cohn, 2026, needs more optimization.
7 402 0.683291958276 Henry Cohn, 2026, needs more optimization.
7 403 0.683318714028 Henry Cohn, 2026, needs more optimization.
7 404 0.683320042580 Henry Cohn, 2026, needs more optimization.
7 405 0.683357014411 Henry Cohn, 2026, needs more optimization.
7 406 0.690932444651 Henry Cohn, 2025, needs more optimization.
7 407 0.691685829843 Henry Cohn, 2026, needs more optimization.
7 408 0.692257645580 Henry Cohn, 2026, needs more optimization.
7 409 0.692332039010 Henry Cohn, 2025, needs more optimization.
7 410 0.692414746541 Henry Cohn, 2025, needs more optimization.
7 411 0.692787928477 Henry Cohn, 2025, needs more optimization.
7 412 0.692964864233 Henry Cohn, 2026, needs more optimization.
7 413 0.693125695547 Henry Cohn, 2025, needs more optimization.
7 414 0.693154749248 Henry Cohn, 2025, needs more optimization.
7 415 0.693162668354 Henry Cohn, 2025, needs more optimization.
7 416 0.694123742176 Henry Cohn, 2025, needs more optimization.
7 417 0.694287009188 Henry Cohn, 2025, needs more optimization.
7 418 0.694523585349 Henry Cohn, 2025, needs more optimization.
7 419 0.694815792826 Henry Cohn, 2026, needs more optimization.
7 420 0.695128563933 Henry Cohn, 2025, needs more optimization.
7 421 0.695130508518 Henry Cohn, 2025, needs more optimization.
7 422 0.695176221166 Henry Cohn, 2025, needs more optimization.
7 423 0.695830132382 Henry Cohn, 2025, needs more optimization.
7 424 0.695880985033 Henry Cohn, 2025, needs more optimization.
7 425 0.696154846704 Henry Cohn, 2025, needs more optimization.
7 426 0.696220870137 Henry Cohn, 2025, needs more optimization.
7 427 0.696335833512 Henry Cohn, 2025, needs more optimization.
7 428 0.696904394283 Henry Cohn, 2026, needs more optimization.
7 429 0.696957305399 Henry Cohn, 2025, needs more optimization.
7 430 0.697024460578 Henry Cohn, 2025, needs more optimization.
7 431 0.697198226158 Henry Cohn, 2025, needs more optimization.
7 432 0.697758355591 Henry Cohn, 2025, needs more optimization.
7 434 0.698064930275 Henry Cohn, 2026, needs more optimization.
7 436 0.698129161773 Henry Cohn, 2025, needs more optimization.
7 438 0.698768530471 Henry Cohn, 2025, needs more optimization.
7 439 0.699057471161 Henry Cohn, 2025, needs more optimization.
7 440 0.699564497374 Henry Cohn, 2025, needs more optimization.
7 441 0.699943203361 Henry Cohn, 2026, needs more optimization.
7 442 0.700293285076 Henry Cohn, 2025, needs more optimization.
7 444 0.700938073780 Henry Cohn, 2025, needs more optimization.
7 445 0.700946567027 Henry Cohn, 2025, needs more optimization.
7 446 0.700962130467 Henry Cohn, 2025, needs more optimization.
7 447 0.701190449341 Henry Cohn, 2025, needs more optimization.
7 448 0.701776571024 Henry Cohn, 2025, needs more optimization.
7 449 0.702022842893 Henry Cohn, 2025, needs more optimization.
7 450 0.702810548686 Henry Cohn, 2025, needs more optimization.
7 451 0.702836794920 Henry Cohn, 2026, needs more optimization.
7 452 0.703109664314 Henry Cohn, 2025, needs more optimization.
7 453 0.703553853189 Henry Cohn, 2025, needs more optimization.
7 454 0.703590992781 Henry Cohn, 2025, needs more optimization.
7 455 0.703646141098 Henry Cohn, 2025, needs more optimization.
7 458 0.704114722772 Henry Cohn, 2025, needs more optimization.
7 459 0.704603392874 Henry Cohn, 2025, needs more optimization.
7 460 0.704708114405 Henry Cohn, 2025, needs more optimization.
7 461 0.705051861668 Henry Cohn, 2026, needs more optimization.
7 462 0.705056506687 Henry Cohn, 2025, needs more optimization.
7 463 0.705379494979 Henry Cohn, 2025, needs more optimization.
7 464 0.705388063719 Henry Cohn, 2025, needs more optimization.
7 465 0.705399208446 Henry Cohn, 2025, needs more optimization.
7 466 0.705439358343 Henry Cohn, 2026, needs more optimization.
7 467 0.705764381751 Henry Cohn, 2025, needs more optimization.
7 468 0.705859692358 Henry Cohn, 2025, needs more optimization.
7 469 0.705879757078 Henry Cohn, 2025, needs more optimization.
7 472 0.706158356996 Henry Cohn, 2025, needs more optimization.
7 473 0.706329190915 Henry Cohn, 2025, needs more optimization.
7 474 0.706718336008 Henry Cohn, 2025, needs more optimization.
7 475 0.707007270167 Henry Cohn, 2025, needs more optimization.
7 476 0.707415911476 Henry Cohn, 2025, needs more optimization.
7 477 0.707552845511 Henry Cohn, 2025, needs more optimization.
7 478 0.707831690404 Henry Cohn, 2026, needs more optimization.
7 479 0.708089164268 Henry Cohn, 2026, needs more optimization.
7 480 0.708092903508 Henry Cohn, 2026, needs more optimization.
7 481 0.708095396023 Henry Cohn, 2025, needs more optimization.
7 482 0.708101389020 Henry Cohn, 2025, needs more optimization.
7 484 0.708113876563 Henry Cohn, 2026, needs more optimization.
7 486 0.708180044040 Henry Cohn, 2026, needs more optimization.
7 488 0.708460763259 Henry Cohn, 2026, needs more optimization.
7 489 0.708483139185 Henry Cohn, 2026, needs more optimization.
7 490 0.708554397780 Henry Cohn, 2026, needs more optimization.
7 491 0.708679022412 Henry Cohn, 2026, needs more optimization.
7 492 0.708950875015 Henry Cohn, 2026, needs more optimization.
7 493 0.709329693366 Henry Cohn, 2026, needs more optimization.
7 495 0.709342566356 Henry Cohn, 2026, needs more optimization.
7 497 0.709385652205 Henry Cohn, 2026, needs more optimization.
7 498 0.710177029821 Henry Cohn, 2026, needs more optimization.
7 500 0.710662666537 Henry Cohn, 2026, needs more optimization.
7 501 0.710715390615 Henry Cohn, 2026, needs more optimization.
7 502 0.710741250118 Henry Cohn, 2026, needs more optimization.
7 503 0.710804090259 Henry Cohn, 2026, needs more optimization.
7 504 0.711088772535 Henry Cohn, 2026, needs more optimization.
7 505 0.711110226360 Henry Cohn, 2026, needs more optimization.
7 506 0.711127506791 Henry Cohn, 2026, needs more optimization.
7 508 0.711500454141 Henry Cohn, 2026, needs more optimization.
7 510 0.711574159107 Henry Cohn, 2026, needs more optimization.
7 512 0.712280029239 Henry Cohn, 2026, needs more optimization.
7 513 0.712509660408 Henry Cohn, 2026, needs more optimization.
7 514 0.712574202709 Henry Cohn, 2026, needs more optimization.
7 516 0.713742845397 Henry Cohn, 2026, needs more optimization.
7 520 0.713756365533 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 0.738212208737 Henry Cohn, 2025, needs more optimization.
7 634 0.738290846780 Henry Cohn, 2025, needs more optimization.
7 635 0.738514957398 Henry Cohn, 2025, needs more optimization.
7 636 0.738698883856 Henry Cohn, 2026, needs more optimization.
7 637 0.738806782327 Henry Cohn, 2026, needs more optimization.
7 638 0.738808878795 Henry Cohn, 2026, needs more optimization.
7 639 0.739206238069 Henry Cohn, 2026, needs more optimization.
7 640 0.739410094536 Henry Cohn, 2026, needs more optimization.
7 641 0.739502099602 Henry Cohn, 2026, needs more optimization.
7 642 0.739557467245 Henry Cohn, 2025, needs more optimization.
7 643 0.739677329979 Henry Cohn, 2025, needs more optimization.
7 644 0.739935385449 Henry Cohn, 2025, needs more optimization.
7 645 0.740062240505 Henry Cohn, 2026, needs more optimization.
7 647 0.740092985796 Henry Cohn, 2025, needs more optimization.
7 648 0.740196705783 Henry Cohn, 2025, needs more optimization.
7 649 0.740485861272 Henry Cohn, 2025, needs more optimization.
7 650 0.740489698240 Henry Cohn, 2025, needs more optimization.
7 651 0.740776270368 Henry Cohn, 2025, needs more optimization.
7 652 0.740795119630 Henry Cohn, 2025, needs more optimization.
7 653 0.740853998009 Henry Cohn, 2025, needs more optimization.
7 654 0.741007859949 Henry Cohn, 2025, needs more optimization.
7 655 0.741108984239 Henry Cohn, 2025, needs more optimization.
7 656 0.741266212351 Henry Cohn, 2025, needs more optimization.
7 657 0.741423963467 Henry Cohn, 2026, needs more optimization.
7 658 0.741587488811 Henry Cohn, 2026, needs more optimization.
7 659 0.741791365530 Henry Cohn, 2025, needs more optimization.
7 660 0.741797653020 Henry Cohn, 2025, needs more optimization.
7 661 0.742249283144 Henry Cohn, 2025, needs more optimization.
7 662 0.742253219354 Henry Cohn, 2025, needs more optimization.
7 663 0.742720226175 Henry Cohn, 2025, needs more optimization.
7 664 0.742758591108 Henry Cohn, 2025, needs more optimization.
7 665 0.742766297023 Henry Cohn, 2025, needs more optimization.
7 666 0.742808097093 Henry Cohn, 2026, needs more optimization.
7 667 0.743019244916 Henry Cohn, 2025, needs more optimization.
7 668 0.743123047682 Henry Cohn, 2026, needs more optimization.
7 669 0.743288678978 Henry Cohn, 2026, needs more optimization.
7 670 0.743468933950 Henry Cohn, 2025, needs more optimization.
7 671 0.743614433987 Henry Cohn, 2025, needs more optimization.
7 672 0.743762300778 Henry Cohn, 2026, needs more optimization.
7 673 0.743822788935 Henry Cohn, 2025, needs more optimization.
7 674 0.744018818012 Henry Cohn, 2025, needs more optimization.
7 675 0.744115543873 Henry Cohn, 2025, needs more optimization.
7 676 0.744122647767 Henry Cohn, 2025, needs more optimization.
7 677 0.744214110035 Henry Cohn, 2025, needs more optimization.
7 678 0.744328612114 Henry Cohn, 2025, needs more optimization.
7 679 0.744583672177 Henry Cohn, 2026, needs more optimization.
7 680 0.744712905884 Henry Cohn, 2026, needs more optimization.
7 682 0.745009803213 Henry Cohn, 2025, needs more optimization.
7 683 0.745055262785 Henry Cohn, 2025, needs more optimization.
7 684 0.745058045885 Henry Cohn, 2026, needs more optimization.
7 685 0.745265338477 Henry Cohn, 2025, needs more optimization.
7 686 0.745379029546 Henry Cohn, 2026, needs more optimization.
7 687 0.745383341663 Henry Cohn, 2025, needs more optimization.
7 688 0.745567673171 Henry Cohn, 2025, needs more optimization.
7 689 0.745734483386 Henry Cohn, 2025, needs more optimization.
7 690 0.746062644359 Henry Cohn, 2025, needs more optimization.
7 691 0.746134729202 Henry Cohn, 2025, needs more optimization.
7 692 0.746182295167 Henry Cohn, 2025, needs more optimization.
7 693 0.746191941399 Henry Cohn, 2025, needs more optimization.
7 694 0.746433240393 Henry Cohn, 2025, needs more optimization.
7 695 0.746453416511 Henry Cohn, 2025, needs more optimization.
7 696 0.746467272171 Henry Cohn, 2025, needs more optimization.
7 697 0.746714567018 Henry Cohn, 2025, needs more optimization.
7 698 0.746721146572 Henry Cohn, 2025, needs more optimization.
7 699 0.746954039717 Henry Cohn, 2025, needs more optimization.
7 700 0.747005610616 Henry Cohn, 2026, needs more optimization.
7 701 0.747371942318 Henry Cohn, 2025, needs more optimization.
7 702 0.747505954487 Henry Cohn, 2025, needs more optimization.
7 703 0.747608060458 Henry Cohn, 2026, needs more optimization.
7 704 0.747814725681 Henry Cohn, 2026, needs more optimization.
7 705 0.747824940385 Henry Cohn, 2025, needs more optimization.
7 706 0.748150243104 Henry Cohn, 2025, needs more optimization.
7 707 0.748167879463 Henry Cohn, 2025, needs more optimization.
7 708 0.748223892857 Henry Cohn, 2026, needs more optimization.
7 709 0.748384853776 Henry Cohn, 2025, needs more optimization.
7 710 0.748428183132 Henry Cohn, 2025, needs more optimization.
7 711 0.748678551785 Henry Cohn, 2026, needs more optimization.
7 712 0.748806097949 Henry Cohn, 2026, needs more optimization.
7 713 0.748972920661 Henry Cohn, 2026, needs more optimization.
7 714 0.749018670235 Henry Cohn, 2025, needs more optimization.
7 715 0.749221951020 Henry Cohn, 2025, needs more optimization.
7 716 0.749387656241 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 0.766304091493 Henry Cohn, 2025, needs more optimization.
7 884 0.766418771944 Henry Cohn, 2025, needs more optimization.
7 885 0.766525239704 Henry Cohn, 2025, needs more optimization.
7 886 0.766527594674 Henry Cohn, 2025, needs more optimization.
7 887 0.766864400562 Henry Cohn, 2026, needs more optimization.
7 888 0.766885779552 Henry Cohn, 2026, needs more optimization.
7 889 0.766889331520 Henry Cohn, 2026, needs more optimization.
7 890 0.767018124487 Henry Cohn, 2025, needs more optimization.
7 891 0.767083852054 Henry Cohn, 2026, needs more optimization.
7 892 0.767231569550 Henry Cohn, 2025, needs more optimization.
7 893 0.767251169955 Henry Cohn, 2026, needs more optimization.
7 894 0.767257094381 Henry Cohn, 2026, needs more optimization.
7 895 0.767391546637 Henry Cohn, 2025, needs more optimization.
7 896 0.767401946186 Henry Cohn, 2025, needs more optimization.
7 897 0.767681720564 Henry Cohn, 2025, needs more optimization.
7 898 0.767731981893 Henry Cohn, 2026, needs more optimization.
7 899 0.767736873146 Henry Cohn, 2025, needs more optimization.
7 900 0.767809065227 Henry Cohn, 2026, needs more optimization.
7 901 0.768010151877 Henry Cohn, 2025, needs more optimization.
7 902 0.768013173488 Henry Cohn, 2025, needs more optimization.
7 904 0.768138005293 Henry Cohn, 2025, needs more optimization.
7 905 0.768349270409 Henry Cohn, 2025, needs more optimization.
7 906 0.768388903761 Henry Cohn, 2026, needs more optimization.
7 907 0.768518067748 Henry Cohn, 2025, needs more optimization.
7 908 0.768580271112 Henry Cohn, 2025, needs more optimization.
7 909 0.768713496939 Henry Cohn, 2025, needs more optimization.
7 910 0.768739341134 Henry Cohn, 2025, needs more optimization.
7 911 0.768770505285 Henry Cohn, 2026, needs more optimization.
7 913 0.768957366848 Henry Cohn, 2025, needs more optimization.
7 914 0.768959087661 Henry Cohn, 2026, needs more optimization.
7 915 0.769192254989 Henry Cohn, 2025, needs more optimization.
7 916 0.769195854871 Henry Cohn, 2026, needs more optimization.
7 917 0.769205025913 Henry Cohn, 2025, needs more optimization.
7 918 0.769532233218 Henry Cohn, 2025, needs more optimization.
7 919 0.769536044854 Henry Cohn, 2025, needs more optimization.
7 920 0.769700440865 Henry Cohn, 2025, needs more optimization.
7 921 0.769706804461 Henry Cohn, 2025, needs more optimization.
7 922 0.769879798173 Henry Cohn, 2026, needs more optimization.
7 923 0.769907148927 Henry Cohn, 2026, needs more optimization.
7 924 0.769923720137 Henry Cohn, 2026, needs more optimization.
7 925 0.769964729931 Henry Cohn, 2025, needs more optimization.
7 926 0.769997961235 Henry Cohn, 2025, needs more optimization.
7 927 0.770123058479 Henry Cohn, 2025, needs more optimization.
7 928 0.770256536122 Henry Cohn, 2026, needs more optimization.
7 929 0.770260744309 Henry Cohn, 2026, needs more optimization.
7 930 0.770302505224 Henry Cohn, 2025, needs more optimization.
7 931 0.770575709793 Henry Cohn, 2025, needs more optimization.
7 932 0.770579743316 Henry Cohn, 2025, needs more optimization.
7 933 0.770595690567 Henry Cohn, 2025, needs more optimization.
7 934 0.770628045341 Henry Cohn, 2025, needs more optimization.
7 935 0.770770168786 Henry Cohn, 2025, needs more optimization.
7 937 0.770899391053 Henry Cohn, 2026, needs more optimization.
7 938 0.771165856307 Henry Cohn, 2025, needs more optimization.
7 939 0.771169572134 Henry Cohn, 2025, needs more optimization.
7 940 0.771215436337 Henry Cohn, 2026, needs more optimization.
7 941 0.771239312708 Henry Cohn, 2025, needs more optimization.
7 943 0.771360024917 Henry Cohn, 2026, needs more optimization.
7 944 0.771503310438 Henry Cohn, 2025, needs more optimization.
7 945 0.771522679568 Henry Cohn, 2026, needs more optimization.
7 946 0.771742521096 Henry Cohn, 2025, needs more optimization.
7 948 0.771748841996 Henry Cohn, 2025, needs more optimization.
7 949 0.771757569216 Henry Cohn, 2025, needs more optimization.
7 950 0.771904683046 Henry Cohn, 2025, needs more optimization.
7 951 0.772123382659 Henry Cohn, 2025, needs more optimization.
7 952 0.772237080380 Henry Cohn, 2026, needs more optimization.
7 953 0.772239159993 Henry Cohn, 2026, needs more optimization.
7 954 0.772255413298 Henry Cohn, 2025, needs more optimization.
7 955 0.772542605323 Henry Cohn, 2025, needs more optimization.
7 956 0.772595320218 Henry Cohn, 2025, needs more optimization.
7 957 0.772601217064 Henry Cohn, 2026, needs more optimization.
7 959 0.772738527814 Henry Cohn, 2025, needs more optimization.
7 960 0.772837170696 Henry Cohn, 2026, needs more optimization.
7 961 0.772843474814 Henry Cohn, 2025, needs more optimization.
7 962 0.772926069897 Henry Cohn, 2025, needs more optimization.
7 963 0.773161630297 Henry Cohn, 2025, needs more optimization.
7 965 0.773200621725 Henry Cohn, 2025, needs more optimization.
7 966 0.773221993721 Henry Cohn, 2026, needs more optimization.
7 967 0.773310465530 Henry Cohn, 2026, needs more optimization.
7 968 0.773534895672 Henry Cohn, 2025, needs more optimization.
7 969 0.773634537960 Henry Cohn, 2025, needs more optimization.
7 970 0.773635294831 Henry Cohn, 2026, needs more optimization.
7 971 0.773822099300 Henry Cohn, 2025, needs more optimization.
7 972 0.773827494958 Henry Cohn, 2025, needs more optimization.
7 973 0.773834788495 Henry Cohn, 2025, needs more optimization.
7 974 0.773952851955 Henry Cohn, 2025, needs more optimization.
7 975 0.774070505394 Henry Cohn, 2026, needs more optimization.
7 976 0.774179541403 Henry Cohn, 2026, needs more optimization.
7 977 0.774221790291 Henry Cohn, 2025, needs more optimization.
7 978 0.774231409619 Henry Cohn, 2025, needs more optimization.
7 979 0.774443310796 Henry Cohn, 2025, needs more optimization.
7 980 0.774464634630 Henry Cohn, 2026, needs more optimization.
7 981 0.774489936361 Henry Cohn, 2025, needs more optimization.
7 982 0.774497955386 Henry Cohn, 2025, needs more optimization.
7 983 0.774644943776 Henry Cohn, 2026, needs more optimization.
7 985 0.774756465462 Henry Cohn, 2025, needs more optimization.
7 986 0.774774748227 Henry Cohn, 2025, needs more optimization.
7 987 0.774872741252 Henry Cohn, 2025, needs more optimization.
7 988 0.775041594845 Henry Cohn, 2025, needs more optimization.
7 989 0.775061512097 Henry Cohn, 2025, needs more optimization.
7 990 0.775268368778 Henry Cohn, 2025, needs more optimization.
7 991 0.775275612377 Henry Cohn, 2025, needs more optimization.
7 992 0.775423925764 Henry Cohn, 2025, needs more optimization.
7 993 0.775430697361 Henry Cohn, 2026, needs more optimization.
7 994 0.775449990401 Henry Cohn, 2026, needs more optimization.
7 995 0.775632598837 Henry Cohn, 2025, needs more optimization.
7 996 0.775669217867 Henry Cohn, 2026, needs more optimization.
7 997 0.775704293887 Henry Cohn, 2025, needs more optimization.
7 998 0.775770821979 Henry Cohn, 2026, needs more optimization.
7 999 0.775775463625 Henry Cohn, 2025, needs more optimization.
7 1000 0.775855223040 Henry Cohn, 2026, needs more optimization.
7 1001 0.776024150867 Henry Cohn, 2025, needs more optimization.
7 1002 0.776036634130 Henry Cohn, 2026, needs more optimization.
7 1003 0.776176572478 Henry Cohn, 2025, needs more optimization.
7 1004 0.776184751487 Henry Cohn, 2025, needs more optimization.
7 1005 0.776327111003 Henry Cohn, 2025, needs more optimization.
7 1006 0.776380105971 Henry Cohn, 2025, needs more optimization.
7 1007 0.776425871372 Henry Cohn, 2025, needs more optimization.
7 1008 0.776753227999 Henry Cohn, 2025, needs more optimization.
7 1009 0.776757501902 Henry Cohn, 2025, needs more optimization.
7 1010 0.776792237242 Henry Cohn, 2026, needs more optimization.
7 1012 0.776978114898 Henry Cohn, 2025, needs more optimization.
7 1013 0.777161042973 Henry Cohn, 2025, needs more optimization.
7 1014 0.777180183121 Henry Cohn, 2025, needs more optimization.
7 1015 0.777231130326 Henry Cohn, 2025, needs more optimization.
7 1016 0.777352916164 Henry Cohn, 2026, needs more optimization.
7 1017 0.777362033599 Henry Cohn, 2025, needs more optimization.
7 1018 0.777407561032 Henry Cohn, 2026, needs more optimization.
7 1019 0.777485256086 Henry Cohn, 2025, needs more optimization.
7 1020 0.777811702770 Henry Cohn, 2025, needs more optimization.
7 1021 0.777828074942 Henry Cohn, 2026, needs more optimization.
7 1022 0.777990478570 Henry Cohn, 2025, needs more optimization.
7 1023 0.777994305436 Henry Cohn, 2025, needs more optimization.
7 1024 0.778006655112 Henry Cohn, 2025, 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 0.315283655377 Henry Cohn, 2025.
8 51 0.316850575857 Henry Cohn, 2023.
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 0.374360545517 Henry Cohn, 2023.
8 74 0.375030122030 Henry Cohn, 2025.
8 75 0.380147254829 Henry Cohn, 2024.
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 0.399272012697 Henry Cohn, 2024.
8 81 0.401670700481 Henry Cohn, 2026, needs more optimization.
8 82 0.402283801532 Henry Cohn, 2025.
8 83 0.405303858040 Henry Cohn, 2026.
8 84 0.405612978673 Henry Cohn, 2026, needs more optimization.
8 85 0.413778833762 Henry Cohn, 2025.
8 86 0.416857867243 Henry Cohn, 2026, needs more optimization.
8 88 0.418782717642 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.
32⁢x3−8⁢x+1
8 89 0.421249110346 Henry Cohn, 2026, needs more optimization.
8 90 0.422389551109 Henry Cohn, 2026, needs more optimization.
8 91 0.423510643961 Henry Cohn, 2026, needs more optimization.
8 92 0.424439081882 Henry Cohn, 2026, needs more optimization.
8 93 0.425292960391 Henry Cohn, 2026, needs more optimization.
8 94 0.425631527117 Henry Cohn, 2026, needs more optimization.
8 95 0.426690121416 Henry Cohn, 2026, needs more optimization.
8 96 0.427525768702 Henry Cohn, 2026, needs more optimization.
8 97 0.428526010827 Henry Cohn, 2025, needs more optimization.
8 99 0.428564490087 Henry Cohn, 2025, needs more optimization.
8 100 0.428571420298 Henry Cohn, 2026, needs more optimization.
8 101 0.428571428376 Henry Cohn, 2026, needs more optimization.
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 0.447648906786 Henry Cohn, 2026, needs more optimization.
8 116 0.448022446705 Henry Cohn, 2026, needs more optimization.
8 117 0.451867492073 Henry Cohn, 2026, needs more optimization.
8 118 0.455382682228 Henry Cohn, 2026, needs more optimization.
8 119 0.461439727641 Henry Cohn, 2026, needs more optimization.
8 121 0.461848100275 Henry Cohn, 2026, needs more optimization.
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 0.468486456439 Henry Cohn, 2026, needs more optimization.
8 139 0.468833310720 Henry Cohn, 2026, needs more optimization.
8 140 0.470970373659 Henry Cohn, 2026, needs more optimization.
8 141 0.472895377418 Henry Cohn, 2026, needs more optimization.
8 143 0.476795268384 Henry Cohn, 2026, needs more optimization.
8 144 0.485909533389 Henry Cohn, 2026, needs more optimization.
8 145 0.487188350515 Henry Cohn, 2026, needs more optimization.
8 146 0.488764586843 Henry Cohn, 2026, needs more optimization.
8 147 0.488771436281 Henry Cohn, 2026, needs more optimization.
8 148 0.490081623969 Henry Cohn, 2026, needs more optimization.
8 149 0.490634833944 Henry Cohn, 2026, needs more optimization.
8 151 0.490701500207 Henry Cohn, 2026, needs more optimization.
8 152 0.491613519779 Henry Cohn, 2026, needs more optimization.
8 153 0.492647014977 Henry Cohn, 2026, needs more optimization.
8 154 0.492959170105 Henry Cohn, 2026, needs more optimization.
8 155 0.493381689601 Henry Cohn, 2026, needs more optimization.
8 156 0.494251104764 Henry Cohn, 2026, needs more optimization.
8 157 0.494689594539 Henry Cohn, 2026, needs more optimization.
8 158 0.494983880679 Henry Cohn, 2026, needs more optimization.
8 159 0.496070148668 Henry Cohn, 2026, needs more optimization.
8 160 0.497671396486 Henry Cohn, 2026, needs more optimization.
8 161 0.497743289608 Henry Cohn, 2026, needs more optimization.
8 163 0.498036850999 Henry Cohn, 2026, needs more optimization.
8 167 0.498497861414 Henry Cohn, 2026, needs more optimization.
8 169 0.499606890510 Henry Cohn, 2026, needs more optimization.
8 170 0.499799425368 Henry Cohn, 2026, needs more optimization.
8 171 0.499928111998 Henry Cohn, 2026, needs more optimization.
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 0.544322669198 Henry Cohn, 2025, needs more optimization.
8 243 0.547703296571 Henry Cohn, 2024, needs more optimization.
8 244 0.550048376215 Henry Cohn, 2026, needs more optimization.
8 245 0.553653350879 Henry Cohn, 2025, needs more optimization.
8 246 0.554250154231 Henry Cohn, 2026, needs more optimization.
8 247 0.555877591876 Henry Cohn, 2026, needs more optimization.
8 248 0.558077949649 Henry Cohn, 2025, needs more optimization.
8 249 0.559446693208 Henry Cohn, 2025, needs more optimization.
8 250 0.560899555304 Henry Cohn, 2026, needs more optimization.
8 251 0.562047246263 Henry Cohn, 2025, needs more optimization.
8 252 0.564084932721 Henry Cohn, 2025, needs more optimization.
8 253 0.564179734130 Henry Cohn, 2026, needs more optimization.
8 254 0.564446060757 Henry Cohn, 2026, needs more optimization.
8 255 0.564558725654 Henry Cohn, 2025, needs more optimization.
8 256 0.564930782139 Henry Cohn, 2026, needs more optimization.
8 257 0.565191770046 Henry Cohn, 2025, needs more optimization.
8 259 0.568921803026 Henry Cohn, 2025, needs more optimization.
8 260 0.570454503740 Henry Cohn, 2026, needs more optimization.
8 261 0.571550056509 Henry Cohn, 2026, needs more optimization.
8 262 0.572820528622 Henry Cohn, 2026, needs more optimization.
8 263 0.573886460433 Henry Cohn, 2026, needs more optimization.
8 264 0.575008884250 Henry Cohn, 2026, needs more optimization.
8 265 0.575339813754 Henry Cohn, 2026, needs more optimization.
8 266 0.575646354485 Henry Cohn, 2026, needs more optimization.
8 267 0.576779204505 Henry Cohn, 2026, needs more optimization.
8 268 0.576850517457 Henry Cohn, 2026, needs more optimization.
8 269 0.576933471753 Henry Cohn, 2026, needs more optimization.
8 270 0.578143903584 Henry Cohn, 2026, needs more optimization.
8 271 0.578167917269 Henry Cohn, 2026, needs more optimization.
8 272 0.579566810513 Henry Cohn, 2026, needs more optimization.
8 273 0.579679677940 Henry Cohn, 2026, needs more optimization.
8 274 0.580059677099 Henry Cohn, 2026, needs more optimization.
8 275 0.581581374637 Henry Cohn, 2026, needs more optimization.
8 279 0.582073972917 Henry Cohn, 2026, needs more optimization.
8 282 0.582626137844 Henry Cohn, 2026, needs more optimization.
8 283 0.584977149361 Henry Cohn, 2026, needs more optimization.
8 284 0.585015614463 Henry Cohn, 2026, needs more optimization.
8 285 0.585071005644 Henry Cohn, 2026, needs more optimization.
8 286 0.585871253791 Henry Cohn, 2026, needs more optimization.
8 287 0.585976173670 Henry Cohn, 2026, needs more optimization.
8 288 0.586253292883 Henry Cohn, 2026, needs more optimization.
8 289 0.586254842860 Henry Cohn, 2026, needs more optimization.
8 290 0.586715382525 Henry Cohn, 2026, needs more optimization.
8 291 0.587456824680 Henry Cohn, 2026, needs more optimization.
8 292 0.587536509739 Henry Cohn, 2026, needs more optimization.
8 293 0.590459812898 Henry Cohn, 2026, needs more optimization.
8 294 0.590524245112 Henry Cohn, 2026, needs more optimization.
8 295 0.590655382592 Henry Cohn, 2026, needs more optimization.
8 296 0.590656469336 Henry Cohn, 2026, needs more optimization.
8 297 0.590892429638 Henry Cohn, 2026, needs more optimization.
8 298 0.590895383586 Henry Cohn, 2026, needs more optimization.
8 300 0.590945528568 Henry Cohn, 2026, needs more optimization.
8 304 0.591537423177 Henry Cohn, 2026, needs more optimization.
8 307 0.592025825256 Henry Cohn, 2026, needs more optimization.
8 309 0.592250069302 Henry Cohn, 2026, needs more optimization.
8 310 0.592250069348 Henry Cohn, 2026, needs more optimization.
8 311 0.600392682840 Henry Cohn, 2025, needs more optimization.
8 312 0.600857275911 Henry Cohn, 2025, needs more optimization.
8 313 0.601247557345 Henry Cohn, 2025, needs more optimization.
8 314 0.601604875833 Henry Cohn, 2025, needs more optimization.
8 315 0.601754794772 Henry Cohn, 2025, needs more optimization.
8 316 0.601886263116 Henry Cohn, 2025, needs more optimization.
8 317 0.602304929605 Henry Cohn, 2025, needs more optimization.
8 318 0.604495111714 Henry Cohn, 2025, needs more optimization.
8 319 0.604822638198 Henry Cohn, 2025, needs more optimization.
8 320 0.605769909395 Henry Cohn, 2026, needs more optimization.
8 321 0.606080632890 Henry Cohn, 2025, needs more optimization.
8 322 0.606676646313 Henry Cohn, 2025, needs more optimization.
8 323 0.606748296967 Henry Cohn, 2025, needs more optimization.
8 325 0.606875669076 Henry Cohn, 2025, needs more optimization.
8 326 0.607207281517 Henry Cohn, 2025, needs more optimization.
8 327 0.608149701647 Henry Cohn, 2025, needs more optimization.
8 328 0.608181717009 Henry Cohn, 2026, needs more optimization.
8 329 0.608320338402 Henry Cohn, 2025, needs more optimization.
8 330 0.609064020319 Henry Cohn, 2025, needs more optimization.
8 331 0.609197149344 Henry Cohn, 2025, needs more optimization.
8 332 0.609790935425 Henry Cohn, 2025, needs more optimization.
8 333 0.609869023821 Henry Cohn, 2025, needs more optimization.
8 334 0.610018411770 Henry Cohn, 2025, needs more optimization.
8 335 0.610073776765 Henry Cohn, 2025, needs more optimization.
8 336 0.610729053233 Henry Cohn, 2026, needs more optimization.
8 337 0.610839137829 Henry Cohn, 2025, needs more optimization.
8 338 0.611612890703 Henry Cohn, 2025, needs more optimization.
8 339 0.611899638127 Henry Cohn, 2025, needs more optimization.
8 340 0.611902448506 Henry Cohn, 2025, needs more optimization.
8 341 0.612146643052 Henry Cohn, 2025, needs more optimization.
8 342 0.612148803025 Henry Cohn, 2025, needs more optimization.
8 343 0.612154038153 Henry Cohn, 2025, needs more optimization.
8 344 0.612780479272 Henry Cohn, 2026, needs more optimization.
8 345 0.612945172261 Henry Cohn, 2025, needs more optimization.
8 346 0.613013252673 Henry Cohn, 2026, needs more optimization.
8 348 0.613901448115 Henry Cohn, 2025, needs more optimization.
8 349 0.613958393143 Henry Cohn, 2025, needs more optimization.
8 350 0.614081594495 Henry Cohn, 2025, needs more optimization.
8 351 0.614693773399 Henry Cohn, 2025, needs more optimization.
8 352 0.615043453221 Henry Cohn, 2026, needs more optimization.
8 353 0.615891488252 Henry Cohn, 2025, needs more optimization.
8 354 0.616147123726 Henry Cohn, 2025, needs more optimization.
8 355 0.616343028699 Henry Cohn, 2025, needs more optimization.
8 356 0.616552318905 Henry Cohn, 2025, needs more optimization.
8 357 0.616557922801 Henry Cohn, 2025, needs more optimization.
8 358 0.616753657402 Henry Cohn, 2025, needs more optimization.
8 359 0.617239684539 Henry Cohn, 2025, needs more optimization.
8 360 0.617327508249 Henry Cohn, 2026, needs more optimization.
8 361 0.617622312575 Henry Cohn, 2025, needs more optimization.
8 363 0.618218429962 Henry Cohn, 2025, needs more optimization.
8 364 0.618873826037 Henry Cohn, 2025, needs more optimization.
8 365 0.618946330794 Henry Cohn, 2025, needs more optimization.
8 366 0.619533958360 Henry Cohn, 2025, needs more optimization.
8 367 0.619566098791 Henry Cohn, 2025, needs more optimization.
8 368 0.620019189187 Henry Cohn, 2025, needs more optimization.
8 369 0.620799329733 Henry Cohn, 2025, needs more optimization.
8 370 0.621212628217 Henry Cohn, 2025, needs more optimization.
8 371 0.621219399291 Henry Cohn, 2025, needs more optimization.
8 372 0.621278546847 Henry Cohn, 2025, needs more optimization.
8 373 0.621439323831 Henry Cohn, 2025, needs more optimization.
8 374 0.621809961723 Henry Cohn, 2025, needs more optimization.
8 375 0.622680026091 Henry Cohn, 2025, needs more optimization.
8 376 0.622721928823 Henry Cohn, 2026, needs more optimization.
8 377 0.623361057450 Henry Cohn, 2025, needs more optimization.
8 378 0.623375974656 Henry Cohn, 2025, needs more optimization.
8 379 0.623561181724 Henry Cohn, 2025, needs more optimization.
8 380 0.623745956911 Henry Cohn, 2025, needs more optimization.
8 381 0.624750658484 Henry Cohn, 2025, needs more optimization.
8 382 0.624770012520 Henry Cohn, 2025, needs more optimization.
8 383 0.624991249003 Henry Cohn, 2025, needs more optimization.
8 384 0.625403316793 Henry Cohn, 2025, needs more optimization.
8 385 0.625724677010 Henry Cohn, 2025, needs more optimization.
8 386 0.626127695908 Henry Cohn, 2025, needs more optimization.
8 388 0.626432231530 Henry Cohn, 2025, needs more optimization.
8 389 0.626962564375 Henry Cohn, 2025, needs more optimization.
8 390 0.627640882088 Henry Cohn, 2025, needs more optimization.
8 391 0.628205858700 Henry Cohn, 2025, needs more optimization.
8 392 0.628294232678 Henry Cohn, 2025, needs more optimization.
8 393 0.628396377236 Henry Cohn, 2025, needs more optimization.
8 394 0.628399885301 Henry Cohn, 2025, needs more optimization.
8 395 0.628659533842 Henry Cohn, 2025, needs more optimization.
8 396 0.629105201649 Henry Cohn, 2025, needs more optimization.
8 397 0.629169317910 Henry Cohn, 2025, needs more optimization.
8 398 0.629882033172 Henry Cohn, 2025, needs more optimization.
8 399 0.629897232379 Henry Cohn, 2025, needs more optimization.
8 400 0.630174839577 Henry Cohn, 2025, needs more optimization.
8 401 0.631382584291 Henry Cohn, 2025, needs more optimization.
8 402 0.631390153886 Henry Cohn, 2025, needs more optimization.
8 403 0.631491811937 Henry Cohn, 2025, needs more optimization.
8 404 0.631523250496 Henry Cohn, 2025, needs more optimization.
8 405 0.632217833561 Henry Cohn, 2025, needs more optimization.
8 406 0.632349801223 Henry Cohn, 2025, needs more optimization.
8 407 0.632398200978 Henry Cohn, 2025, needs more optimization.
8 408 0.632751021452 Henry Cohn, 2025, needs more optimization.
8 409 0.632771125197 Henry Cohn, 2025, needs more optimization.
8 410 0.633663719121 Henry Cohn, 2025, needs more optimization.
8 411 0.633684274566 Henry Cohn, 2025, needs more optimization.
8 412 0.634038324108 Henry Cohn, 2025, needs more optimization.
8 413 0.634054592998 Henry Cohn, 2025, needs more optimization.
8 414 0.634320629040 Henry Cohn, 2025, needs more optimization.
8 415 0.634728376576 Henry Cohn, 2025, needs more optimization.
8 416 0.634814438444 Henry Cohn, 2025, needs more optimization.
8 417 0.634837438867 Henry Cohn, 2025, needs more optimization.
8 418 0.634934621158 Henry Cohn, 2025, needs more optimization.
8 419 0.635070107909 Henry Cohn, 2025, needs more optimization.
8 420 0.635489301536 Henry Cohn, 2025, needs more optimization.
8 421 0.636141198917 Henry Cohn, 2025, needs more optimization.
8 423 0.636176710499 Henry Cohn, 2025, needs more optimization.
8 424 0.636318728782 Henry Cohn, 2026, needs more optimization.
8 425 0.637001897162 Henry Cohn, 2025, needs more optimization.
8 426 0.637023119393 Henry Cohn, 2025, needs more optimization.
8 427 0.637087408572 Henry Cohn, 2025, needs more optimization.
8 428 0.637089357587 Henry Cohn, 2025, needs more optimization.
8 429 0.637091035838 Henry Cohn, 2025, needs more optimization.
8 430 0.637597366016 Henry Cohn, 2025, needs more optimization.
8 431 0.637929976400 Henry Cohn, 2026, needs more optimization.
8 432 0.638116238897 Henry Cohn, 2025, needs more optimization.
8 433 0.638534297751 Henry Cohn, 2025, needs more optimization.
8 434 0.638897270433 Henry Cohn, 2025, needs more optimization.
8 435 0.639069879825 Henry Cohn, 2025, needs more optimization.
8 436 0.639792064682 Henry Cohn, 2025, needs more optimization.
8 437 0.639809402862 Henry Cohn, 2025, needs more optimization.
8 438 0.640047960605 Henry Cohn, 2025, needs more optimization.
8 439 0.640157825639 Henry Cohn, 2025, needs more optimization.
8 440 0.640469991884 Henry Cohn, 2025, needs more optimization.
8 441 0.640506385547 Henry Cohn, 2025, needs more optimization.
8 443 0.640766099500 Henry Cohn, 2025, needs more optimization.
8 445 0.641262965109 Henry Cohn, 2025, needs more optimization.
8 446 0.641438529490 Henry Cohn, 2025, needs more optimization.
8 447 0.641482891413 Henry Cohn, 2025, needs more optimization.
8 448 0.641496880893 Henry Cohn, 2025, needs more optimization.
8 449 0.641578861091 Henry Cohn, 2025, needs more optimization.
8 450 0.641641003734 Henry Cohn, 2025, needs more optimization.
8 451 0.641797750053 Henry Cohn, 2025, needs more optimization.
8 452 0.641811557867 Henry Cohn, 2025, needs more optimization.
8 453 0.641908870744 Henry Cohn, 2025, needs more optimization.
8 454 0.641978565813 Henry Cohn, 2025, needs more optimization.
8 455 0.642174437296 Henry Cohn, 2025, needs more optimization.
8 456 0.642217378185 Henry Cohn, 2025, needs more optimization.
8 457 0.642229200426 Henry Cohn, 2025, needs more optimization.
8 458 0.642270284839 Henry Cohn, 2025, needs more optimization.
8 459 0.642632119105 Henry Cohn, 2025, needs more optimization.
8 460 0.643407825528 Henry Cohn, 2025, needs more optimization.
8 461 0.643491563350 Henry Cohn, 2025, needs more optimization.
8 462 0.643496044258 Henry Cohn, 2025, needs more optimization.
8 463 0.643541281167 Henry Cohn, 2025, needs more optimization.
8 464 0.643549393561 Henry Cohn, 2025, needs more optimization.
8 465 0.643579577026 Henry Cohn, 2025, needs more optimization.
8 466 0.643718584379 Henry Cohn, 2025, needs more optimization.
8 467 0.643732809840 Henry Cohn, 2025, needs more optimization.
8 468 0.644388241331 Henry Cohn, 2026, needs more optimization.
8 469 0.644393228166 Henry Cohn, 2025, needs more optimization.
8 470 0.644461578333 Henry Cohn, 2025, needs more optimization.
8 471 0.645133996535 Henry Cohn, 2025, needs more optimization.
8 472 0.645158393914 Henry Cohn, 2025, needs more optimization.
8 473 0.645195224081 Henry Cohn, 2025, needs more optimization.
8 474 0.645247851108 Henry Cohn, 2025, needs more optimization.
8 475 0.645262692751 Henry Cohn, 2025, needs more optimization.
8 476 0.646060671921 Henry Cohn, 2026, needs more optimization.
8 477 0.646072431746 Henry Cohn, 2025, needs more optimization.
8 478 0.646125842259 Henry Cohn, 2025, needs more optimization.
8 479 0.647189050236 Henry Cohn, 2025, needs more optimization.
8 480 0.648172971263 Henry Cohn, 2026, needs more optimization.
8 481 0.648203278480 Henry Cohn, 2025, needs more optimization.
8 482 0.648231152639 Henry Cohn, 2025, needs more optimization.
8 483 0.648257524986 Henry Cohn, 2025, needs more optimization.
8 484 0.648301006016 Henry Cohn, 2025, needs more optimization.
8 485 0.648304156375 Henry Cohn, 2025, needs more optimization.
8 486 0.648379802504 Henry Cohn, 2025, needs more optimization.
8 488 0.648409107473 Henry Cohn, 2025, needs more optimization.
8 489 0.648878574511 Henry Cohn, 2025, needs more optimization.
8 491 0.648969005235 Henry Cohn, 2025, needs more optimization.
8 492 0.649044714764 Henry Cohn, 2026, needs more optimization.
8 495 0.649395489506 Henry Cohn, 2025, needs more optimization.
8 496 0.650342450429 Henry Cohn, 2026, needs more optimization.
8 497 0.650460855550 Henry Cohn, 2026, needs more optimization.
8 498 0.651812874290 Henry Cohn, 2025, needs more optimization.
8 499 0.651821743715 Henry Cohn, 2025, needs more optimization.
8 500 0.651864776838 Henry Cohn, 2025, needs more optimization.
8 501 0.651903079136 Henry Cohn, 2025, needs more optimization.
8 504 0.651983459840 Henry Cohn, 2026, needs more optimization.
8 506 0.652606806992 Henry Cohn, 2025, needs more optimization.
8 508 0.652625400184 Henry Cohn, 2026, needs more optimization.
8 509 0.652692843143 Henry Cohn, 2025, needs more optimization.
8 510 0.652761675344 Henry Cohn, 2025, needs more optimization.
8 511 0.653822844364 Henry Cohn, 2025, needs more optimization.
8 512 0.653824945416 Henry Cohn, 2025, needs more optimization.
8 513 0.653916433203 Henry Cohn, 2025, needs more optimization.
8 514 0.653949826228 Henry Cohn, 2025, needs more optimization.
8 515 0.653957938818 Henry Cohn, 2025, needs more optimization.
8 517 0.654161754594 Henry Cohn, 2025, needs more optimization.
8 519 0.654636126810 Henry Cohn, 2025, needs more optimization.
8 520 0.655352966131 Henry Cohn, 2025, needs more optimization.
8 522 0.655378986905 Henry Cohn, 2025, needs more optimization.
8 523 0.655409138883 Henry Cohn, 2025, needs more optimization.
8 524 0.655432550572 Henry Cohn, 2025, needs more optimization.
8 526 0.656607371810 Henry Cohn, 2025, needs more optimization.
8 528 0.656622819844 Henry Cohn, 2026, needs more optimization.
8 529 0.656662772223 Henry Cohn, 2025, needs more optimization.
8 530 0.656667219490 Henry Cohn, 2025, needs more optimization.
8 531 0.656677786317 Henry Cohn, 2025, needs more optimization.
8 532 0.656705658565 Henry Cohn, 2026, needs more optimization.
8 534 0.656816987118 Henry Cohn, 2025, needs more optimization.
8 535 0.657707828098 Henry Cohn, 2025, needs more optimization.
8 536 0.657712569744 Henry Cohn, 2025, needs more optimization.
8 537 0.657727538788 Henry Cohn, 2025, needs more optimization.
8 538 0.657963683933 Henry Cohn, 2026, needs more optimization.
8 539 0.659017871832 Henry Cohn, 2025, needs more optimization.
8 540 0.659064677191 Henry Cohn, 2026, needs more optimization.
8 541 0.659074917342 Henry Cohn, 2025, needs more optimization.
8 542 0.659268935193 Henry Cohn, 2025, needs more optimization.
8 543 0.660020360645 Henry Cohn, 2025, needs more optimization.
8 544 0.660026024022 Henry Cohn, 2025, needs more optimization.
8 545 0.660034658104 Henry Cohn, 2025, needs more optimization.
8 546 0.660039231384 Henry Cohn, 2025, needs more optimization.
8 547 0.660052739108 Henry Cohn, 2025, needs more optimization.
8 548 0.660077488246 Henry Cohn, 2026, needs more optimization.
8 551 0.660974086809 Henry Cohn, 2025, needs more optimization.
8 552 0.660987073712 Henry Cohn, 2025, needs more optimization.
8 553 0.661549468537 Henry Cohn, 2025, needs more optimization.
8 554 0.661937000088 Henry Cohn, 2025, needs more optimization.
8 555 0.661938005024 Henry Cohn, 2025, needs more optimization.
8 556 0.661961369488 Henry Cohn, 2025, needs more optimization.
8 557 0.662037705835 Henry Cohn, 2025, needs more optimization.
8 558 0.662468653075 Henry Cohn, 2025, needs more optimization.
8 561 0.662973680970 Henry Cohn, 2025, needs more optimization.
8 563 0.663021420021 Henry Cohn, 2025, needs more optimization.
8 564 0.663029029492 Henry Cohn, 2025, needs more optimization.
8 565 0.663035818985 Henry Cohn, 2025, needs more optimization.
8 566 0.663101282161 Henry Cohn, 2025, needs more optimization.
8 567 0.663892412862 Henry Cohn, 2025, needs more optimization.
8 568 0.663926371318 Henry Cohn, 2025, needs more optimization.
8 569 0.664046024545 Henry Cohn, 2025, needs more optimization.
8 570 0.664623961042 Henry Cohn, 2025, needs more optimization.
8 571 0.664637068515 Henry Cohn, 2025, needs more optimization.
8 572 0.664702818723 Henry Cohn, 2026, needs more optimization.
8 576 0.665248884435 Henry Cohn, 2026, needs more optimization.
8 580 0.665302826327 Henry Cohn, 2026, needs more optimization.
8 581 0.665350887801 Henry Cohn, 2025, needs more optimization.
8 584 0.665379649120 Henry Cohn, 2025, needs more optimization.
8 586 0.665380549827 Henry Cohn, 2025, needs more optimization.
8 587 0.665435047722 Henry Cohn, 2025, needs more optimization.
8 588 0.665445319204 Henry Cohn, 2025, needs more optimization.
8 592 0.665561282339 Henry Cohn, 2025, needs more optimization.
8 594 0.666130895250 Henry Cohn, 2026, needs more optimization.
8 595 0.666130895254 Henry Cohn, 2025, needs more optimization.
8 596 0.666387024705 Henry Cohn, 2025, needs more optimization.
8 599 0.666397358052 Henry Cohn, 2025, needs more optimization.
8 600 0.666602509895 Henry Cohn, 2026, needs more optimization.
8 601 0.666965063068 Henry Cohn, 2025, needs more optimization.
8 603 0.666985574341 Henry Cohn, 2025, needs more optimization.
8 604 0.667055396755 Henry Cohn, 2026, needs more optimization.
8 605 0.667060658637 Henry Cohn, 2025, needs more optimization.
8 606 0.667072130559 Henry Cohn, 2025, needs more optimization.
8 607 0.667087479684 Henry Cohn, 2025, needs more optimization.
8 608 0.667089302599 Henry Cohn, 2025, needs more optimization.
8 609 0.667095398399 Henry Cohn, 2025, needs more optimization.
8 610 0.667099364039 Henry Cohn, 2025, needs more optimization.
8 611 0.667108979091 Henry Cohn, 2025, needs more optimization.
8 613 0.667111574246 Henry Cohn, 2025, needs more optimization.
8 614 0.667138324876 Henry Cohn, 2025, needs more optimization.
8 615 0.667483585956 Henry Cohn, 2025, needs more optimization.
8 616 0.667623615616 Henry Cohn, 2025, needs more optimization.
8 617 0.667658585372 Henry Cohn, 2025, needs more optimization.
8 618 0.667665939580 Henry Cohn, 2025, needs more optimization.
8 620 0.667678310990 Henry Cohn, 2025, needs more optimization.
8 621 0.667691025236 Henry Cohn, 2025, needs more optimization.
8 622 0.667692412190 Henry Cohn, 2025, needs more optimization.
8 623 0.667736479972 Henry Cohn, 2025, needs more optimization.
8 624 0.667737235348 Henry Cohn, 2025, needs more optimization.
8 625 0.667790082788 Henry Cohn, 2025, needs more optimization.
8 626 0.667856165492 Henry Cohn, 2025, needs more optimization.
8 628 0.667862843031 Henry Cohn, 2026, needs more optimization.
8 632 0.667996157491 Henry Cohn, 2026, needs more optimization.
8 633 0.668028469835 Henry Cohn, 2025, needs more optimization.
8 634 0.668098972215 Henry Cohn, 2025, needs more optimization.
8 635 0.668103995122 Henry Cohn, 2025, needs more optimization.
8 636 0.668296451526 Henry Cohn, 2026, needs more optimization.
8 637 0.668744675880 Henry Cohn, 2025, needs more optimization.
8 638 0.668765396908 Henry Cohn, 2025, needs more optimization.
8 639 0.668781500950 Henry Cohn, 2025, needs more optimization.
8 640 0.668796717281 Henry Cohn, 2026, needs more optimization.
8 641 0.668821436898 Henry Cohn, 2025, needs more optimization.
8 643 0.668849763782 Henry Cohn, 2025, needs more optimization.
8 644 0.668888933796 Henry Cohn, 2026, needs more optimization.
8 645 0.668913424501 Henry Cohn, 2025, needs more optimization.
8 646 0.668925108447 Henry Cohn, 2025, needs more optimization.
8 648 0.670118418002 Henry Cohn, 2025, needs more optimization.
8 649 0.670137153286 Henry Cohn, 2025, needs more optimization.
8 651 0.670169070821 Henry Cohn, 2025, needs more optimization.
8 652 0.670175947064 Henry Cohn, 2025, needs more optimization.
8 653 0.670249265653 Henry Cohn, 2025, needs more optimization.
8 654 0.670496836573 Henry Cohn, 2025, needs more optimization.
8 656 0.670540356874 Henry Cohn, 2025, needs more optimization.
8 657 0.670625558936 Henry Cohn, 2026, needs more optimization.
8 658 0.670943098239 Henry Cohn, 2026, needs more optimization.
8 660 0.671405900252 Henry Cohn, 2026, needs more optimization.
8 661 0.671576063393 Henry Cohn, 2026, needs more optimization.
8 662 0.672361517486 Henry Cohn, 2025, needs more optimization.
8 663 0.672376082884 Henry Cohn, 2025, needs more optimization.
8 664 0.672381833357 Henry Cohn, 2025, needs more optimization.
8 665 0.672388136782 Henry Cohn, 2025, needs more optimization.
8 668 0.672402986964 Henry Cohn, 2025, needs more optimization.
8 669 0.672405478766 Henry Cohn, 2025, needs more optimization.
8 671 0.672433821191 Henry Cohn, 2025, needs more optimization.
8 673 0.672444029762 Henry Cohn, 2025, needs more optimization.
8 674 0.672920393834 Henry Cohn, 2025, needs more optimization.
8 675 0.673610862017 Henry Cohn, 2025, needs more optimization.
8 676 0.673615460560 Henry Cohn, 2025, needs more optimization.
8 677 0.673654129403 Henry Cohn, 2025, needs more optimization.
8 678 0.673656323795 Henry Cohn, 2025, needs more optimization.
8 681 0.673674600224 Henry Cohn, 2025, needs more optimization.
8 682 0.673708965600 Henry Cohn, 2025, needs more optimization.
8 683 0.676263648596 Henry Cohn, 2025, needs more optimization.
8 684 0.676421990904 Henry Cohn, 2026, needs more optimization.
8 685 0.677531018202 Henry Cohn, 2025, needs more optimization.
8 686 0.677544477572 Henry Cohn, 2025, needs more optimization.
8 687 0.677555611920 Henry Cohn, 2025, needs more optimization.
8 689 0.677559094580 Henry Cohn, 2025, needs more optimization.
8 690 0.677573227978 Henry Cohn, 2025, needs more optimization.
8 691 0.677899660426 Henry Cohn, 2025, needs more optimization.
8 692 0.678679769647 Henry Cohn, 2025, needs more optimization.
8 693 0.678688084707 Henry Cohn, 2025, needs more optimization.
8 694 0.678720290855 Henry Cohn, 2025, needs more optimization.
8 695 0.678729793454 Henry Cohn, 2025, needs more optimization.
8 696 0.678735778078 Henry Cohn, 2025, needs more optimization.
8 697 0.678782198352 Henry Cohn, 2025, needs more optimization.
8 698 0.678784004008 Henry Cohn, 2025, needs more optimization.
8 700 0.679658794379 Henry Cohn, 2025, needs more optimization.
8 701 0.680815834525 Henry Cohn, 2025, needs more optimization.
8 702 0.680825164121 Henry Cohn, 2025, needs more optimization.
8 704 0.680860712448 Henry Cohn, 2025, needs more optimization.
8 705 0.681761519941 Henry Cohn, 2025, needs more optimization.
8 706 0.681769624673 Henry Cohn, 2025, needs more optimization.
8 707 0.681783437957 Henry Cohn, 2025, needs more optimization.
8 708 0.681790375821 Henry Cohn, 2025, needs more optimization.
8 709 0.681807845025 Henry Cohn, 2025, needs more optimization.
8 710 0.681819621502 Henry Cohn, 2025, needs more optimization.
8 711 0.682547829724 Henry Cohn, 2025, needs more optimization.
8 712 0.682556151636 Henry Cohn, 2025, needs more optimization.
8 713 0.682631957791 Henry Cohn, 2025, needs more optimization.
8 714 0.682647104955 Henry Cohn, 2025, needs more optimization.
8 715 0.682724276874 Henry Cohn, 2025, needs more optimization.
8 716 0.683299678822 Henry Cohn, 2025, needs more optimization.
8 717 0.683347815941 Henry Cohn, 2025, needs more optimization.
8 718 0.684191236637 Henry Cohn, 2025, needs more optimization.
8 720 0.684198725768 Henry Cohn, 2025, needs more optimization.
8 721 0.684209256236 Henry Cohn, 2025, needs more optimization.
8 722 0.684552996041 Henry Cohn, 2025, needs more optimization.
8 723 0.684597203485 Henry Cohn, 2025, needs more optimization.
8 725 0.685637290899 Henry Cohn, 2025, needs more optimization.
8 727 0.685651013687 Henry Cohn, 2025, needs more optimization.
8 728 0.686655440089 Henry Cohn, 2025, needs more optimization.
8 730 0.686764596522 Henry Cohn, 2025, needs more optimization.
8 731 0.687195507005 Henry Cohn, 2025, needs more optimization.
8 732 0.687199858892 Henry Cohn, 2025, needs more optimization.
8 733 0.687556618604 Henry Cohn, 2025, needs more optimization.
8 734 0.687560122508 Henry Cohn, 2025, needs more optimization.
8 735 0.687565651641 Henry Cohn, 2025, needs more optimization.
8 736 0.687595156374 Henry Cohn, 2025, needs more optimization.
8 737 0.688320161391 Henry Cohn, 2025, needs more optimization.
8 739 0.688340073834 Henry Cohn, 2025, needs more optimization.
8 741 0.688352439514 Henry Cohn, 2025, needs more optimization.
8 742 0.688390759878 Henry Cohn, 2025, needs more optimization.
8 743 0.689087386175 Henry Cohn, 2025, needs more optimization.
8 744 0.689093364046 Henry Cohn, 2025, needs more optimization.
8 745 0.689245371248 Henry Cohn, 2025, needs more optimization.
8 746 0.689257208969 Henry Cohn, 2025, needs more optimization.
8 747 0.689285686948 Henry Cohn, 2025, needs more optimization.
8 748 0.689650119683 Henry Cohn, 2025, needs more optimization.
8 749 0.689654681524 Henry Cohn, 2025, needs more optimization.
8 751 0.689712820395 Henry Cohn, 2025, needs more optimization.
8 753 0.690221625290 Henry Cohn, 2025, needs more optimization.
8 754 0.690249738820 Henry Cohn, 2025, needs more optimization.
8 756 0.690254002412 Henry Cohn, 2025, needs more optimization.
8 757 0.690262706824 Henry Cohn, 2025, needs more optimization.
8 758 0.690269097024 Henry Cohn, 2025, needs more optimization.
8 760 0.690275149052 Henry Cohn, 2025, needs more optimization.
8 761 0.690423995807 Henry Cohn, 2025, needs more optimization.
8 762 0.690931028446 Henry Cohn, 2025, needs more optimization.
8 763 0.690985339857 Henry Cohn, 2025, needs more optimization.
8 764 0.691649582708 Henry Cohn, 2025, needs more optimization.
8 765 0.691657242200 Henry Cohn, 2025, needs more optimization.
8 766 0.691660459895 Henry Cohn, 2025, needs more optimization.
8 767 0.691733318685 Henry Cohn, 2025, needs more optimization.
8 768 0.691738086675 Henry Cohn, 2025, needs more optimization.
8 770 0.691756855104 Henry Cohn, 2025, needs more optimization.
8 771 0.691764059186 Henry Cohn, 2025, needs more optimization.
8 772 0.691769701878 Henry Cohn, 2025, needs more optimization.
8 773 0.692188715910 Henry Cohn, 2025, needs more optimization.
8 774 0.692427638048 Henry Cohn, 2025, needs more optimization.
8 775 0.692465210450 Henry Cohn, 2025, needs more optimization.
8 776 0.692503031109 Henry Cohn, 2026, needs more optimization.
8 777 0.692507780945 Henry Cohn, 2025, needs more optimization.
8 778 0.692685446443 Henry Cohn, 2025, needs more optimization.
8 779 0.692696406897 Henry Cohn, 2025, needs more optimization.
8 780 0.692703051394 Henry Cohn, 2025, needs more optimization.
8 781 0.692707887399 Henry Cohn, 2025, needs more optimization.
8 782 0.692758858442 Henry Cohn, 2025, needs more optimization.
8 783 0.692780451895 Henry Cohn, 2025, needs more optimization.
8 784 0.692817786168 Henry Cohn, 2025, needs more optimization.
8 785 0.693746730553 Henry Cohn, 2025, needs more optimization.
8 786 0.693749065175 Henry Cohn, 2025, needs more optimization.
8 787 0.693809101014 Henry Cohn, 2025, needs more optimization.
8 788 0.693820391069 Henry Cohn, 2025, needs more optimization.
8 789 0.694271052652 Henry Cohn, 2025, needs more optimization.
8 790 0.694297113974 Henry Cohn, 2025, needs more optimization.
8 791 0.694304362807 Henry Cohn, 2025, needs more optimization.
8 792 0.694317963429 Henry Cohn, 2025, needs more optimization.
8 794 0.694664633550 Henry Cohn, 2025, needs more optimization.
8 795 0.694703983569 Henry Cohn, 2025, needs more optimization.
8 797 0.694715522952 Henry Cohn, 2025, needs more optimization.
8 799 0.694912235139 Henry Cohn, 2025, needs more optimization.
8 800 0.695331096435 Henry Cohn, 2025, needs more optimization.
8 801 0.695383678268 Henry Cohn, 2025, needs more optimization.
8 802 0.695653080170 Henry Cohn, 2025, needs more optimization.
8 803 0.695703246342 Henry Cohn, 2025, needs more optimization.
8 804 0.696078886015 Henry Cohn, 2025, needs more optimization.
8 805 0.696404294257 Henry Cohn, 2025, needs more optimization.
8 806 0.696420678624 Henry Cohn, 2025, needs more optimization.
8 807 0.696427726754 Henry Cohn, 2025, needs more optimization.
8 808 0.696450883362 Henry Cohn, 2025, needs more optimization.
8 809 0.696493755900 Henry Cohn, 2025, needs more optimization.
8 810 0.696527868450 Henry Cohn, 2025, needs more optimization.
8 811 0.696772294525 Henry Cohn, 2025, needs more optimization.
8 812 0.696772875652 Henry Cohn, 2025, needs more optimization.
8 813 0.696926164631 Henry Cohn, 2025, needs more optimization.
8 814 0.697612546310 Henry Cohn, 2025, needs more optimization.
8 815 0.697613780682 Henry Cohn, 2025, needs more optimization.
8 817 0.697625402129 Henry Cohn, 2025, needs more optimization.
8 818 0.697635270970 Henry Cohn, 2025, needs more optimization.
8 819 0.697656849098 Henry Cohn, 2025, needs more optimization.
8 820 0.697735882156 Henry Cohn, 2025, needs more optimization.
8 821 0.697770280526 Henry Cohn, 2025, needs more optimization.
8 822 0.698096884954 Henry Cohn, 2025, needs more optimization.
8 823 0.698109445083 Henry Cohn, 2025, needs more optimization.
8 824 0.698158922001 Henry Cohn, 2025, needs more optimization.
8 825 0.698171458389 Henry Cohn, 2025, needs more optimization.
8 826 0.698267233858 Henry Cohn, 2025, needs more optimization.
8 828 0.698680526523 Henry Cohn, 2025, needs more optimization.
8 829 0.698698277435 Henry Cohn, 2025, needs more optimization.
8 833 0.699228866288 Henry Cohn, 2025, needs more optimization.
8 834 0.699236866590 Henry Cohn, 2025, needs more optimization.
8 835 0.699541731401 Henry Cohn, 2025, needs more optimization.
8 838 0.699976879270 Henry Cohn, 2025, needs more optimization.
8 839 0.699989920786 Henry Cohn, 2025, needs more optimization.
8 840 0.700052149297 Henry Cohn, 2025, needs more optimization.
8 842 0.700537963096 Henry Cohn, 2025, needs more optimization.
8 844 0.700579575605 Henry Cohn, 2025, needs more optimization.
8 846 0.700582454670 Henry Cohn, 2025, needs more optimization.
8 847 0.700585511073 Henry Cohn, 2025, needs more optimization.
8 848 0.700783071915 Henry Cohn, 2026, needs more optimization.
8 850 0.701194373603 Henry Cohn, 2025, needs more optimization.
8 851 0.701205442734 Henry Cohn, 2025, needs more optimization.
8 852 0.701300853845 Henry Cohn, 2025, needs more optimization.
8 853 0.701627111266 Henry Cohn, 2025, needs more optimization.
8 854 0.701647154743 Henry Cohn, 2025, needs more optimization.
8 856 0.702140146489 Henry Cohn, 2025, needs more optimization.
8 857 0.702140752693 Henry Cohn, 2025, needs more optimization.
8 858 0.702160184811 Henry Cohn, 2025, needs more optimization.
8 859 0.702369007300 Henry Cohn, 2025, needs more optimization.
8 860 0.702635130955 Henry Cohn, 2026, needs more optimization.
8 861 0.702639415712 Henry Cohn, 2025, needs more optimization.
8 863 0.703047455658 Henry Cohn, 2025, needs more optimization.
8 864 0.703075542271 Henry Cohn, 2025, needs more optimization.
8 865 0.703086668407 Henry Cohn, 2025, needs more optimization.
8 866 0.703089439857 Henry Cohn, 2025, needs more optimization.
8 868 0.703400832635 Henry Cohn, 2025, needs more optimization.
8 870 0.703490358965 Henry Cohn, 2025, needs more optimization.
8 871 0.703728936164 Henry Cohn, 2025, needs more optimization.
8 872 0.703743378781 Henry Cohn, 2026, needs more optimization.
8 873 0.703890487142 Henry Cohn, 2025, needs more optimization.
8 874 0.703929272417 Henry Cohn, 2025, needs more optimization.
8 875 0.703937923467 Henry Cohn, 2025, needs more optimization.
8 876 0.703952340476 Henry Cohn, 2025, needs more optimization.
8 877 0.704409953183 Henry Cohn, 2025, needs more optimization.
8 879 0.704413282221 Henry Cohn, 2025, needs more optimization.
8 880 0.704445046575 Henry Cohn, 2025, needs more optimization.
8 881 0.704454523140 Henry Cohn, 2025, needs more optimization.
8 882 0.704500987909 Henry Cohn, 2025, needs more optimization.
8 883 0.704812314689 Henry Cohn, 2025, needs more optimization.
8 884 0.704825256769 Henry Cohn, 2025, needs more optimization.
8 886 0.705062062139 Henry Cohn, 2025, needs more optimization.
8 887 0.705062193245 Henry Cohn, 2025, needs more optimization.
8 888 0.705070441205 Henry Cohn, 2025, needs more optimization.
8 889 0.705080235144 Henry Cohn, 2025, needs more optimization.
8 890 0.705113042198 Henry Cohn, 2025, needs more optimization.
8 891 0.705712899680 Henry Cohn, 2025, needs more optimization.
8 892 0.705721402518 Henry Cohn, 2025, needs more optimization.
8 893 0.705729660190 Henry Cohn, 2025, needs more optimization.
8 894 0.705734532374 Henry Cohn, 2025, needs more optimization.
8 895 0.705745173745 Henry Cohn, 2025, needs more optimization.
8 896 0.705761190193 Henry Cohn, 2025, needs more optimization.
8 897 0.705764606541 Henry Cohn, 2025, needs more optimization.
8 899 0.705821749669 Henry Cohn, 2025, needs more optimization.
8 902 0.705829679270 Henry Cohn, 2025, needs more optimization.
8 903 0.705835670346 Henry Cohn, 2025, needs more optimization.
8 904 0.706104844872 Henry Cohn, 2025, needs more optimization.
8 905 0.706106342062 Henry Cohn, 2025, needs more optimization.
8 908 0.706543218819 Henry Cohn, 2025, needs more optimization.
8 909 0.706548180413 Henry Cohn, 2025, needs more optimization.
8 910 0.706549815083 Henry Cohn, 2025, needs more optimization.
8 911 0.706561407014 Henry Cohn, 2025, needs more optimization.
8 914 0.706571631333 Henry Cohn, 2025, needs more optimization.
8 915 0.707004569607 Henry Cohn, 2025, needs more optimization.
8 916 0.707012136771 Henry Cohn, 2025, needs more optimization.
8 917 0.707013838812 Henry Cohn, 2025, needs more optimization.
8 919 0.707190386128 Henry Cohn, 2025, needs more optimization.
8 920 0.707192636288 Henry Cohn, 2025, needs more optimization.
8 921 0.707670415856 Henry Cohn, 2025, needs more optimization.
8 923 0.707676716516 Henry Cohn, 2025, needs more optimization.
8 925 0.707694037021 Henry Cohn, 2025, needs more optimization.
8 926 0.707707856101 Henry Cohn, 2025, needs more optimization.
8 928 0.707991000305 Henry Cohn, 2025, needs more optimization.
8 930 0.707996589845 Henry Cohn, 2025, needs more optimization.
8 931 0.708062645930 Henry Cohn, 2025, needs more optimization.
8 932 0.708150395923 Henry Cohn, 2026, needs more optimization.
8 933 0.708152389831 Henry Cohn, 2025, needs more optimization.
8 935 0.708475101327 Henry Cohn, 2025, needs more optimization.
8 936 0.708482055285 Henry Cohn, 2026, needs more optimization.
8 937 0.708608860965 Henry Cohn, 2025, needs more optimization.
8 938 0.708946530234 Henry Cohn, 2026, needs more optimization.
8 939 0.708951251854 Henry Cohn, 2026, needs more optimization.
8 941 0.708963902315 Henry Cohn, 2025, needs more optimization.
8 942 0.708966792925 Henry Cohn, 2026, needs more optimization.
8 943 0.709002441249 Henry Cohn, 2026, needs more optimization.
8 944 0.709064950292 Henry Cohn, 2025, needs more optimization.
8 946 0.709192766988 Henry Cohn, 2026, needs more optimization.
8 947 0.709257078933 Henry Cohn, 2025, needs more optimization.
8 949 0.709561805584 Henry Cohn, 2025, needs more optimization.
8 950 0.709568370738 Henry Cohn, 2025, needs more optimization.
8 952 0.709580083659 Henry Cohn, 2025, needs more optimization.
8 953 0.709592878533 Henry Cohn, 2026, needs more optimization.
8 954 0.709623358917 Henry Cohn, 2025, needs more optimization.
8 955 0.710013127623 Henry Cohn, 2025, needs more optimization.
8 956 0.710025120237 Henry Cohn, 2025, needs more optimization.
8 957 0.710043299869 Henry Cohn, 2026, needs more optimization.
8 958 0.710045768660 Henry Cohn, 2026, needs more optimization.
8 960 0.710351161619 Henry Cohn, 2026, needs more optimization.
8 961 0.710358683147 Henry Cohn, 2026, needs more optimization.
8 962 0.710762505973 Henry Cohn, 2025, needs more optimization.
8 963 0.710768583393 Henry Cohn, 2026, needs more optimization.
8 964 0.710786430671 Henry Cohn, 2026, needs more optimization.
8 967 0.710794195804 Henry Cohn, 2025, needs more optimization.
8 968 0.710800955289 Henry Cohn, 2025, needs more optimization.
8 969 0.710847532911 Henry Cohn, 2025, needs more optimization.
8 970 0.710949866180 Henry Cohn, 2025, needs more optimization.
8 971 0.711447595345 Henry Cohn, 2026, needs more optimization.
8 972 0.711498673462 Henry Cohn, 2026, needs more optimization.
8 973 0.711510485535 Henry Cohn, 2026, needs more optimization.
8 974 0.711571576014 Henry Cohn, 2025, needs more optimization.
8 975 0.711583352192 Henry Cohn, 2026, needs more optimization.
8 976 0.711588575557 Henry Cohn, 2026, needs more optimization.
8 977 0.711611710434 Henry Cohn, 2025, needs more optimization.
8 978 0.711684297881 Henry Cohn, 2026, needs more optimization.
8 979 0.711962486346 Henry Cohn, 2025, needs more optimization.
8 980 0.711968317112 Henry Cohn, 2026, needs more optimization.
8 981 0.712057436736 Henry Cohn, 2025, needs more optimization.
8 983 0.712080270091 Henry Cohn, 2025, needs more optimization.
8 984 0.712092572803 Henry Cohn, 2026, needs more optimization.
8 986 0.712394668618 Henry Cohn, 2025, needs more optimization.
8 987 0.712408844609 Henry Cohn, 2025, needs more optimization.
8 988 0.712468855396 Henry Cohn, 2026, needs more optimization.
8 989 0.712714678610 Henry Cohn, 2025, needs more optimization.
8 990 0.713101116160 Henry Cohn, 2026, needs more optimization.
8 991 0.713103386410 Henry Cohn, 2025, needs more optimization.
8 992 0.713104668986 Henry Cohn, 2025, needs more optimization.
8 995 0.713130158410 Henry Cohn, 2025, needs more optimization.
8 996 0.713140398164 Henry Cohn, 2025, needs more optimization.
8 1024 0.714285714286 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−5
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 0.2 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
9 37 0.213781170696 Henry Cohn, 2025.
9 38 0.217703240659 Henry Cohn, 2025.
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 0.266202150382 Henry Cohn, 2025.
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 0.297700422270 Henry Cohn, 2023.
9 62 0.299407593895 Henry Cohn, 2026.
9 63 0.302685227391 Henry Cohn, 2025.
9 64 0.306653313780 Henry Cohn, 2023.
9 65 0.310477119131 Henry Cohn, 2026, needs more optimization.
9 66 0.314219501967 Henry Cohn, 2024.
9 67 0.319305112920 Henry Cohn, 2025.
9 68 0.322050465427 Henry Cohn, 2025.
9 69 0.324666182383 Henry Cohn, 2025.
9 70 0.328463499925 Henry Cohn, 2026, needs more optimization.
9 71 0.329783133617 Henry Cohn, 2026.
9 72 0.330036093460 Henry Cohn, 2025, needs more optimization.
9 73 0.330041808451 Henry Cohn, 2025, needs more optimization.
9 74 0.330099461319 Henry Cohn, 2026, needs more optimization.
9 75 0.330101783843 Henry Cohn, 2025, needs more optimization.
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 0.378530782312 Henry Cohn, 2026, needs more optimization.
9 103 0.378850283307 Henry Cohn, 2026, needs more optimization.
9 104 0.379137241782 Henry Cohn, 2025, needs more optimization.
9 105 0.391682453674 Henry Cohn, 2026, needs more optimization.
9 106 0.395189700208 Henry Cohn, 2026, needs more optimization.
9 107 0.398154557489 Henry Cohn, 2026, needs more optimization.
9 108 0.400036672753 Henry Cohn, 2026, needs more optimization.
9 109 0.403046937070 Henry Cohn, 2026, needs more optimization.
9 110 0.405589538580 Henry Cohn, 2026, needs more optimization.
9 111 0.407513805241 Henry Cohn, 2026, needs more optimization.
9 112 0.408810852793 Henry Cohn, 2026, needs more optimization.
9 113 0.411622580981 Henry Cohn, 2026, needs more optimization.
9 114 0.413335694595 Henry Cohn, 2026, needs more optimization.
9 115 0.413676808831 Henry Cohn, 2026, needs more optimization.
9 116 0.414974186672 Henry Cohn, 2026, needs more optimization.
9 117 0.415244157452 Henry Cohn, 2026, needs more optimization.
9 118 0.416790418651 Henry Cohn, 2026, needs more optimization.
9 119 0.417758145362 Henry Cohn, 2025, needs more optimization.
9 120 0.418016338583 Henry Cohn, 2026, needs more optimization.
9 121 0.418798416161 Henry Cohn, 2026, needs more optimization.
9 122 0.420162951570 Henry Cohn, 2026, needs more optimization.
9 123 0.421688820130 Henry Cohn, 2026, needs more optimization.
9 124 0.422247974303 Henry Cohn, 2026, needs more optimization.
9 125 0.422395353957 Henry Cohn, 2026, needs more optimization.
9 126 0.423548828341 Henry Cohn, 2026, needs more optimization.
9 127 0.424952701197 Henry Cohn, 2026, needs more optimization.
9 128 0.426696464552 Henry Cohn, 2026, needs more optimization.
9 129 0.428279428430 Henry Cohn, 2026, needs more optimization.
9 130 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
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 0.442932166416 Henry Cohn, 2026, needs more optimization.
9 148 0.444909715608 Henry Cohn, 2026, needs more optimization.
9 149 0.448517564473 Henry Cohn, 2026, needs more optimization.
9 150 0.450668005681 Henry Cohn, 2026, needs more optimization.
9 151 0.452380018311 Henry Cohn, 2026, needs more optimization.
9 152 0.454421279218 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
9 166 0.463049784257 Henry Cohn, 2026, needs more optimization.
9 167 0.464177306278 Henry Cohn, 2026, needs more optimization.
9 168 0.467119012852 Henry Cohn, 2026, needs more optimization.
9 169 0.470028567891 Henry Cohn, 2026, needs more optimization.
9 170 0.470472711331 Henry Cohn, 2026, needs more optimization.
9 171 0.471098162029 Henry Cohn, 2026, needs more optimization.
9 172 0.473486883865 Henry Cohn, 2026, needs more optimization.
9 173 0.473517238507 Henry Cohn, 2025, needs more optimization.
9 174 0.473604016858 Henry Cohn, 2026, needs more optimization.
9 175 0.473899443814 Henry Cohn, 2026, needs more optimization.
9 176 0.474199469108 Henry Cohn, 2026, needs more optimization.
9 177 0.474690676718 Henry Cohn, 2026, needs more optimization.
9 178 0.475611201967 Henry Cohn, 2026, needs more optimization.
9 179 0.475764562294 Henry Cohn, 2026, needs more optimization.
9 180 0.476131499428 Henry Cohn, 2026, needs more optimization.
9 181 0.476974776235 Henry Cohn, 2026, needs more optimization.
9 182 0.476976861362 Henry Cohn, 2026, needs more optimization.
9 183 0.477898514388 Henry Cohn, 2026, needs more optimization.
9 184 0.477963079845 Henry Cohn, 2026, needs more optimization.
9 185 0.478262530970 Henry Cohn, 2026, needs more optimization.
9 186 0.479219877528 Henry Cohn, 2026, needs more optimization.
9 187 0.479532573313 Henry Cohn, 2026, needs more optimization.
9 188 0.480058083370 Henry Cohn, 2025, needs more optimization.
9 189 0.480321672624 Henry Cohn, 2026, needs more optimization.
9 190 0.480514791926 Henry Cohn, 2025, needs more optimization.
9 191 0.481423660967 Henry Cohn, 2025, needs more optimization.
9 192 0.482213922573 Henry Cohn, 2026, needs more optimization.
9 193 0.482676130493 Henry Cohn, 2026, needs more optimization.
9 194 0.483686161785 Henry Cohn, 2026, needs more optimization.
9 195 0.484721410010 Henry Cohn, 2026, needs more optimization.
9 196 0.484960159278 Henry Cohn, 2026, needs more optimization.
9 197 0.485125511701 Henry Cohn, 2026, needs more optimization.
9 198 0.486164425291 Henry Cohn, 2026, needs more optimization.
9 199 0.486334754136 Henry Cohn, 2026, needs more optimization.
9 200 0.486637780776 Henry Cohn, 2026, needs more optimization.
9 201 0.486923552060 Henry Cohn, 2026, needs more optimization.
9 202 0.487542459477 Henry Cohn, 2026, needs more optimization.
9 203 0.487888050195 Henry Cohn, 2026, needs more optimization.
9 204 0.488717800450 Henry Cohn, 2026, needs more optimization.
9 205 0.489800010772 Henry Cohn, 2026, needs more optimization.
9 206 0.490109265727 Henry Cohn, 2026, needs more optimization.
9 207 0.490288109236 Henry Cohn, 2026, needs more optimization.
9 208 0.491009751672 Henry Cohn, 2026, needs more optimization.
9 209 0.491452927298 Henry Cohn, 2026, needs more optimization.
9 210 0.491506550772 Henry Cohn, 2026, needs more optimization.
9 211 0.494071857364 Henry Cohn, 2026, needs more optimization.
9 212 0.494192922361 Henry Cohn, 2026, needs more optimization.
9 213 0.495212900755 Henry Cohn, 2025, needs more optimization.
9 214 0.495420075988 Henry Cohn, 2026, needs more optimization.
9 215 0.495678049387 Henry Cohn, 2026, needs more optimization.
9 216 0.496674766111 Henry Cohn, 2026, needs more optimization.
9 217 0.496874961077 Henry Cohn, 2026, needs more optimization.
9 218 0.498087526099 Henry Cohn, 2026, needs more optimization.
9 219 0.498088567075 Henry Cohn, 2026, needs more optimization.
9 221 0.498899445428 Henry Cohn, 2026, needs more optimization.
9 222 0.498911623597 Henry Cohn, 2026, needs more optimization.
9 223 0.499436655922 Henry Cohn, 2026, needs more optimization.
9 226 0.499490926221 Henry Cohn, 2026, needs more optimization.
9 227 0.499565847311 Henry Cohn, 2026, needs more optimization.
9 230 0.499873727620 Henry Cohn, 2026, needs more optimization.
9 233 0.499931516232 Henry Cohn, 2026, needs more optimization.
9 236 0.499981673823 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 0.517341896236 Henry Cohn, 2024, needs more optimization.
9 308 0.527038274963 Henry Cohn, 2026, needs more optimization.
9 309 0.528129183932 Henry Cohn, 2026, needs more optimization.
9 310 0.536081315987 Henry Cohn, 2026, needs more optimization.
9 311 0.536081422599 Henry Cohn, 2025, needs more optimization.
9 312 0.536116067832 Henry Cohn, 2026, needs more optimization.
9 314 0.536129423307 Henry Cohn, 2025, needs more optimization.
9 316 0.536754266934 Henry Cohn, 2025, needs more optimization.
9 317 0.536763015062 Henry Cohn, 2025, needs more optimization.
9 319 0.536799577609 Henry Cohn, 2025, needs more optimization.
9 320 0.536802180194 Henry Cohn, 2026, needs more optimization.
9 323 0.536809663363 Henry Cohn, 2025, needs more optimization.
9 328 0.536825498604 Henry Cohn, 2026, needs more optimization.
9 331 0.536841662552 Henry Cohn, 2025, needs more optimization.
9 332 0.536873025733 Henry Cohn, 2025, needs more optimization.
9 333 0.537239953366 Henry Cohn, 2026, needs more optimization.
9 334 0.537943633154 Henry Cohn, 2025, needs more optimization.
9 335 0.537980963423 Henry Cohn, 2026, needs more optimization.
9 336 0.539493189916 Henry Cohn, 2026, needs more optimization.
9 337 0.540140136178 Henry Cohn, 2025, needs more optimization.
9 338 0.541254001703 Henry Cohn, 2025, needs more optimization.
9 340 0.543920185018 Henry Cohn, 2026, needs more optimization.
9 341 0.544090835364 Henry Cohn, 2026, needs more optimization.
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
9 610 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 0.614174874984 Henry Cohn, 2025, needs more optimization.
9 614 0.614786340484 Henry Cohn, 2025, needs more optimization.
9 615 0.614905078465 Henry Cohn, 2025, needs more optimization.
9 616 0.615168409892 Henry Cohn, 2026, needs more optimization.
9 617 0.616077792127 Henry Cohn, 2025, needs more optimization.
9 618 0.616092533017 Henry Cohn, 2025, needs more optimization.
9 619 0.616436132892 Henry Cohn, 2025, needs more optimization.
9 636 0.618033985078 Henry Cohn, 2026, needs more optimization.
9 640 0.618033987180 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 0.642621614971 Henry Cohn, 2025, needs more optimization.
9 724 0.642759824040 Henry Cohn, 2026, needs more optimization.
9 725 0.642942346565 Henry Cohn, 2025, needs more optimization.
9 726 0.643197872157 Henry Cohn, 2025, needs more optimization.
9 727 0.643264138767 Henry Cohn, 2025, needs more optimization.
9 728 0.643367753818 Henry Cohn, 2025, needs more optimization.
9 729 0.643669813440 Henry Cohn, 2025, needs more optimization.
9 730 0.643682075440 Henry Cohn, 2025, needs more optimization.
9 731 0.643709726592 Henry Cohn, 2025, needs more optimization.
9 732 0.643712370360 Henry Cohn, 2026, needs more optimization.
9 733 0.643833843770 Henry Cohn, 2025, needs more optimization.
9 735 0.644276242524 Henry Cohn, 2025, needs more optimization.
9 736 0.644496407810 Henry Cohn, 2025, needs more optimization.
9 737 0.644577686472 Henry Cohn, 2025, needs more optimization.
9 738 0.644591860201 Henry Cohn, 2025, needs more optimization.
9 739 0.644986723180 Henry Cohn, 2025, needs more optimization.
9 740 0.645107975569 Henry Cohn, 2025, needs more optimization.
9 741 0.645116699616 Henry Cohn, 2025, needs more optimization.
9 742 0.645214426924 Henry Cohn, 2025, needs more optimization.
9 743 0.645220929540 Henry Cohn, 2025, needs more optimization.
9 744 0.645358015488 Henry Cohn, 2026, needs more optimization.
9 745 0.645661683498 Henry Cohn, 2025, needs more optimization.
9 746 0.645666772249 Henry Cohn, 2025, needs more optimization.
9 747 0.645677484301 Henry Cohn, 2025, needs more optimization.
9 748 0.645733908744 Henry Cohn, 2026, needs more optimization.
9 749 0.645793318913 Henry Cohn, 2025, needs more optimization.
9 750 0.646063702380 Henry Cohn, 2025, needs more optimization.
9 751 0.646119592607 Henry Cohn, 2025, needs more optimization.
9 752 0.646447386259 Henry Cohn, 2025, needs more optimization.
9 753 0.646636838574 Henry Cohn, 2025, needs more optimization.
9 754 0.646642011818 Henry Cohn, 2025, needs more optimization.
9 755 0.646654817535 Henry Cohn, 2025, needs more optimization.
9 756 0.646809620524 Henry Cohn, 2026, needs more optimization.
9 757 0.647021021451 Henry Cohn, 2025, needs more optimization.
9 758 0.647189680108 Henry Cohn, 2025, needs more optimization.
9 760 0.647415975407 Henry Cohn, 2025, needs more optimization.
9 761 0.647455380135 Henry Cohn, 2025, needs more optimization.
9 762 0.647502587848 Henry Cohn, 2025, needs more optimization.
9 763 0.647890382897 Henry Cohn, 2025, needs more optimization.
9 764 0.647911180488 Henry Cohn, 2026, needs more optimization.
9 765 0.648153662294 Henry Cohn, 2025, needs more optimization.
9 766 0.648179398056 Henry Cohn, 2025, needs more optimization.
9 767 0.648205669668 Henry Cohn, 2025, needs more optimization.
9 768 0.648276344216 Henry Cohn, 2026, needs more optimization.
9 769 0.648498850472 Henry Cohn, 2025, needs more optimization.
9 770 0.648527170367 Henry Cohn, 2025, needs more optimization.
9 771 0.648980224016 Henry Cohn, 2025, needs more optimization.
9 772 0.648988014765 Henry Cohn, 2025, needs more optimization.
9 773 0.649001453595 Henry Cohn, 2025, needs more optimization.
9 774 0.649052638921 Henry Cohn, 2025, needs more optimization.
9 776 0.649337034538 Henry Cohn, 2026, needs more optimization.
9 777 0.649384395508 Henry Cohn, 2025, needs more optimization.
9 778 0.649386637141 Henry Cohn, 2025, needs more optimization.
9 779 0.649893766152 Henry Cohn, 2025, needs more optimization.
9 780 0.649924079901 Henry Cohn, 2025, needs more optimization.
9 781 0.649983318032 Henry Cohn, 2025, needs more optimization.
9 782 0.650115707659 Henry Cohn, 2025, needs more optimization.
9 783 0.650132298446 Henry Cohn, 2025, needs more optimization.
9 784 0.650177798115 Henry Cohn, 2026, needs more optimization.
9 785 0.650209071935 Henry Cohn, 2025, needs more optimization.
9 786 0.650694177064 Henry Cohn, 2025, needs more optimization.
9 787 0.650727478554 Henry Cohn, 2025, needs more optimization.
9 788 0.650760346949 Henry Cohn, 2026, needs more optimization.
9 789 0.650845223621 Henry Cohn, 2025, needs more optimization.
9 790 0.651077270625 Henry Cohn, 2025, needs more optimization.
9 791 0.651297099799 Henry Cohn, 2025, needs more optimization.
9 792 0.651301357390 Henry Cohn, 2025, needs more optimization.
9 793 0.651428922736 Henry Cohn, 2025, needs more optimization.
9 794 0.651529133702 Henry Cohn, 2025, needs more optimization.
9 795 0.651650729064 Henry Cohn, 2025, needs more optimization.
9 796 0.651657860374 Henry Cohn, 2025, needs more optimization.
9 797 0.651683050917 Henry Cohn, 2025, needs more optimization.
9 798 0.651902962494 Henry Cohn, 2025, needs more optimization.
9 799 0.652152977981 Henry Cohn, 2025, needs more optimization.
9 800 0.652161370068 Henry Cohn, 2026, needs more optimization.
9 801 0.652216667734 Henry Cohn, 2025, needs more optimization.
9 802 0.652274917244 Henry Cohn, 2025, needs more optimization.
9 803 0.652517319296 Henry Cohn, 2025, needs more optimization.
9 804 0.652549189881 Henry Cohn, 2026, needs more optimization.
9 805 0.652558339614 Henry Cohn, 2025, needs more optimization.
9 806 0.652702545100 Henry Cohn, 2025, needs more optimization.
9 807 0.652908801011 Henry Cohn, 2025, needs more optimization.
9 808 0.652955833314 Henry Cohn, 2026, needs more optimization.
9 809 0.653154055619 Henry Cohn, 2025, needs more optimization.
9 810 0.653167846920 Henry Cohn, 2025, needs more optimization.
9 811 0.653237964994 Henry Cohn, 2025, needs more optimization.
9 812 0.653369918581 Henry Cohn, 2025, needs more optimization.
9 813 0.653468008252 Henry Cohn, 2025, needs more optimization.
9 814 0.653679949265 Henry Cohn, 2025, needs more optimization.
9 815 0.653810905202 Henry Cohn, 2025, needs more optimization.
9 816 0.653818231082 Henry Cohn, 2025, needs more optimization.
9 817 0.653850602560 Henry Cohn, 2025, needs more optimization.
9 818 0.653922630908 Henry Cohn, 2025, needs more optimization.
9 819 0.654183709186 Henry Cohn, 2025, needs more optimization.
9 820 0.654189110499 Henry Cohn, 2026, needs more optimization.
9 821 0.654222384679 Henry Cohn, 2025, needs more optimization.
9 822 0.654258849453 Henry Cohn, 2025, needs more optimization.
9 823 0.654391315013 Henry Cohn, 2025, needs more optimization.
9 824 0.654468550447 Henry Cohn, 2025, needs more optimization.
9 825 0.654615045723 Henry Cohn, 2025, needs more optimization.
9 826 0.654822548018 Henry Cohn, 2025, needs more optimization.
9 827 0.655001601010 Henry Cohn, 2025, needs more optimization.
9 828 0.655004842296 Henry Cohn, 2025, needs more optimization.
9 829 0.655220733720 Henry Cohn, 2025, needs more optimization.
9 830 0.655442763615 Henry Cohn, 2025, needs more optimization.
9 831 0.655452949080 Henry Cohn, 2025, needs more optimization.
9 832 0.655463034710 Henry Cohn, 2026, needs more optimization.
9 833 0.655679432859 Henry Cohn, 2025, needs more optimization.
9 834 0.655684380911 Henry Cohn, 2025, needs more optimization.
9 835 0.655845468606 Henry Cohn, 2025, needs more optimization.
9 836 0.655868714138 Henry Cohn, 2026, needs more optimization.
9 837 0.656262456101 Henry Cohn, 2025, needs more optimization.
9 838 0.656291424591 Henry Cohn, 2025, needs more optimization.
9 839 0.656381129178 Henry Cohn, 2025, needs more optimization.
9 840 0.656565559996 Henry Cohn, 2025, needs more optimization.
9 842 0.656812710999 Henry Cohn, 2025, needs more optimization.
9 843 0.657094679486 Henry Cohn, 2025, needs more optimization.
9 844 0.657098253250 Henry Cohn, 2025, needs more optimization.
9 845 0.657208605166 Henry Cohn, 2025, needs more optimization.
9 846 0.657393872630 Henry Cohn, 2025, needs more optimization.
9 847 0.657415668854 Henry Cohn, 2025, needs more optimization.
9 848 0.657418448672 Henry Cohn, 2025, needs more optimization.
9 849 0.657451067624 Henry Cohn, 2025, needs more optimization.
9 850 0.657531881331 Henry Cohn, 2025, needs more optimization.
9 851 0.657751538905 Henry Cohn, 2025, needs more optimization.
9 852 0.657805663087 Henry Cohn, 2026, needs more optimization.
9 853 0.657807774320 Henry Cohn, 2025, needs more optimization.
9 854 0.657818197729 Henry Cohn, 2025, needs more optimization.
9 855 0.658005911534 Henry Cohn, 2025, needs more optimization.
9 856 0.658328451121 Henry Cohn, 2025, needs more optimization.
9 857 0.658392377535 Henry Cohn, 2025, needs more optimization.
9 858 0.658606176209 Henry Cohn, 2025, needs more optimization.
9 859 0.658612838651 Henry Cohn, 2025, needs more optimization.
9 860 0.658835820210 Henry Cohn, 2026, needs more optimization.
9 861 0.658839041199 Henry Cohn, 2025, needs more optimization.
9 862 0.659031437873 Henry Cohn, 2025, needs more optimization.
9 863 0.659046632503 Henry Cohn, 2025, needs more optimization.
9 864 0.659261179677 Henry Cohn, 2025, needs more optimization.
9 865 0.659346409902 Henry Cohn, 2025, needs more optimization.
9 866 0.659356134011 Henry Cohn, 2025, needs more optimization.
9 867 0.659595134719 Henry Cohn, 2025, needs more optimization.
9 868 0.659605999850 Henry Cohn, 2025, needs more optimization.
9 869 0.659633383665 Henry Cohn, 2025, needs more optimization.
9 870 0.659786044638 Henry Cohn, 2025, needs more optimization.
9 871 0.659790551741 Henry Cohn, 2025, needs more optimization.
9 872 0.660017704676 Henry Cohn, 2026, needs more optimization.
9 873 0.660131662979 Henry Cohn, 2025, needs more optimization.
9 874 0.660231825451 Henry Cohn, 2025, needs more optimization.
9 875 0.660493680174 Henry Cohn, 2025, needs more optimization.
9 876 0.660497979113 Henry Cohn, 2026, needs more optimization.
9 877 0.660503958980 Henry Cohn, 2025, needs more optimization.
9 878 0.660529606642 Henry Cohn, 2025, needs more optimization.
9 879 0.660588079957 Henry Cohn, 2025, needs more optimization.
9 880 0.660632906756 Henry Cohn, 2026, needs more optimization.
9 881 0.660977908488 Henry Cohn, 2025, needs more optimization.
9 882 0.661024368372 Henry Cohn, 2025, needs more optimization.
9 883 0.661040763292 Henry Cohn, 2025, needs more optimization.
9 884 0.661155559221 Henry Cohn, 2026, needs more optimization.
9 885 0.661241996052 Henry Cohn, 2025, needs more optimization.
9 886 0.661245073071 Henry Cohn, 2025, needs more optimization.
9 887 0.661291585997 Henry Cohn, 2025, needs more optimization.
9 888 0.661647282768 Henry Cohn, 2026, needs more optimization.
9 889 0.661698386742 Henry Cohn, 2025, needs more optimization.
9 890 0.661736930393 Henry Cohn, 2025, needs more optimization.
9 891 0.661744741460 Henry Cohn, 2025, needs more optimization.
9 892 0.661934946059 Henry Cohn, 2026, needs more optimization.
9 893 0.661993639527 Henry Cohn, 2025, needs more optimization.
9 894 0.662034529021 Henry Cohn, 2025, needs more optimization.
9 895 0.662247016230 Henry Cohn, 2025, needs more optimization.
9 896 0.662283643031 Henry Cohn, 2026, needs more optimization.
9 897 0.662309931828 Henry Cohn, 2025, needs more optimization.
9 898 0.662527580512 Henry Cohn, 2025, needs more optimization.
9 899 0.662537919598 Henry Cohn, 2025, needs more optimization.
9 900 0.662636126846 Henry Cohn, 2025, needs more optimization.
9 901 0.662642382986 Henry Cohn, 2025, needs more optimization.
9 902 0.663094849224 Henry Cohn, 2025, needs more optimization.
9 903 0.663138901634 Henry Cohn, 2025, needs more optimization.
9 904 0.663151783688 Henry Cohn, 2025, needs more optimization.
9 905 0.663186631313 Henry Cohn, 2025, needs more optimization.
9 906 0.663321732544 Henry Cohn, 2025, needs more optimization.
9 907 0.663376500633 Henry Cohn, 2025, needs more optimization.
9 908 0.663412535064 Henry Cohn, 2026, needs more optimization.
9 909 0.663585246596 Henry Cohn, 2025, needs more optimization.
9 910 0.663640556847 Henry Cohn, 2025, needs more optimization.
9 911 0.663880945005 Henry Cohn, 2025, needs more optimization.
9 912 0.663891728453 Henry Cohn, 2026, needs more optimization.
9 913 0.663893472277 Henry Cohn, 2025, needs more optimization.
9 914 0.663907334507 Henry Cohn, 2025, needs more optimization.
9 915 0.664027862761 Henry Cohn, 2025, needs more optimization.
9 916 0.664221329263 Henry Cohn, 2026, needs more optimization.
9 917 0.664228513191 Henry Cohn, 2025, needs more optimization.
9 918 0.664319093900 Henry Cohn, 2025, needs more optimization.
9 919 0.664694543885 Henry Cohn, 2025, needs more optimization.
9 920 0.664707746199 Henry Cohn, 2026, needs more optimization.
9 921 0.664729861899 Henry Cohn, 2025, needs more optimization.
9 922 0.665008783421 Henry Cohn, 2025, needs more optimization.
9 923 0.665059203223 Henry Cohn, 2025, needs more optimization.
9 924 0.665085819662 Henry Cohn, 2026, needs more optimization.
9 925 0.665334349699 Henry Cohn, 2025, needs more optimization.
9 926 0.665365772605 Henry Cohn, 2025, needs more optimization.
9 927 0.665376822237 Henry Cohn, 2025, needs more optimization.
9 928 0.665655225021 Henry Cohn, 2025, needs more optimization.
9 929 0.665658867246 Henry Cohn, 2025, needs more optimization.
9 930 0.665736469099 Henry Cohn, 2025, needs more optimization.
9 931 0.666044425708 Henry Cohn, 2025, 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 0.210550138817 Henry Cohn, 2025.
10 45 0.210753585520 Henry Cohn, 2025.
10 46 0.210850169054 Henry Cohn, 2025.
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 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 0.253695768464 Henry Cohn, 2024.
10 60 0.254730982571 Henry Cohn, 2026.
10 63 0.257944905339 Henry Cohn, 2025.
10 64 0.260558294282 Henry Cohn, 2026, needs more optimization.
10 65 0.264885834877 Henry Cohn, 2025.
10 66 0.265168946762 Henry Cohn, 2025.
10 67 0.268064425530 Henry Cohn, 2025.
10 68 0.269390887696 Henry Cohn, 2026, needs more optimization.
10 69 0.269775337251 Henry Cohn, 2026, needs more optimization.
10 70 0.271729029650 Henry Cohn, 2026, needs more optimization.
10 71 0.272041687092 Henry Cohn, 2026, needs more optimization.
10 72 0.274480977473 Henry Cohn, 2026, needs more optimization.
10 73 0.275987133320 Henry Cohn, 2025.
10 74 0.279604561566 Henry Cohn, 2025.
10 76 0.284096667917 Henry Cohn, 2025.
10 77 0.284910960402 Henry Cohn, 2025.
10 78 0.289897948557 Henry Cohn, 2026.
5⁢x2+2⁢x−1
10 79 0.295299509598 Henry Cohn, 2026, needs more optimization.
10 80 0.299108578097 Henry Cohn, 2026, needs more optimization.
10 81 0.301784416185 Henry Cohn, 2026, needs more optimization.
10 82 0.304464263754 Henry Cohn, 2026, needs more optimization.
10 83 0.308261736865 Henry Cohn, 2026, needs more optimization.
10 84 0.311155299338 Henry Cohn, 2026, needs more optimization.
10 85 0.318255786436 Henry Cohn, 2026, needs more optimization.
10 86 0.322964721658 Henry Cohn, 2026, needs more optimization.
10 87 0.323798687008 Henry Cohn, 2026, needs more optimization.
10 88 0.324407524635 Henry Cohn, 2026, needs more optimization.
10 89 0.324779870327 Henry Cohn, 2026, needs more optimization.
10 90 0.325682059268 Henry Cohn, 2026, needs more optimization.
10 91 0.326706273644 Henry Cohn, 2026, needs more optimization.
10 92 0.328560709595 Henry Cohn, 2026, needs more optimization.
10 93 0.329063708307 Henry Cohn, 2026, needs more optimization.
10 94 0.329784568962 Henry Cohn, 2026, needs more optimization.
10 95 0.329854854198 Henry Cohn, 2025, needs more optimization.
10 96 0.330315697732 Henry Cohn, 2025, needs more optimization.
10 97 0.330625864546 Henry Cohn, 2026, needs more optimization.
10 98 0.330715014152 Henry Cohn, 2026, needs more optimization.
10 99 0.330884838173 Henry Cohn, 2026, needs more optimization.
10 100 0.331093369801 Henry Cohn, 2026, needs more optimization.
10 101 0.331208870453 Henry Cohn, 2026, needs more optimization.
10 102 0.331404620390 Henry Cohn, 2026, needs more optimization.
10 103 0.333258404202 Henry Cohn, 2025, needs more optimization.
10 104 0.333261975589 Henry Cohn, 2025, needs more optimization.
10 105 0.333276446551 Henry Cohn, 2025, needs more optimization.
10 107 0.333327625778 Henry Cohn, 2023, needs more optimization.
10 108 0.333329834036 Henry Cohn, 2023, needs more optimization.
10 109 0.335271812065 Henry Cohn, 2026, needs more optimization.
10 110 0.339668963152 Henry Cohn, 2026, needs more optimization.
10 111 0.342369261176 Henry Cohn, 2024, needs more optimization.
10 112 0.347037575649 Henry Cohn, 2023, needs more optimization.
10 113 0.348033914968 Henry Cohn, 2026, needs more optimization.
10 114 0.350518184001 Henry Cohn, 2026, needs more optimization.
10 115 0.352629567807 Henry Cohn, 2023, needs more optimization.
10 116 0.354068896924 Henry Cohn, 2026, needs more optimization.
10 117 0.360200923787 Henry Cohn, 2026, needs more optimization.
10 118 0.362516515684 Henry Cohn, 2023, needs more optimization.
10 119 0.363780698985 Henry Cohn, 2026, needs more optimization.
10 120 0.364675140118 Henry Cohn, 2026, needs more optimization.
10 121 0.365330581483 Henry Cohn, 2026, needs more optimization.
10 122 0.365464158252 Henry Cohn, 2026, needs more optimization.
10 124 0.365550207044 Henry Cohn, 2026, needs more optimization.
10 125 0.365553853161 Henry Cohn, 2026, needs more optimization.
10 126 0.365563082891 Henry Cohn, 2026, needs more optimization.
10 127 0.366035053027 Henry Cohn, 2024.
10 128 0.367843527953 Henry Cohn, 2026, needs more optimization.
10 129 0.370543052906 Henry Cohn, 2026, needs more optimization.
10 130 0.371247320309 Henry Cohn, 2026, needs more optimization.
10 131 0.371343753631 Henry Cohn, 2026, needs more optimization.
10 132 0.371412003523 Henry Cohn, 2026, needs more optimization.
10 133 0.385292741257 Henry Cohn, 2026, needs more optimization.
10 134 0.390476943883 Henry Cohn, 2026, needs more optimization.
10 135 0.392391815274 Henry Cohn, 2026, needs more optimization.
10 136 0.393639637890 Henry Cohn, 2026, needs more optimization.
10 137 0.396306376247 Henry Cohn, 2026, needs more optimization.
10 138 0.398853758731 Henry Cohn, 2025, needs more optimization.
10 139 0.400408788420 Henry Cohn, 2026, needs more optimization.
10 140 0.401844253131 Henry Cohn, 2026, needs more optimization.
10 141 0.403158267053 Henry Cohn, 2025, needs more optimization.
10 142 0.404535417245 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 0.414646097105 Henry Cohn, 2026, needs more optimization.
10 158 0.414911201421 Henry Cohn, 2026, needs more optimization.
10 159 0.415368955508 Henry Cohn, 2026, needs more optimization.
10 160 0.416953634447 Henry Cohn, 2026, needs more optimization.
10 161 0.417894789995 Henry Cohn, 2026, needs more optimization.
10 162 0.419543577933 Henry Cohn, 2026, needs more optimization.
10 163 0.419892782802 Henry Cohn, 2026, needs more optimization.
10 164 0.420793340453 Henry Cohn, 2026, needs more optimization.
10 165 0.421707771881 Henry Cohn, 2026, needs more optimization.
10 166 0.422770461139 Henry Cohn, 2026, needs more optimization.
10 167 0.423657504213 Henry Cohn, 2026, needs more optimization.
10 168 0.424628264143 Henry Cohn, 2026, needs more optimization.
10 169 0.425668006394 Henry Cohn, 2026, needs more optimization.
10 170 0.427422494876 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 0.438794942781 Henry Cohn, 2026, needs more optimization.
10 196 0.451060501819 Henry Cohn, 2025, needs more optimization.
10 197 0.451465402893 Henry Cohn, 2026, needs more optimization.
10 198 0.453065126367 Henry Cohn, 2026, needs more optimization.
10 199 0.453656142674 Henry Cohn, 2026, needs more optimization.
10 200 0.454379582219 Henry Cohn, 2026, needs more optimization.
10 201 0.454546767517 Henry Cohn, 2026, needs more optimization.
10 202 0.455182476156 Henry Cohn, 2026, needs more optimization.
10 203 0.456231972410 Henry Cohn, 2026, needs more optimization.
10 204 0.456659923741 Henry Cohn, 2026, needs more optimization.
10 205 0.457096182418 Henry Cohn, 2026, needs more optimization.
10 206 0.457898912267 Henry Cohn, 2026, needs more optimization.
10 207 0.458777826487 Henry Cohn, 2026, needs more optimization.
10 208 0.459639459542 Henry Cohn, 2026, needs more optimization.
10 209 0.460080182418 Henry Cohn, 2026, needs more optimization.
10 210 0.460475540482 Henry Cohn, 2026, needs more optimization.
10 211 0.461218963169 Henry Cohn, 2026, needs more optimization.
10 212 0.462186967562 Henry Cohn, 2025, needs more optimization.
10 213 0.462432095737 Henry Cohn, 2026, needs more optimization.
10 214 0.462951044906 Henry Cohn, 2026, needs more optimization.
10 215 0.463515956227 Henry Cohn, 2026, needs more optimization.
10 216 0.464088335808 Henry Cohn, 2026, needs more optimization.
10 217 0.465092144941 Henry Cohn, 2026, needs more optimization.
10 218 0.465904649761 Henry Cohn, 2026, needs more optimization.
10 219 0.466060250348 Henry Cohn, 2026, needs more optimization.
10 220 0.466969257468 Henry Cohn, 2026, needs more optimization.
10 221 0.467482112413 Henry Cohn, 2026, needs more optimization.
10 222 0.468061072174 Henry Cohn, 2026, needs more optimization.
10 223 0.468157456685 Henry Cohn, 2026, needs more optimization.
10 224 0.469170170457 Henry Cohn, 2026, needs more optimization.
10 225 0.469584222301 Henry Cohn, 2026, needs more optimization.
10 226 0.470458414305 Henry Cohn, 2026, needs more optimization.
10 227 0.470668002387 Henry Cohn, 2026, needs more optimization.
10 228 0.471513884513 Henry Cohn, 2026, needs more optimization.
10 229 0.472012735283 Henry Cohn, 2026, needs more optimization.
10 230 0.472312694860 Henry Cohn, 2026, needs more optimization.
10 231 0.473038122940 Henry Cohn, 2026, needs more optimization.
10 232 0.473654445513 Henry Cohn, 2026, needs more optimization.
10 233 0.474225192722 Henry Cohn, 2026, needs more optimization.
10 234 0.474856685492 Henry Cohn, 2026, needs more optimization.
10 235 0.475609641310 Henry Cohn, 2026, needs more optimization.
10 236 0.475887735542 Henry Cohn, 2026, needs more optimization.
10 237 0.476614761037 Henry Cohn, 2026, needs more optimization.
10 238 0.476849474029 Henry Cohn, 2026, needs more optimization.
10 239 0.477375802062 Henry Cohn, 2026, needs more optimization.
10 240 0.477989623034 Henry Cohn, 2026, needs more optimization.
10 241 0.478625589992 Henry Cohn, 2026, needs more optimization.
10 242 0.478836680841 Henry Cohn, 2026, needs more optimization.
10 243 0.479804581520 Henry Cohn, 2026, needs more optimization.
10 244 0.480174862321 Henry Cohn, 2025, needs more optimization.
10 245 0.480656799369 Henry Cohn, 2026, needs more optimization.
10 246 0.480823597780 Henry Cohn, 2026, needs more optimization.
10 247 0.481640880417 Henry Cohn, 2026, needs more optimization.
10 248 0.482126232909 Henry Cohn, 2026, needs more optimization.
10 249 0.482343451625 Henry Cohn, 2026, needs more optimization.
10 250 0.483178176586 Henry Cohn, 2026, needs more optimization.
10 251 0.483751253565 Henry Cohn, 2026, needs more optimization.
10 252 0.483931373585 Henry Cohn, 2026, needs more optimization.
10 253 0.484298065498 Henry Cohn, 2026, needs more optimization.
10 254 0.484907365786 Henry Cohn, 2026, needs more optimization.
10 255 0.485447578924 Henry Cohn, 2025, needs more optimization.
10 256 0.485731865466 Henry Cohn, 2026, needs more optimization.
10 257 0.486672423361 Henry Cohn, 2025, needs more optimization.
10 258 0.486776582276 Henry Cohn, 2026, needs more optimization.
10 259 0.487018831175 Henry Cohn, 2026, needs more optimization.
10 260 0.487248712943 Henry Cohn, 2026, needs more optimization.
10 261 0.487929839871 Henry Cohn, 2025, needs more optimization.
10 262 0.488010638917 Henry Cohn, 2026, needs more optimization.
10 263 0.488239068865 Henry Cohn, 2025, needs more optimization.
10 264 0.488516850916 Henry Cohn, 2026, needs more optimization.
10 266 0.489123105197 Henry Cohn, 2026, needs more optimization.
10 267 0.489406647251 Henry Cohn, 2025, needs more optimization.
10 268 0.489432185993 Henry Cohn, 2026, needs more optimization.
10 269 0.489460592787 Henry Cohn, 2026, needs more optimization.
10 270 0.489779664020 Henry Cohn, 2026, needs more optimization.
10 271 0.490498162985 Henry Cohn, 2026, needs more optimization.
10 272 0.491244721518 Henry Cohn, 2025, needs more optimization.
10 273 0.491972289470 Henry Cohn, 2026, needs more optimization.
10 274 0.492815363438 Henry Cohn, 2026, needs more optimization.
10 275 0.492974194470 Henry Cohn, 2025, needs more optimization.
10 276 0.493652933296 Henry Cohn, 2026, needs more optimization.
10 277 0.494231294583 Henry Cohn, 2025, needs more optimization.
10 278 0.494572195718 Henry Cohn, 2025, needs more optimization.
10 279 0.495102468877 Henry Cohn, 2026, needs more optimization.
10 280 0.495331458923 Henry Cohn, 2026, needs more optimization.
10 281 0.495864792167 Henry Cohn, 2026, needs more optimization.
10 282 0.496305591849 Henry Cohn, 2025, needs more optimization.
10 284 0.496801495945 Henry Cohn, 2026, needs more optimization.
10 285 0.497348375179 Henry Cohn, 2026, needs more optimization.
10 286 0.497472935288 Henry Cohn, 2026, needs more optimization.
10 287 0.497733487648 Henry Cohn, 2026, needs more optimization.
10 288 0.498485715924 Henry Cohn, 2026, needs more optimization.
10 289 0.498730653434 Henry Cohn, 2026, needs more optimization.
10 290 0.499127242647 Henry Cohn, 2026, needs more optimization.
10 291 0.499804808742 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
10 596 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
10 740 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 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 0.204931262058 Henry Cohn, 2025.
11 51 0.204957387535 Henry Cohn, 2023.
Minimal polynomial listed in plain text data
11 52 0.208005237402 Henry Cohn, 2024.
11 53 0.209775126698 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.
11 70 0.244726315701 Henry Cohn, 2026.
11 71 0.255919437719 Henry Cohn, 2026, needs more optimization.
11 72 0.256522543100 Henry Cohn, 2026, needs more optimization.
11 73 0.259229428292 Henry Cohn, 2026, needs more optimization.
11 74 0.259520094012 Henry Cohn, 2026, needs more optimization.
11 75 0.259754902333 Henry Cohn, 2026, needs more optimization.
11 76 0.260611782278 Henry Cohn, 2026, needs more optimization.
11 77 0.260659763728 Henry Cohn, 2026, needs more optimization.
11 78 0.260823410840 Henry Cohn, 2026, needs more optimization.
11 79 0.261256577214 Henry Cohn, 2026, needs more optimization.
11 80 0.261313630060 Henry Cohn, 2026, needs more optimization.
11 81 0.262008277852 Henry Cohn, 2026, needs more optimization.
11 82 0.263455977123 Henry Cohn, 2026, needs more optimization.
11 83 0.264198763290 Henry Cohn, 2026, needs more optimization.
11 84 0.265230263349 Henry Cohn, 2026, needs more optimization.
11 85 0.266225985351 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 0.280653491593 Henry Cohn, 2026, needs more optimization.
11 93 0.281719240084 Henry Cohn, 2026, needs more optimization.
11 94 0.282962812797 Henry Cohn, 2026, needs more optimization.
11 95 0.283938928367 Henry Cohn, 2026, needs more optimization.
11 96 0.285631420356 Henry Cohn, 2026, needs more optimization.
11 97 0.286255983593 Henry Cohn, 2026, needs more optimization.
11 98 0.287807016130 Henry Cohn, 2026, needs more optimization.
11 99 0.289831202843 Henry Cohn, 2026, needs more optimization.
11 100 0.299916810123 Henry Cohn, 2026, needs more optimization.
11 101 0.302930032464 Henry Cohn, 2026, needs more optimization.
11 102 0.304623603863 Henry Cohn, 2026, needs more optimization.
11 103 0.305756497969 Henry Cohn, 2026, needs more optimization.
11 104 0.306554014217 Henry Cohn, 2026, needs more optimization.
11 105 0.307098305054 Henry Cohn, 2026, needs more optimization.
11 106 0.307737954219 Henry Cohn, 2026, needs more optimization.
11 107 0.310786210625 Henry Cohn, 2026, needs more optimization.
11 108 0.317734326003 Henry Cohn, 2026, needs more optimization.
11 109 0.320412997083 Henry Cohn, 2026, needs more optimization.
11 110 0.321720197391 Henry Cohn, 2026, needs more optimization.
11 111 0.324384996533 Henry Cohn, 2026, needs more optimization.
11 112 0.324893808198 Henry Cohn, 2026, needs more optimization.
11 113 0.325064953334 Henry Cohn, 2026, needs more optimization.
11 114 0.325267918624 Henry Cohn, 2026, needs more optimization.
11 115 0.325412321402 Henry Cohn, 2026, needs more optimization.
11 116 0.325687794553 Henry Cohn, 2026, needs more optimization.
11 117 0.325913410900 Henry Cohn, 2026, needs more optimization.
11 118 0.326109198423 Henry Cohn, 2026, needs more optimization.
11 119 0.326373145257 Henry Cohn, 2026, needs more optimization.
11 120 0.326580746251 Henry Cohn, 2026, needs more optimization.
11 121 0.326847196383 Henry Cohn, 2026, needs more optimization.
11 122 0.327076280459 Henry Cohn, 2026, needs more optimization.
11 123 0.328161428278 Henry Cohn, 2026, needs more optimization.
11 124 0.328656833607 Henry Cohn, 2026, needs more optimization.
11 125 0.332693323364 Henry Cohn, 2026, needs more optimization.
11 126 0.332775966757 Henry Cohn, 2026, needs more optimization.
11 127 0.332908701031 Henry Cohn, 2026, needs more optimization.
11 128 0.333030047873 Henry Cohn, 2026, needs more optimization.
11 129 0.333274996083 Henry Cohn, 2024, needs more optimization.
11 130 0.333276029314 Henry Cohn, 2024, needs more optimization.
11 131 0.333329294372 Henry Cohn, 2026, needs more optimization.
11 132 0.333331284034 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 0.361871578594 Henry Cohn, 2026, needs more optimization.
11 158 0.368903940543 Henry Cohn, 2026, needs more optimization.
11 159 0.370393229037 Henry Cohn, 2026, needs more optimization.
11 160 0.372498608301 Henry Cohn, 2026, needs more optimization.
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 0.387129328095 Henry Cohn, 2026, needs more optimization.
11 168 0.389321608022 Henry Cohn, 2025, needs more optimization.
11 169 0.390164355694 Henry Cohn, 2025, needs more optimization.
11 170 0.391469832105 Henry Cohn, 2026, needs more optimization.
11 171 0.392664148377 Henry Cohn, 2026, needs more optimization.
11 172 0.393647384217 Henry Cohn, 2025, needs more optimization.
11 173 0.395017527530 Henry Cohn, 2025, needs more optimization.
11 174 0.395791313909 Henry Cohn, 2025, needs more optimization.
11 175 0.396712060503 Henry Cohn, 2025, needs more optimization.
11 176 0.398320474845 Henry Cohn, 2025, needs more optimization.
11 177 0.398807260566 Henry Cohn, 2026, needs more optimization.
11 178 0.400111193039 Henry Cohn, 2025, needs more optimization.
11 179 0.401138936288 Henry Cohn, 2026, needs more optimization.
11 180 0.401818618573 Henry Cohn, 2026, needs more optimization.
11 181 0.402834072497 Henry Cohn, 2025, needs more optimization.
11 182 0.404024048903 Henry Cohn, 2025, needs more optimization.
11 183 0.404473828764 Henry Cohn, 2025, needs more optimization.
11 184 0.405385624737 Henry Cohn, 2026, needs more optimization.
11 185 0.405516170418 Henry Cohn, 2026, needs more optimization.
11 186 0.406191917009 Henry Cohn, 2025, needs more optimization.
11 187 0.406636306148 Henry Cohn, 2025, needs more optimization.
11 188 0.406810650281 Henry Cohn, 2026, needs more optimization.
11 189 0.407525213298 Henry Cohn, 2026, needs more optimization.
11 190 0.408464811335 Henry Cohn, 2026, needs more optimization.
11 191 0.408949708303 Henry Cohn, 2026, needs more optimization.
11 192 0.409413416152 Henry Cohn, 2026, needs more optimization.
11 193 0.409973956997 Henry Cohn, 2026, needs more optimization.
11 194 0.410641931743 Henry Cohn, 2026, needs more optimization.
11 195 0.410908028917 Henry Cohn, 2026, needs more optimization.
11 196 0.411546245104 Henry Cohn, 2026, needs more optimization.
11 197 0.411563541077 Henry Cohn, 2026, needs more optimization.
11 198 0.412407006885 Henry Cohn, 2026, needs more optimization.
11 199 0.412661829407 Henry Cohn, 2026, needs more optimization.
11 200 0.412794093538 Henry Cohn, 2026, needs more optimization.
11 201 0.413238205963 Henry Cohn, 2026, needs more optimization.
11 202 0.414788699064 Henry Cohn, 2025, needs more optimization.
11 203 0.414789789276 Henry Cohn, 2026, needs more optimization.
11 204 0.415132896875 Henry Cohn, 2026, needs more optimization.
11 205 0.415625525721 Henry Cohn, 2026, needs more optimization.
11 206 0.416228960526 Henry Cohn, 2026, needs more optimization.
11 207 0.416426947491 Henry Cohn, 2026, needs more optimization.
11 208 0.417194329314 Henry Cohn, 2026, needs more optimization.
11 209 0.417962402219 Henry Cohn, 2025, needs more optimization.
11 210 0.418303651500 Henry Cohn, 2025, needs more optimization.
11 211 0.418487108010 Henry Cohn, 2026, needs more optimization.
11 212 0.418605249931 Henry Cohn, 2026, needs more optimization.
11 213 0.419803232871 Henry Cohn, 2026, needs more optimization.
11 214 0.419967985473 Henry Cohn, 2026, needs more optimization.
11 215 0.420474972106 Henry Cohn, 2026, needs more optimization.
11 216 0.420948725440 Henry Cohn, 2026, needs more optimization.
11 217 0.421612058094 Henry Cohn, 2026, needs more optimization.
11 218 0.421854105128 Henry Cohn, 2026, needs more optimization.
11 219 0.422413323623 Henry Cohn, 2026, needs more optimization.
11 220 0.422710611253 Henry Cohn, 2026, needs more optimization.
11 221 0.422953187802 Henry Cohn, 2026, needs more optimization.
11 222 0.423387422808 Henry Cohn, 2026, needs more optimization.
11 223 0.423737855406 Henry Cohn, 2026, needs more optimization.
11 224 0.423855689534 Henry Cohn, 2026, needs more optimization.
11 225 0.424282626872 Henry Cohn, 2026, needs more optimization.
11 227 0.424798964888 Henry Cohn, 2026, needs more optimization.
11 228 0.425263132645 Henry Cohn, 2026, needs more optimization.
11 229 0.425730816505 Henry Cohn, 2026, needs more optimization.
11 230 0.426310086126 Henry Cohn, 2026, needs more optimization.
11 231 0.426829251740 Henry Cohn, 2026, needs more optimization.
11 232 0.427184290541 Henry Cohn, 2026, needs more optimization.
11 233 0.427343615460 Henry Cohn, 2026, needs more optimization.
11 234 0.427754465305 Henry Cohn, 2026, needs more optimization.
11 235 0.428178914369 Henry Cohn, 2026, needs more optimization.
11 236 0.428610289631 Henry Cohn, 2026, needs more optimization.
11 237 0.428640653788 Henry Cohn, 2026, needs more optimization.
11 238 0.428806027244 Henry Cohn, 2026, needs more optimization.
11 239 0.429040628376 Henry Cohn, 2026, needs more optimization.
11 240 0.429098742027 Henry Cohn, 2025, needs more optimization.
11 241 0.429973355888 Henry Cohn, 2025, needs more optimization.
11 242 0.430928428639 Henry Cohn, 2026, needs more optimization.
11 243 0.432354797268 Henry Cohn, 2026, needs more optimization.
11 244 0.432605295540 Henry Cohn, 2026, needs more optimization.
11 245 0.432620932549 Henry Cohn, 2026, needs more optimization.
11 246 0.433233245052 Henry Cohn, 2026, needs more optimization.
11 247 0.433610805513 Henry Cohn, 2026, needs more optimization.
11 248 0.434145308382 Henry Cohn, 2026, needs more optimization.
11 249 0.435006394286 Henry Cohn, 2026, needs more optimization.
11 250 0.437697146612 Henry Cohn, 2026, needs more optimization.
11 251 0.437744973709 Henry Cohn, 2026, needs more optimization.
11 252 0.437751154860 Henry Cohn, 2026, needs more optimization.
11 253 0.437987871131 Henry Cohn, 2026, needs more optimization.
11 254 0.438011072834 Henry Cohn, 2026, needs more optimization.
11 255 0.438876428807 Henry Cohn, 2026, needs more optimization.
11 256 0.438958419338 Henry Cohn, 2026, needs more optimization.
11 257 0.439482788001 Henry Cohn, 2026, needs more optimization.
11 258 0.439582725446 Henry Cohn, 2026, needs more optimization.
11 259 0.440625030991 Henry Cohn, 2026, needs more optimization.
11 260 0.440640903720 Henry Cohn, 2026, needs more optimization.
11 261 0.440833425178 Henry Cohn, 2026, needs more optimization.
11 262 0.440866174416 Henry Cohn, 2026, needs more optimization.
11 263 0.440946596287 Henry Cohn, 2026, needs more optimization.
11 264 0.440968477193 Henry Cohn, 2026, needs more optimization.
11 265 0.440994816052 Henry Cohn, 2026, needs more optimization.
11 266 0.441320475867 Henry Cohn, 2026, needs more optimization.
11 267 0.441370306663 Henry Cohn, 2026, needs more optimization.
11 268 0.441429961676 Henry Cohn, 2026, needs more optimization.
11 269 0.442518769590 Henry Cohn, 2026, needs more optimization.
11 270 0.442557055621 Henry Cohn, 2026, needs more optimization.
11 271 0.442743424981 Henry Cohn, 2026, needs more optimization.
11 272 0.443016067299 Henry Cohn, 2026, needs more optimization.
11 273 0.443092684846 Henry Cohn, 2026, needs more optimization.
11 274 0.443114814092 Henry Cohn, 2026, needs more optimization.
11 275 0.443268846145 Henry Cohn, 2026, needs more optimization.
11 276 0.443749607790 Henry Cohn, 2026, needs more optimization.
11 277 0.443777633208 Henry Cohn, 2026, needs more optimization.
11 278 0.444838011725 Henry Cohn, 2026, needs more optimization.
11 279 0.444852397481 Henry Cohn, 2026, needs more optimization.
11 280 0.445590332885 Henry Cohn, 2026, needs more optimization.
11 281 0.445679295848 Henry Cohn, 2026, needs more optimization.
11 282 0.446793868294 Henry Cohn, 2026, needs more optimization.
11 283 0.447200862398 Henry Cohn, 2026, needs more optimization.
11 284 0.447212698987 Henry Cohn, 2026, needs more optimization.
11 285 0.447227399440 Henry Cohn, 2026, needs more optimization.
11 286 0.447240900911 Henry Cohn, 2026, needs more optimization.
11 289 0.447266123833 Henry Cohn, 2026, needs more optimization.
11 290 0.448535371375 Henry Cohn, 2026, needs more optimization.
11 291 0.449410970035 Henry Cohn, 2026, needs more optimization.
11 292 0.449459638926 Henry Cohn, 2026, needs more optimization.
11 293 0.449602715871 Henry Cohn, 2026, needs more optimization.
11 294 0.449609561912 Henry Cohn, 2026, needs more optimization.
11 295 0.450711720752 Henry Cohn, 2026, needs more optimization.
11 296 0.451526964848 Henry Cohn, 2026, needs more optimization.
11 297 0.454535253827 Henry Cohn, 2026, needs more optimization.
11 298 0.458129466397 Henry Cohn, 2026, needs more optimization.
11 299 0.458858549866 Henry Cohn, 2026, needs more optimization.
11 300 0.459021622171 Henry Cohn, 2026, needs more optimization.
11 301 0.459639328973 Henry Cohn, 2025, needs more optimization.
11 302 0.460203223454 Henry Cohn, 2025, needs more optimization.
11 303 0.460288477586 Henry Cohn, 2025, needs more optimization.
11 304 0.460862225321 Henry Cohn, 2026, needs more optimization.
11 305 0.461268830255 Henry Cohn, 2025, needs more optimization.
11 306 0.461721343172 Henry Cohn, 2025, needs more optimization.
11 307 0.462044048096 Henry Cohn, 2025, needs more optimization.
11 308 0.462399539817 Henry Cohn, 2025, needs more optimization.
11 309 0.462994444527 Henry Cohn, 2025, needs more optimization.
11 310 0.463544165000 Henry Cohn, 2025, needs more optimization.
11 311 0.463659643751 Henry Cohn, 2025, needs more optimization.
11 312 0.464359894912 Henry Cohn, 2026, needs more optimization.
11 313 0.464976892208 Henry Cohn, 2025, needs more optimization.
11 314 0.465091025246 Henry Cohn, 2025, needs more optimization.
11 315 0.465715320515 Henry Cohn, 2025, needs more optimization.
11 316 0.465900306780 Henry Cohn, 2025, needs more optimization.
11 317 0.465904310823 Henry Cohn, 2025, needs more optimization.
11 318 0.466097303368 Henry Cohn, 2025, needs more optimization.
11 319 0.466267282465 Henry Cohn, 2025, needs more optimization.
11 320 0.467028400033 Henry Cohn, 2026, needs more optimization.
11 321 0.467258854327 Henry Cohn, 2025, needs more optimization.
11 322 0.467511739233 Henry Cohn, 2025, needs more optimization.
11 323 0.468182878263 Henry Cohn, 2025, needs more optimization.
11 324 0.470472334177 Henry Cohn, 2025, needs more optimization.
11 325 0.471201521874 Henry Cohn, 2025, needs more optimization.
11 326 0.471702531797 Henry Cohn, 2025, needs more optimization.
11 327 0.471894887006 Henry Cohn, 2025, needs more optimization.
11 328 0.472633915840 Henry Cohn, 2026, needs more optimization.
11 329 0.472833096322 Henry Cohn, 2025, needs more optimization.
11 330 0.473098656858 Henry Cohn, 2025, needs more optimization.
11 331 0.473467506404 Henry Cohn, 2025, needs more optimization.
11 332 0.473867904590 Henry Cohn, 2025, needs more optimization.
11 333 0.473871803646 Henry Cohn, 2025, needs more optimization.
11 334 0.474236401896 Henry Cohn, 2025, needs more optimization.
11 335 0.474719431936 Henry Cohn, 2025, needs more optimization.
11 336 0.474724651842 Henry Cohn, 2026, needs more optimization.
11 337 0.475243110879 Henry Cohn, 2025, needs more optimization.
11 338 0.475609826115 Henry Cohn, 2025, needs more optimization.
11 339 0.475701250198 Henry Cohn, 2025, needs more optimization.
11 340 0.475934479081 Henry Cohn, 2025, needs more optimization.
11 341 0.476285444701 Henry Cohn, 2025, needs more optimization.
11 342 0.476354680116 Henry Cohn, 2025, needs more optimization.
11 343 0.476618421655 Henry Cohn, 2025, needs more optimization.
11 344 0.476716590023 Henry Cohn, 2026, needs more optimization.
11 345 0.476956469542 Henry Cohn, 2025, needs more optimization.
11 346 0.477307252247 Henry Cohn, 2025, needs more optimization.
11 347 0.478281760346 Henry Cohn, 2025, needs more optimization.
11 348 0.478300347621 Henry Cohn, 2025, needs more optimization.
11 349 0.479176122649 Henry Cohn, 2025, needs more optimization.
11 350 0.479210833472 Henry Cohn, 2025, needs more optimization.
11 351 0.479489173418 Henry Cohn, 2025, needs more optimization.
11 352 0.479982048056 Henry Cohn, 2025, needs more optimization.
11 353 0.480077140051 Henry Cohn, 2025, needs more optimization.
11 354 0.480183713218 Henry Cohn, 2025, needs more optimization.
11 355 0.480436888208 Henry Cohn, 2025, needs more optimization.
11 356 0.480487166888 Henry Cohn, 2025, needs more optimization.
11 357 0.480842494444 Henry Cohn, 2025, needs more optimization.
11 358 0.480902210072 Henry Cohn, 2025, needs more optimization.
11 359 0.481274495959 Henry Cohn, 2025, needs more optimization.
11 360 0.481291506240 Henry Cohn, 2025, needs more optimization.
11 361 0.481741529691 Henry Cohn, 2025, needs more optimization.
11 362 0.481995028899 Henry Cohn, 2025, needs more optimization.
11 363 0.482103941912 Henry Cohn, 2025, needs more optimization.
11 364 0.482290195550 Henry Cohn, 2025, needs more optimization.
11 365 0.482303853060 Henry Cohn, 2025, needs more optimization.
11 366 0.482501512317 Henry Cohn, 2025, needs more optimization.
11 367 0.483057849632 Henry Cohn, 2025, needs more optimization.
11 368 0.483246288551 Henry Cohn, 2026, needs more optimization.
11 369 0.483262726267 Henry Cohn, 2025, needs more optimization.
11 370 0.483583948555 Henry Cohn, 2025, needs more optimization.
11 371 0.483706899316 Henry Cohn, 2025, needs more optimization.
11 372 0.483722683915 Henry Cohn, 2025, needs more optimization.
11 373 0.484043235518 Henry Cohn, 2025, needs more optimization.
11 374 0.484097153813 Henry Cohn, 2025, needs more optimization.
11 376 0.484538913691 Henry Cohn, 2026, needs more optimization.
11 377 0.485141337715 Henry Cohn, 2025, needs more optimization.
11 378 0.485150414751 Henry Cohn, 2025, needs more optimization.
11 379 0.485977589895 Henry Cohn, 2025, needs more optimization.
11 380 0.485982957540 Henry Cohn, 2025, needs more optimization.
11 381 0.486020085020 Henry Cohn, 2025, needs more optimization.
11 382 0.486040770663 Henry Cohn, 2025, needs more optimization.
11 383 0.486097954624 Henry Cohn, 2025, needs more optimization.
11 384 0.486113457975 Henry Cohn, 2026, needs more optimization.
11 385 0.486126091016 Henry Cohn, 2025, needs more optimization.
11 386 0.486381949776 Henry Cohn, 2025, needs more optimization.
11 387 0.486469389022 Henry Cohn, 2025, needs more optimization.
11 388 0.486486010528 Henry Cohn, 2025, needs more optimization.
11 389 0.486579853534 Henry Cohn, 2025, needs more optimization.
11 390 0.486591059814 Henry Cohn, 2025, needs more optimization.
11 392 0.487378958415 Henry Cohn, 2026, needs more optimization.
11 393 0.487401897134 Henry Cohn, 2025, needs more optimization.
11 394 0.487409887893 Henry Cohn, 2025, needs more optimization.
11 395 0.487417126467 Henry Cohn, 2025, needs more optimization.
11 396 0.487555259930 Henry Cohn, 2026, needs more optimization.
11 397 0.488352351257 Henry Cohn, 2026, needs more optimization.
11 398 0.488437617194 Henry Cohn, 2025, needs more optimization.
11 400 0.488675285089 Henry Cohn, 2026, needs more optimization.
11 401 0.490210887347 Henry Cohn, 2026, needs more optimization.
11 403 0.490210887455 Henry Cohn, 2025, needs more optimization.
11 404 0.490239534679 Henry Cohn, 2025, needs more optimization.
11 405 0.490253634370 Henry Cohn, 2025, needs more optimization.
11 406 0.491282760871 Henry Cohn, 2025, needs more optimization.
11 408 0.491614827339 Henry Cohn, 2026, needs more optimization.
11 409 0.491734488110 Henry Cohn, 2025, needs more optimization.
11 410 0.492513510937 Henry Cohn, 2026, needs more optimization.
11 411 0.492513511025 Henry Cohn, 2025, needs more optimization.
11 412 0.492718967900 Henry Cohn, 2026, needs more optimization.
11 415 0.492734383686 Henry Cohn, 2026, needs more optimization.
11 416 0.492812844913 Henry Cohn, 2026, needs more optimization.
11 417 0.492828395878 Henry Cohn, 2025, needs more optimization.
11 418 0.493129409762 Henry Cohn, 2026, needs more optimization.
11 419 0.493274992243 Henry Cohn, 2026, needs more optimization.
11 421 0.493916610675 Henry Cohn, 2026, needs more optimization.
11 422 0.493945089141 Henry Cohn, 2025, needs more optimization.
11 423 0.493970791475 Henry Cohn, 2025, needs more optimization.
11 424 0.493985756792 Henry Cohn, 2025, needs more optimization.
11 425 0.494037829338 Henry Cohn, 2025, needs more optimization.
11 426 0.494051876349 Henry Cohn, 2025, needs more optimization.
11 427 0.494082410490 Henry Cohn, 2026, needs more optimization.
11 429 0.494119524472 Henry Cohn, 2026, needs more optimization.
11 430 0.494207621254 Henry Cohn, 2026, needs more optimization.
11 431 0.494208897310 Henry Cohn, 2026, needs more optimization.
11 432 0.494214749693 Henry Cohn, 2026, needs more optimization.
11 434 0.494311598236 Henry Cohn, 2025, needs more optimization.
11 435 0.494313766122 Henry Cohn, 2025, needs more optimization.
11 436 0.494539720884 Henry Cohn, 2025, needs more optimization.
11 438 0.494865572262 Henry Cohn, 2025, needs more optimization.
11 439 0.494939689263 Henry Cohn, 2026, needs more optimization.
11 440 0.495001803697 Henry Cohn, 2025, needs more optimization.
11 441 0.495208013246 Henry Cohn, 2025, needs more optimization.
11 442 0.495240503799 Henry Cohn, 2026, needs more optimization.
11 443 0.495240503803 Henry Cohn, 2026, needs more optimization.
11 445 0.496354649532 Henry Cohn, 2026, needs more optimization.
11 446 0.496423782539 Henry Cohn, 2025, needs more optimization.
11 449 0.496522031081 Henry Cohn, 2026, needs more optimization.
11 450 0.496883465367 Henry Cohn, 2025, needs more optimization.
11 451 0.496942224687 Henry Cohn, 2026, needs more optimization.
11 452 0.496973862488 Henry Cohn, 2026, needs more optimization.
11 472 0.499957673075 Henry Cohn, 2025, needs more optimization.
11 593 0.499999989608 A. Novikov, N. Vu, M. Eisenberger, E. Dupont, P.-S. Huang, A. Z. Wagner, S. Shirobokov, B. Kozlovskii, F. J. R. Ruiz, A. Mehrabian, M. P. Kumar, A. See, S. Chaudhuri, G. Holland, A. Davies, S. Nowozin, P. Kohli, and M. Balog, AlphaEvolve: A coding agent for scientific and algorithmic discovery, Google DeepMind white paper, 2025, after some further optimization.
11 594 0.500278631151 Henry Cohn, 2026, needs more optimization.
11 595 0.501006358091 Henry Cohn, 2026, needs more optimization.
11 596 0.501441454208 Henry Cohn, 2026, needs more optimization.
11 597 0.520255490104 Henry Cohn, 2025, needs more optimization.
11 598 0.520331537319 Henry Cohn, 2025, needs more optimization.
11 600 0.520405377653 Henry Cohn, 2026, needs more optimization.
11 604 0.521043245819 Henry Cohn, 2026, needs more optimization.
11 605 0.521318118650 Henry Cohn, 2026, needs more optimization.
11 606 0.521353070721 Henry Cohn, 2026, needs more optimization.
11 608 0.521425128897 Henry Cohn, 2026, needs more optimization.
11 609 0.521600438331 Henry Cohn, 2026, needs more optimization.
11 611 0.521854890548 Henry Cohn, 2025, needs more optimization.
11 612 0.523617017905 Henry Cohn, 2026, needs more optimization.
11 616 0.523839473739 Henry Cohn, 2026, needs more optimization.
11 617 0.524032119163 Henry Cohn, 2025, needs more optimization.
11 620 0.524033456003 Henry Cohn, 2026, needs more optimization.
11 621 0.524091054566 Henry Cohn, 2025, needs more optimization.
11 623 0.524096196647 Henry Cohn, 2025, needs more optimization.
11 624 0.525155603305 Henry Cohn, 2026, needs more optimization.
11 628 0.525283801910 Henry Cohn, 2026, needs more optimization.
11 630 0.525675334247 Henry Cohn, 2026, needs more optimization.
11 631 0.525682491562 Henry Cohn, 2025, needs more optimization.
11 632 0.525941594293 Henry Cohn, 2026, needs more optimization.
11 633 0.527485789217 Henry Cohn, 2025, needs more optimization.
11 636 0.527549701492 Henry Cohn, 2026, needs more optimization.
11 637 0.527569511004 Henry Cohn, 2025, needs more optimization.
11 640 0.528850538035 Henry Cohn, 2026, needs more optimization.
11 644 0.529185588858 Henry Cohn, 2026, needs more optimization.
11 646 0.529335846381 Henry Cohn, 2025, needs more optimization.
11 647 0.530846594391 Henry Cohn, 2025, needs more optimization.
11 648 0.530881393746 Henry Cohn, 2026, needs more optimization.
11 649 0.531044621234 Henry Cohn, 2025, needs more optimization.
11 650 0.531139104296 Henry Cohn, 2025, needs more optimization.
11 652 0.532332389863 Henry Cohn, 2026, needs more optimization.
11 653 0.532366999013 Henry Cohn, 2025, needs more optimization.
11 656 0.532386749828 Henry Cohn, 2026, needs more optimization.
11 657 0.532392160573 Henry Cohn, 2025, needs more optimization.
11 658 0.532401095302 Henry Cohn, 2025, needs more optimization.
11 659 0.532467715439 Henry Cohn, 2025, needs more optimization.
11 660 0.532683682665 Henry Cohn, 2026, needs more optimization.
11 661 0.534392831481 Henry Cohn, 2025, needs more optimization.
11 662 0.534401715093 Henry Cohn, 2025, needs more optimization.
11 663 0.534422746084 Henry Cohn, 2025, needs more optimization.
11 664 0.535698338176 Henry Cohn, 2026, needs more optimization.
11 665 0.535702593944 Henry Cohn, 2025, needs more optimization.
11 666 0.535725882319 Henry Cohn, 2025, needs more optimization.
11 667 0.535746493888 Henry Cohn, 2025, needs more optimization.
11 668 0.536717879016 Henry Cohn, 2026, needs more optimization.
11 669 0.536758892961 Henry Cohn, 2025, needs more optimization.
11 670 0.536786559175 Henry Cohn, 2025, needs more optimization.
11 672 0.536789415949 Henry Cohn, 2026, needs more optimization.
11 673 0.536806501096 Henry Cohn, 2025, needs more optimization.
11 676 0.539142438831 Henry Cohn, 2026, needs more optimization.
11 677 0.539251824581 Henry Cohn, 2025, needs more optimization.
11 678 0.539285306592 Henry Cohn, 2026, needs more optimization.
11 679 0.539314255561 Henry Cohn, 2026, needs more optimization.
11 680 0.539330726828 Henry Cohn, 2026, needs more optimization.
11 681 0.539565443765 Henry Cohn, 2026, needs more optimization.
11 683 0.541618940674 Henry Cohn, 2025, needs more optimization.
11 684 0.541626134008 Henry Cohn, 2026, needs more optimization.
11 686 0.541698047302 Henry Cohn, 2025, needs more optimization.
11 687 0.541917098259 Henry Cohn, 2025, needs more optimization.
11 688 0.542939046711 Henry Cohn, 2026, needs more optimization.
11 692 0.543069833915 Henry Cohn, 2026, needs more optimization.
11 693 0.543396266703 Henry Cohn, 2026, needs more optimization.
11 694 0.545961161013 Henry Cohn, 2025, needs more optimization.
11 695 0.545969774608 Henry Cohn, 2025, needs more optimization.
11 696 0.546017681485 Henry Cohn, 2026, needs more optimization.
11 697 0.546071440016 Henry Cohn, 2025, needs more optimization.
11 698 0.546909865387 Henry Cohn, 2025, needs more optimization.
11 699 0.546915672479 Henry Cohn, 2025, needs more optimization.
11 700 0.546970395971 Henry Cohn, 2026, needs more optimization.
11 701 0.547105417013 Henry Cohn, 2025, needs more optimization.
11 702 0.549155079102 Henry Cohn, 2025, needs more optimization.
11 703 0.550249089558 Henry Cohn, 2025, 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 0.588808434262 Henry Cohn, 2025, needs more optimization.
11 984 0.588842803390 Henry Cohn, 2026, needs more optimization.
11 985 0.589065956887 Henry Cohn, 2025, needs more optimization.
11 986 0.589080885292 Henry Cohn, 2025, needs more optimization.
11 987 0.589337788121 Henry Cohn, 2025, needs more optimization.
11 988 0.589474269186 Henry Cohn, 2026, needs more optimization.
11 989 0.589493230922 Henry Cohn, 2025, needs more optimization.
11 990 0.589494231559 Henry Cohn, 2025, needs more optimization.
11 991 0.589724651603 Henry Cohn, 2025, needs more optimization.
11 992 0.589729337081 Henry Cohn, 2026, needs more optimization.
11 993 0.589747194595 Henry Cohn, 2025, needs more optimization.
11 994 0.589777803169 Henry Cohn, 2025, needs more optimization.
11 996 0.589929252049 Henry Cohn, 2026, needs more optimization.
11 997 0.590217455898 Henry Cohn, 2025, needs more optimization.
11 998 0.590283571891 Henry Cohn, 2025, needs more optimization.
11 999 0.590290163347 Henry Cohn, 2025, needs more optimization.
11 1000 0.590342544738 Henry Cohn, 2026, needs more optimization.
11 1001 0.590366225530 Henry Cohn, 2025, needs more optimization.
11 1002 0.590628709920 Henry Cohn, 2025, needs more optimization.
11 1003 0.590659823164 Henry Cohn, 2025, needs more optimization.
11 1004 0.590674113006 Henry Cohn, 2026, needs more optimization.
11 1005 0.590861588302 Henry Cohn, 2026, needs more optimization.
11 1006 0.590981361414 Henry Cohn, 2026, needs more optimization.
11 1007 0.591030480092 Henry Cohn, 2025, needs more optimization.
11 1008 0.591238716992 Henry Cohn, 2026, needs more optimization.
11 1009 0.591282497506 Henry Cohn, 2025, needs more optimization.
11 1010 0.591400741854 Henry Cohn, 2025, needs more optimization.
11 1011 0.591405377429 Henry Cohn, 2025, needs more optimization.
11 1012 0.591437856314 Henry Cohn, 2026, needs more optimization.
11 1013 0.591631264119 Henry Cohn, 2025, needs more optimization.
11 1014 0.591657175256 Henry Cohn, 2026, needs more optimization.
11 1015 0.591883276887 Henry Cohn, 2025, needs more optimization.
11 1016 0.591904113557 Henry Cohn, 2026, needs more optimization.
11 1017 0.591917458356 Henry Cohn, 2025, needs more optimization.
11 1018 0.592152389992 Henry Cohn, 2026, needs more optimization.
11 1019 0.592164252037 Henry Cohn, 2025, needs more optimization.
11 1020 0.592205871152 Henry Cohn, 2026, needs more optimization.
11 1021 0.592232252111 Henry Cohn, 2026, needs more optimization.
11 1022 0.592586779414 Henry Cohn, 2025, needs more optimization.
11 1023 0.592595642913 Henry Cohn, 2025, needs more optimization.
11 1024 0.592628472863 Henry Cohn, 2026, needs more optimization.
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 0.187411648808 Henry Cohn, 2025.
12 54 0.189746662791 Henry Cohn, 2024.
12 55 0.193319611131 Henry Cohn, 2025.
12 56 0.200925636261 Henry Cohn, 2025.
12 57 0.201958116645 Henry Cohn, 2025.
12 58 0.203749632752 Henry Cohn, 2025.
12 59 0.205147720753 Henry Cohn, 2025.
12 60 0.207649060826 Henry Cohn, 2026, needs more optimization.
12 61 0.211404126394 Henry Cohn, 2025.
12 62 0.213863503460 Henry Cohn, 2025.
12 63 0.214059912690 Henry Cohn, 2026, needs more optimization.
12 64 0.214265545848 Henry Cohn, 2026, needs more optimization.
12 65 0.214419129479 Henry Cohn, 2026, needs more optimization.
12 66 0.215065521490 Henry Cohn, 2026, needs more optimization.
12 67 0.220122276110 Henry Cohn, 2026, needs more optimization.
12 68 0.222609489598 Henry Cohn, 2026, needs more optimization.
12 69 0.225818419964 Henry Cohn, 2026, needs more optimization.
12 70 0.228656013972 Henry Cohn, 2026, needs more optimization.
12 71 0.232255775950 Henry Cohn, 2025.
12 72 0.233344424897 Henry Cohn, 2026.
12 73 0.234628999325 Henry Cohn, 2026, needs more optimization.
12 74 0.235166207807 Henry Cohn, 2026, needs more optimization.
12 75 0.236566313789 Henry Cohn, 2026, needs more optimization.
12 76 0.237336218342 Henry Cohn, 2025.
12 77 0.237968057446 Henry Cohn, 2025.
12 78 0.241648057068 Henry Cohn, 2025.
12 79 0.243234050771 Henry Cohn, 2025.
12 80 0.247423282562 Henry Cohn, 2026, needs more optimization.
12 81 0.25 C. Ma, T. T. Zhaowei, 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
12 82 0.255753795402 Henry Cohn, 2026, needs more optimization.
12 83 0.258657193037 Henry Cohn, 2026, needs more optimization.
12 84 0.259080241278 Henry Cohn, 2026, needs more optimization.
12 85 0.260700618907 Henry Cohn, 2026, needs more optimization.
12 86 0.261584332921 Henry Cohn, 2026, needs more optimization.
12 87 0.261666113899 Henry Cohn, 2026, needs more optimization.
12 88 0.261873213364 Henry Cohn, 2026, needs more optimization.
12 89 0.262213877969 Henry Cohn, 2026, needs more optimization.
12 90 0.262685089966 Henry Cohn, 2026, needs more optimization.
12 91 0.263153180377 Henry Cohn, 2026, needs more optimization.
12 92 0.263539603169 Henry Cohn, 2026, needs more optimization.
12 93 0.264145863655 Henry Cohn, 2026, needs more optimization.
12 94 0.265194206852 Henry Cohn, 2026, needs more optimization.
12 95 0.265548936855 Henry Cohn, 2026, needs more optimization.
12 96 0.265982067744 Henry Cohn, 2026, needs more optimization.
12 97 0.266109762761 Henry Cohn, 2026, needs more optimization.
12 98 0.266808143783 Henry Cohn, 2026, needs more optimization.
12 100 0.267113377119 Henry Cohn, 2026, needs more optimization.
12 101 0.267198319814 Henry Cohn, 2026, needs more optimization.
12 102 0.267201610320 Henry Cohn, 2026, needs more optimization.
12 103 0.269832699377 Henry Cohn, 2026, needs more optimization.
12 104 0.271875489833 Henry Cohn, 2026, needs more optimization.
12 105 0.273461339500 Henry Cohn, 2026, needs more optimization.
12 106 0.274917636997 Henry Cohn, 2026, needs more optimization.
12 107 0.276917906014 Henry Cohn, 2026, needs more optimization.
12 108 0.276965352595 Henry Cohn, 2026, needs more optimization.
12 109 0.277603311786 Henry Cohn, 2026, needs more optimization.
12 110 0.278352312623 Henry Cohn, 2026, needs more optimization.
12 111 0.278780094721 Henry Cohn, 2026, needs more optimization.
12 112 0.281101493533 Henry Cohn, 2026, needs more optimization.
12 113 0.282021066887 Henry Cohn, 2026, needs more optimization.
12 114 0.291611802601 Henry Cohn, 2026, needs more optimization.
12 115 0.292493595651 Henry Cohn, 2026, needs more optimization.
12 116 0.293189008248 Henry Cohn, 2026, needs more optimization.
12 117 0.294031290192 Henry Cohn, 2026, needs more optimization.
12 118 0.294318328878 Henry Cohn, 2026, needs more optimization.
12 121 0.294708984749 Henry Cohn, 2026, needs more optimization.
12 122 0.304154401283 Henry Cohn, 2026, needs more optimization.
12 123 0.305712625663 Henry Cohn, 2026, needs more optimization.
12 124 0.305740747326 Henry Cohn, 2026, needs more optimization.
12 125 0.305884478708 Henry Cohn, 2026, needs more optimization.
12 126 0.306653138440 Henry Cohn, 2026, needs more optimization.
12 127 0.307716181568 Henry Cohn, 2026, needs more optimization.
12 128 0.308118778763 Henry Cohn, 2026, needs more optimization.
12 129 0.309039276967 Henry Cohn, 2026, needs more optimization.
12 130 0.310042584977 Henry Cohn, 2026, needs more optimization.
12 131 0.310612329510 Henry Cohn, 2026, needs more optimization.
12 132 0.314077437468 Henry Cohn, 2026, needs more optimization.
12 133 0.317037278561 Henry Cohn, 2026, needs more optimization.
12 134 0.317394821581 Henry Cohn, 2026, needs more optimization.
12 135 0.319133732677 Henry Cohn, 2026, needs more optimization.
12 136 0.320347422238 Henry Cohn, 2026, needs more optimization.
12 137 0.321472607148 Henry Cohn, 2026, needs more optimization.
12 138 0.322251886146 Henry Cohn, 2026, needs more optimization.
12 139 0.322315947380 Henry Cohn, 2026, needs more optimization.
12 140 0.322566656825 Henry Cohn, 2026, needs more optimization.
12 141 0.322680868656 Henry Cohn, 2026, needs more optimization.
12 142 0.322936703966 Henry Cohn, 2026, needs more optimization.
12 143 0.323149651816 Henry Cohn, 2026, needs more optimization.
12 144 0.323789285899 Henry Cohn, 2026, needs more optimization.
12 145 0.324280773706 Henry Cohn, 2026, needs more optimization.
12 146 0.324403499498 Henry Cohn, 2026, needs more optimization.
12 147 0.324845922285 Henry Cohn, 2026, needs more optimization.
12 148 0.325225308691 Henry Cohn, 2026, needs more optimization.
12 149 0.325731127286 Henry Cohn, 2026, needs more optimization.
12 150 0.326790061973 Henry Cohn, 2026, needs more optimization.
12 151 0.327219040307 Henry Cohn, 2026, needs more optimization.
12 152 0.327880690570 Henry Cohn, 2026, needs more optimization.
12 153 0.328491673622 Henry Cohn, 2026, needs more optimization.
12 154 0.329235554955 Henry Cohn, 2026, needs more optimization.
12 155 0.329524083273 Henry Cohn, 2026, needs more optimization.
12 156 0.329662053655 Henry Cohn, 2026, needs more optimization.
12 157 0.329909671542 Henry Cohn, 2026, needs more optimization.
12 158 0.330020811470 Henry Cohn, 2026, needs more optimization.
12 160 0.330027572668 Henry Cohn, 2026, needs more optimization.
12 161 0.330889962310 Henry Cohn, 2026, needs more optimization.
12 162 0.331403287521 Henry Cohn, 2026, needs more optimization.
12 163 0.331524578950 Henry Cohn, 2026, needs more optimization.
12 164 0.331691650682 Henry Cohn, 2026, needs more optimization.
12 165 0.332358406160 Henry Cohn, 2026, needs more optimization.
12 166 0.332735270172 Henry Cohn, 2026, needs more optimization.
12 167 0.332838574719 Henry Cohn, 2026, needs more optimization.
12 168 0.332884792222 Henry Cohn, 2026, needs more optimization.
12 169 0.333009577938 Henry Cohn, 2026, needs more optimization.
12 170 0.333079424538 Henry Cohn, 2026, needs more optimization.
12 171 0.333080044912 Henry Cohn, 2026, needs more optimization.
12 172 0.333177912649 Henry Cohn, 2026, needs more optimization.
12 173 0.333187717662 Henry Cohn, 2026, needs more optimization.
12 174 0.333199904968 Henry Cohn, 2026, needs more optimization.
12 175 0.333238999487 Henry Cohn, 2026, needs more optimization.
12 178 0.333324189280 Henry Cohn, 2026, needs more optimization.
12 179 0.333907699235 Henry Cohn, 2026, needs more optimization.
12 180 0.336269891292 Henry Cohn, 2026, needs more optimization.
12 181 0.359985226456 Henry Cohn, 2026, needs more optimization.
12 182 0.360402952992 Henry Cohn, 2025, needs more optimization.
12 183 0.362484635454 Henry Cohn, 2026, needs more optimization.
12 184 0.362745548851 Henry Cohn, 2026, needs more optimization.
12 185 0.364367631183 Henry Cohn, 2025, needs more optimization.
12 186 0.364670452890 Henry Cohn, 2025, needs more optimization.
12 187 0.366217681782 Henry Cohn, 2025, needs more optimization.
12 188 0.367431150262 Henry Cohn, 2026, needs more optimization.
12 189 0.368825305337 Henry Cohn, 2026, needs more optimization.
12 190 0.369101197600 Henry Cohn, 2026, needs more optimization.
12 191 0.370826193104 Henry Cohn, 2025, needs more optimization.
12 192 0.372264325065 Henry Cohn, 2026, needs more optimization.
12 193 0.373197987134 Henry Cohn, 2026, needs more optimization.
12 194 0.374237876109 Henry Cohn, 2025, needs more optimization.
12 195 0.374683778682 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 0.388879475154 Henry Cohn, 2026, needs more optimization.
12 212 0.390251393251 Henry Cohn, 2026, needs more optimization.
12 213 0.390710750979 Henry Cohn, 2026, needs more optimization.
12 214 0.391703113754 Henry Cohn, 2026, needs more optimization.
12 219 0.392341362442 Henry Cohn, 2026, needs more optimization.
12 220 0.392657559572 Henry Cohn, 2026, needs more optimization.
12 223 0.392659642924 Henry Cohn, 2026, needs more optimization.
12 224 0.394012062949 Henry Cohn, 2026, needs more optimization.
12 225 0.394101016972 Henry Cohn, 2026, needs more optimization.
12 226 0.394108358740 Henry Cohn, 2026, needs more optimization.
12 227 0.394924076574 Henry Cohn, 2025, needs more optimization.
12 228 0.394926385731 Henry Cohn, 2026, needs more optimization.
12 229 0.395023232683 Henry Cohn, 2026, needs more optimization.
12 230 0.395104309471 Henry Cohn, 2025, needs more optimization.
12 231 0.395165390251 Henry Cohn, 2026, needs more optimization.
12 232 0.395426138850 Henry Cohn, 2025, needs more optimization.
12 233 0.395438351667 Henry Cohn, 2025, needs more optimization.
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
12 289 0.429257726236 Henry Cohn, 2026, needs more optimization.
12 290 0.429516989942 Henry Cohn, 2026, needs more optimization.
12 291 0.429724400063 Henry Cohn, 2026, needs more optimization.
12 292 0.430276574302 Henry Cohn, 2026, needs more optimization.
12 293 0.430777180445 Henry Cohn, 2026, needs more optimization.
12 294 0.431063166183 Henry Cohn, 2026, needs more optimization.
12 295 0.431534989927 Henry Cohn, 2026, needs more optimization.
12 296 0.431883081034 Henry Cohn, 2026, needs more optimization.
12 297 0.432324975418 Henry Cohn, 2026, needs more optimization.
12 298 0.432646995746 Henry Cohn, 2026, needs more optimization.
12 299 0.433106225107 Henry Cohn, 2026, needs more optimization.
12 300 0.433427389628 Henry Cohn, 2026, needs more optimization.
12 301 0.434535342630 Henry Cohn, 2025, needs more optimization.
12 302 0.434926474027 Henry Cohn, 2025, needs more optimization.
12 303 0.434992118487 Henry Cohn, 2025, needs more optimization.
12 304 0.435787865770 Henry Cohn, 2026, needs more optimization.
12 305 0.436091314812 Henry Cohn, 2025, needs more optimization.
12 306 0.436200612561 Henry Cohn, 2025, needs more optimization.
12 307 0.436754844887 Henry Cohn, 2025, needs more optimization.
12 308 0.436880238634 Henry Cohn, 2025, needs more optimization.
12 309 0.437471102535 Henry Cohn, 2025, needs more optimization.
12 310 0.437980374395 Henry Cohn, 2025, needs more optimization.
12 311 0.438025357358 Henry Cohn, 2025, needs more optimization.
12 312 0.438348402475 Henry Cohn, 2026, needs more optimization.
12 313 0.438801707762 Henry Cohn, 2025, needs more optimization.
12 314 0.439391293125 Henry Cohn, 2025, needs more optimization.
12 315 0.439830965838 Henry Cohn, 2025, needs more optimization.
12 316 0.440284598571 Henry Cohn, 2025, needs more optimization.
12 317 0.440347172791 Henry Cohn, 2025, needs more optimization.
12 318 0.440664248160 Henry Cohn, 2025, needs more optimization.
12 319 0.440947160843 Henry Cohn, 2025, needs more optimization.
12 320 0.441432018302 Henry Cohn, 2026, needs more optimization.
12 321 0.441715277767 Henry Cohn, 2025, needs more optimization.
12 322 0.442415599278 Henry Cohn, 2025, needs more optimization.
12 323 0.442750465096 Henry Cohn, 2025, needs more optimization.
12 324 0.443348620398 Henry Cohn, 2025, needs more optimization.
12 325 0.443421088838 Henry Cohn, 2025, 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 0.460317420652 Henry Cohn, 2025, needs more optimization.
12 410 0.460787274926 Henry Cohn, 2025, needs more optimization.
12 411 0.460890339256 Henry Cohn, 2025, needs more optimization.
12 412 0.460915331651 Henry Cohn, 2025, needs more optimization.
12 413 0.461342872888 Henry Cohn, 2025, needs more optimization.
12 414 0.461344809904 Henry Cohn, 2025, needs more optimization.
12 416 0.461623163776 Henry Cohn, 2026, needs more optimization.
12 417 0.462223153465 Henry Cohn, 2025, needs more optimization.
12 418 0.462255100448 Henry Cohn, 2025, needs more optimization.
12 419 0.462598213897 Henry Cohn, 2025, needs more optimization.
12 420 0.462987080581 Henry Cohn, 2025, needs more optimization.
12 422 0.463280003332 Henry Cohn, 2025, needs more optimization.
12 423 0.463392436162 Henry Cohn, 2025, needs more optimization.
12 424 0.464265187939 Henry Cohn, 2025, needs more optimization.
12 425 0.464291111787 Henry Cohn, 2025, needs more optimization.
12 426 0.464311724026 Henry Cohn, 2025, needs more optimization.
12 427 0.464333823925 Henry Cohn, 2025, needs more optimization.
12 428 0.464627087320 Henry Cohn, 2025, needs more optimization.
12 429 0.464633106668 Henry Cohn, 2025, needs more optimization.
12 430 0.464892455907 Henry Cohn, 2025, needs more optimization.
12 431 0.465132401439 Henry Cohn, 2025, needs more optimization.
12 432 0.465182768608 Henry Cohn, 2026, needs more optimization.
12 433 0.465278387386 Henry Cohn, 2025, needs more optimization.
12 434 0.465332550195 Henry Cohn, 2025, needs more optimization.
12 435 0.465390209709 Henry Cohn, 2025, needs more optimization.
12 436 0.465431254972 Henry Cohn, 2025, needs more optimization.
12 437 0.466609299805 Henry Cohn, 2025, needs more optimization.
12 438 0.466691757522 Henry Cohn, 2025, needs more optimization.
12 439 0.466712521703 Henry Cohn, 2025, needs more optimization.
12 440 0.466742768731 Henry Cohn, 2026, needs more optimization.
12 441 0.467305772666 Henry Cohn, 2025, needs more optimization.
12 442 0.467360243002 Henry Cohn, 2025, needs more optimization.
12 443 0.468001139329 Henry Cohn, 2025, needs more optimization.
12 444 0.468124044852 Henry Cohn, 2025, needs more optimization.
12 445 0.468136232732 Henry Cohn, 2025, needs more optimization.
12 446 0.468143718124 Henry Cohn, 2025, needs more optimization.
12 447 0.468255536845 Henry Cohn, 2025, needs more optimization.
12 448 0.468743091391 Henry Cohn, 2026, needs more optimization.
12 449 0.468997460954 Henry Cohn, 2025, needs more optimization.
12 450 0.469053022621 Henry Cohn, 2025, needs more optimization.
12 452 0.469731464656 Henry Cohn, 2025, needs more optimization.
12 453 0.469782575302 Henry Cohn, 2025, needs more optimization.
12 454 0.470059344042 Henry Cohn, 2025, needs more optimization.
12 455 0.470156999977 Henry Cohn, 2025, needs more optimization.
12 456 0.470337981255 Henry Cohn, 2026, needs more optimization.
12 457 0.470513260720 Henry Cohn, 2025, needs more optimization.
12 458 0.471173867096 Henry Cohn, 2025, needs more optimization.
12 459 0.471208941422 Henry Cohn, 2025, needs more optimization.
12 460 0.471276953125 Henry Cohn, 2025, needs more optimization.
12 461 0.471288301089 Henry Cohn, 2025, needs more optimization.
12 462 0.471681640270 Henry Cohn, 2025, needs more optimization.
12 463 0.471694744636 Henry Cohn, 2025, needs more optimization.
12 464 0.471725401825 Henry Cohn, 2026, needs more optimization.
12 465 0.472115369833 Henry Cohn, 2025, needs more optimization.
12 466 0.472257537181 Henry Cohn, 2025, needs more optimization.
12 467 0.472299875569 Henry Cohn, 2025, needs more optimization.
12 468 0.472594888906 Henry Cohn, 2026, needs more optimization.
12 469 0.472775609459 Henry Cohn, 2026, needs more optimization.
12 470 0.472775609464 Henry Cohn, 2025, needs more optimization.
12 471 0.472810005882 Henry Cohn, 2025, needs more optimization.
12 472 0.473173758951 Henry Cohn, 2026, needs more optimization.
12 473 0.473794201790 Henry Cohn, 2025, needs more optimization.
12 474 0.473863242716 Henry Cohn, 2025, needs more optimization.
12 475 0.473893985623 Henry Cohn, 2025, needs more optimization.
12 476 0.474320570192 Henry Cohn, 2026, needs more optimization.
12 477 0.474360536795 Henry Cohn, 2025, needs more optimization.
12 478 0.474490315931 Henry Cohn, 2025, needs more optimization.
12 480 0.474794911276 Henry Cohn, 2026, needs more optimization.
12 481 0.474879578957 Henry Cohn, 2025, needs more optimization.
12 482 0.474928668984 Henry Cohn, 2025, needs more optimization.
12 484 0.475384553366 Henry Cohn, 2025, needs more optimization.
12 485 0.475402119032 Henry Cohn, 2025, needs more optimization.
12 486 0.475751688822 Henry Cohn, 2025, needs more optimization.
12 487 0.475962860199 Henry Cohn, 2025, needs more optimization.
12 488 0.475978252243 Henry Cohn, 2025, needs more optimization.
12 489 0.476034756004 Henry Cohn, 2025, needs more optimization.
12 490 0.476066967305 Henry Cohn, 2025, needs more optimization.
12 491 0.476292844955 Henry Cohn, 2025, needs more optimization.
12 492 0.476360069412 Henry Cohn, 2026, needs more optimization.
12 493 0.476671821079 Henry Cohn, 2025, needs more optimization.
12 494 0.476699405344 Henry Cohn, 2025, needs more optimization.
12 495 0.476903460299 Henry Cohn, 2025, needs more optimization.
12 496 0.476988548405 Henry Cohn, 2026, needs more optimization.
12 497 0.477416237012 Henry Cohn, 2025, needs more optimization.
12 498 0.477438126906 Henry Cohn, 2025, needs more optimization.
12 499 0.477742523402 Henry Cohn, 2025, needs more optimization.
12 500 0.477788141354 Henry Cohn, 2026, needs more optimization.
12 501 0.477904125544 Henry Cohn, 2025, needs more optimization.
12 502 0.478134902016 Henry Cohn, 2025, needs more optimization.
12 503 0.478244559820 Henry Cohn, 2025, needs more optimization.
12 504 0.478375815422 Henry Cohn, 2026, needs more optimization.
12 505 0.479030950504 Henry Cohn, 2025, needs more optimization.
12 506 0.479034888824 Henry Cohn, 2025, needs more optimization.
12 507 0.479068778130 Henry Cohn, 2025, needs more optimization.
12 508 0.479086144303 Henry Cohn, 2025, needs more optimization.
12 510 0.479645243250 Henry Cohn, 2025, needs more optimization.
12 512 0.480566845577 Henry Cohn, 2026, needs more optimization.
12 514 0.481118705232 Henry Cohn, 2026, needs more optimization.
12 516 0.481445633633 Henry Cohn, 2026, needs more optimization.
12 517 0.481538968635 Henry Cohn, 2025, needs more optimization.
12 518 0.481559092706 Henry Cohn, 2025, needs more optimization.
12 519 0.481578191340 Henry Cohn, 2025, needs more optimization.
12 520 0.482341468928 Henry Cohn, 2026, needs more optimization.
12 521 0.482378058943 Henry Cohn, 2025, needs more optimization.
12 522 0.483196968224 Henry Cohn, 2025, needs more optimization.
12 524 0.483206384836 Henry Cohn, 2026, needs more optimization.
12 525 0.483287748702 Henry Cohn, 2025, needs more optimization.
12 527 0.483322567657 Henry Cohn, 2025, needs more optimization.
12 528 0.483329276639 Henry Cohn, 2026, needs more optimization.
12 529 0.483358658357 Henry Cohn, 2025, needs more optimization.
12 530 0.484548061479 Henry Cohn, 2025, needs more optimization.
12 532 0.484699586469 Henry Cohn, 2026, needs more optimization.
12 536 0.484768870016 Henry Cohn, 2026, needs more optimization.
12 537 0.484864119566 Henry Cohn, 2025, needs more optimization.
12 538 0.484903697721 Henry Cohn, 2025, needs more optimization.
12 539 0.484958011729 Henry Cohn, 2025, needs more optimization.
12 540 0.485896973842 Henry Cohn, 2026, needs more optimization.
12 541 0.486194227603 Henry Cohn, 2026, needs more optimization.
12 542 0.486194882963 Henry Cohn, 2026, needs more optimization.
12 543 0.486597296157 Henry Cohn, 2025, needs more optimization.
12 544 0.486636925471 Henry Cohn, 2026, needs more optimization.
12 545 0.486766063233 Henry Cohn, 2025, needs more optimization.
12 546 0.487222361280 Henry Cohn, 2025, needs more optimization.
12 547 0.487239709562 Henry Cohn, 2025, needs more optimization.
12 548 0.487250378747 Henry Cohn, 2026, needs more optimization.
12 549 0.487273017307 Henry Cohn, 2025, needs more optimization.
12 550 0.487290268268 Henry Cohn, 2025, needs more optimization.
12 552 0.487400548117 Henry Cohn, 2026, needs more optimization.
12 553 0.487478028553 Henry Cohn, 2025, needs more optimization.
12 554 0.487495550184 Henry Cohn, 2025, needs more optimization.
12 555 0.488070925645 Henry Cohn, 2025, needs more optimization.
12 556 0.488235125090 Henry Cohn, 2026, needs more optimization.
12 560 0.488333474035 Henry Cohn, 2026, needs more optimization.
12 561 0.488631669139 Henry Cohn, 2026, needs more optimization.
12 562 0.488673191441 Henry Cohn, 2026, needs more optimization.
12 563 0.488692205136 Henry Cohn, 2025, needs more optimization.
12 564 0.488697936674 Henry Cohn, 2025, needs more optimization.
12 565 0.488729497352 Henry Cohn, 2025, needs more optimization.
12 567 0.488739871268 Henry Cohn, 2025, needs more optimization.
12 569 0.488805387350 Henry Cohn, 2025, needs more optimization.
12 570 0.488818462647 Henry Cohn, 2025, needs more optimization.
12 571 0.488851947408 Henry Cohn, 2025, needs more optimization.
12 572 0.488933504580 Henry Cohn, 2026, needs more optimization.
12 573 0.488973658224 Henry Cohn, 2025, needs more optimization.
12 576 0.490363963922 Henry Cohn, 2026, needs more optimization.
12 577 0.490399992850 Henry Cohn, 2025, needs more optimization.
12 580 0.490441894573 Henry Cohn, 2025, needs more optimization.
12 581 0.490446236902 Henry Cohn, 2025, needs more optimization.
12 582 0.490487778114 Henry Cohn, 2025, needs more optimization.
12 583 0.490489697030 Henry Cohn, 2025, needs more optimization.
12 584 0.490498468096 Henry Cohn, 2025, needs more optimization.
12 585 0.490571683932 Henry Cohn, 2025, needs more optimization.
12 586 0.490675334189 Henry Cohn, 2025, needs more optimization.
12 587 0.490727775175 Henry Cohn, 2025, needs more optimization.
12 588 0.491084938853 Henry Cohn, 2026, needs more optimization.
12 590 0.492134418268 Henry Cohn, 2026, needs more optimization.
12 592 0.492137811490 Henry Cohn, 2026, needs more optimization.
12 593 0.492236784269 Henry Cohn, 2026, needs more optimization.
12 594 0.492236784461 Henry Cohn, 2025, needs more optimization.
12 595 0.492685621409 Henry Cohn, 2025, needs more optimization.
12 596 0.492773181556 Henry Cohn, 2026, needs more optimization.
12 597 0.492846250626 Henry Cohn, 2025, needs more optimization.
12 598 0.492886170361 Henry Cohn, 2025, needs more optimization.
12 599 0.494041598615 Henry Cohn, 2025, needs more optimization.
12 600 0.494044369153 Henry Cohn, 2025, needs more optimization.
12 601 0.494051376278 Henry Cohn, 2025, needs more optimization.
12 602 0.494067679491 Henry Cohn, 2025, needs more optimization.
12 603 0.494100934195 Henry Cohn, 2025, needs more optimization.
12 604 0.494121975732 Henry Cohn, 2025, needs more optimization.
12 605 0.494122442112 Henry Cohn, 2025, needs more optimization.
12 606 0.494180738460 Henry Cohn, 2025, needs more optimization.
12 607 0.494205393288 Henry Cohn, 2025, needs more optimization.
12 608 0.494260657622 Henry Cohn, 2026, needs more optimization.
12 609 0.494324177554 Henry Cohn, 2025, needs more optimization.
12 612 0.494325629276 Henry Cohn, 2025, needs more optimization.
12 613 0.494328327521 Henry Cohn, 2025, needs more optimization.
12 614 0.494645394585 Henry Cohn, 2025, needs more optimization.
12 615 0.495631117365 Henry Cohn, 2025, needs more optimization.
12 616 0.495637728423 Henry Cohn, 2025, needs more optimization.
12 619 0.495680470469 Henry Cohn, 2025, needs more optimization.
12 620 0.495681323654 Henry Cohn, 2025, needs more optimization.
12 621 0.495691130937 Henry Cohn, 2025, needs more optimization.
12 622 0.495692432016 Henry Cohn, 2025, needs more optimization.
12 623 0.495762354085 Henry Cohn, 2025, needs more optimization.
12 624 0.495762862636 Henry Cohn, 2025, needs more optimization.
12 625 0.495771634360 Henry Cohn, 2025, needs more optimization.
12 626 0.495855676060 Henry Cohn, 2025, needs more optimization.
12 628 0.495910771147 Henry Cohn, 2026, needs more optimization.
12 631 0.495949749227 Henry Cohn, 2025, needs more optimization.
12 635 0.496047783172 Henry Cohn, 2025, needs more optimization.
12 637 0.496050596998 Henry Cohn, 2025, needs more optimization.
12 638 0.496058274498 Henry Cohn, 2025, needs more optimization.
12 639 0.496064688904 Henry Cohn, 2025, needs more optimization.
12 643 0.496108643131 Henry Cohn, 2025, needs more optimization.
12 644 0.496129625185 Henry Cohn, 2025, needs more optimization.
12 645 0.496129835698 Henry Cohn, 2025, needs more optimization.
12 646 0.496131641462 Henry Cohn, 2025, needs more optimization.
12 647 0.496166216666 Henry Cohn, 2025, needs more optimization.
12 651 0.496193623279 Henry Cohn, 2025, needs more optimization.
12 653 0.496200069913 Henry Cohn, 2025, needs more optimization.
12 654 0.496204823044 Henry Cohn, 2025, needs more optimization.
12 655 0.496224318704 Henry Cohn, 2025, needs more optimization.
12 657 0.496249829119 Henry Cohn, 2025, needs more optimization.
12 658 0.496250534692 Henry Cohn, 2025, needs more optimization.
12 659 0.496251039019 Henry Cohn, 2025, needs more optimization.
12 662 0.496285882740 Henry Cohn, 2025, needs more optimization.
12 663 0.496286510903 Henry Cohn, 2025, needs more optimization.
12 665 0.496310481951 Henry Cohn, 2025, needs more optimization.
12 666 0.496347765652 Henry Cohn, 2025, needs more optimization.
12 669 0.496398243691 Henry Cohn, 2025, needs more optimization.
12 670 0.496539115043 Henry Cohn, 2025, needs more optimization.
12 671 0.496539947668 Henry Cohn, 2025, needs more optimization.
12 672 0.496554860611 Henry Cohn, 2025, needs more optimization.
12 673 0.496730130552 Henry Cohn, 2025, needs more optimization.
12 674 0.496751043235 Henry Cohn, 2025, needs more optimization.
12 675 0.496751547917 Henry Cohn, 2025, needs more optimization.
12 676 0.496753236333 Henry Cohn, 2025, needs more optimization.
12 677 0.496783428091 Henry Cohn, 2025, needs more optimization.
12 678 0.496793437471 Henry Cohn, 2025, needs more optimization.
12 679 0.496795660943 Henry Cohn, 2025, needs more optimization.
12 680 0.496798825093 Henry Cohn, 2025, needs more optimization.
12 681 0.496812843857 Henry Cohn, 2025, needs more optimization.
12 682 0.496831444646 Henry Cohn, 2025, needs more optimization.
12 683 0.496845437127 Henry Cohn, 2025, needs more optimization.
12 685 0.496851590651 Henry Cohn, 2025, needs more optimization.
12 686 0.496851824199 Henry Cohn, 2025, needs more optimization.
12 687 0.496852290623 Henry Cohn, 2025, needs more optimization.
12 688 0.496853086617 Henry Cohn, 2025, needs more optimization.
12 689 0.496854473038 Henry Cohn, 2025, needs more optimization.
12 690 0.496856167771 Henry Cohn, 2025, needs more optimization.
12 691 0.496867036500 Henry Cohn, 2025, needs more optimization.
12 692 0.496916615838 Henry Cohn, 2025, needs more optimization.
12 693 0.496939035923 Henry Cohn, 2025, needs more optimization.
12 694 0.496939223105 Henry Cohn, 2025, needs more optimization.
12 695 0.496939429832 Henry Cohn, 2025, needs more optimization.
12 696 0.496987330577 Henry Cohn, 2025, needs more optimization.
12 697 0.497010713022 Henry Cohn, 2025, needs more optimization.
12 698 0.497019280717 Henry Cohn, 2025, needs more optimization.
12 699 0.497020722181 Henry Cohn, 2025, needs more optimization.
12 700 0.497021648148 Henry Cohn, 2025, needs more optimization.
12 701 0.497047186556 Henry Cohn, 2025, needs more optimization.
12 702 0.497047692253 Henry Cohn, 2025, needs more optimization.
12 703 0.497070451054 Henry Cohn, 2025, needs more optimization.
12 704 0.497074985031 Henry Cohn, 2025, needs more optimization.
12 705 0.497081067707 Henry Cohn, 2025, needs more optimization.
12 706 0.497085905576 Henry Cohn, 2025, needs more optimization.
12 707 0.497097469933 Henry Cohn, 2025, needs more optimization.
12 708 0.497117601389 Henry Cohn, 2025, needs more optimization.
12 712 0.497131515815 Henry Cohn, 2025, needs more optimization.
12 715 0.497132897391 Henry Cohn, 2025, needs more optimization.
12 716 0.497135687687 Henry Cohn, 2025, needs more optimization.
12 717 0.497143746739 Henry Cohn, 2025, needs more optimization.
12 718 0.497173466190 Henry Cohn, 2025, needs more optimization.
12 719 0.497263801905 Henry Cohn, 2025, needs more optimization.
12 721 0.497286042343 Henry Cohn, 2025, needs more optimization.
12 722 0.497290449234 Henry Cohn, 2025, needs more optimization.
12 723 0.497312775454 Henry Cohn, 2025, needs more optimization.
12 724 0.497329208844 Henry Cohn, 2025, needs more optimization.
12 725 0.497387109813 Henry Cohn, 2025, needs more optimization.
12 726 0.497394178916 Henry Cohn, 2025, needs more optimization.
12 728 0.497399332025 Henry Cohn, 2025, needs more optimization.
12 729 0.497420674493 Henry Cohn, 2025, needs more optimization.
12 730 0.497432979281 Henry Cohn, 2025, needs more optimization.
12 731 0.497433272235 Henry Cohn, 2025, needs more optimization.
12 735 0.497433741405 Henry Cohn, 2025, needs more optimization.
12 736 0.497434002036 Henry Cohn, 2025, needs more optimization.
12 737 0.497434977729 Henry Cohn, 2025, needs more optimization.
12 739 0.497438545873 Henry Cohn, 2025, needs more optimization.
12 740 0.497468963170 Henry Cohn, 2025, needs more optimization.
12 741 0.497479222995 Henry Cohn, 2025, needs more optimization.
12 742 0.497480363182 Henry Cohn, 2025, needs more optimization.
12 743 0.497482876559 Henry Cohn, 2025, needs more optimization.
12 744 0.497514619542 Henry Cohn, 2025, needs more optimization.
12 745 0.497543875236 Henry Cohn, 2025, needs more optimization.
12 746 0.497559732219 Henry Cohn, 2025, needs more optimization.
12 747 0.497577967446 Henry Cohn, 2025, needs more optimization.
12 748 0.497599189314 Henry Cohn, 2025, needs more optimization.
12 749 0.497680832175 Henry Cohn, 2025, needs more optimization.
12 750 0.497693229718 Henry Cohn, 2025, needs more optimization.
12 751 0.497710692954 Henry Cohn, 2025, needs more optimization.
12 752 0.497711277067 Henry Cohn, 2025, needs more optimization.
12 753 0.497838301804 Henry Cohn, 2025, needs more optimization.
12 754 0.497973147105 Henry Cohn, 2025, needs more optimization.
12 755 0.498281596307 Henry Cohn, 2025, needs more optimization.
12 756 0.499541791587 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, after some further optimization.
12 840 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, 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
12 842 0.535506227518 Henry Cohn, 2025, needs more optimization.
12 843 0.535563528698 Henry Cohn, 2025, needs more optimization.
12 844 0.535853239784 Henry Cohn, 2026, needs more optimization.
12 845 0.535859256181 Henry Cohn, 2025, needs more optimization.
12 846 0.535865587028 Henry Cohn, 2025, needs more optimization.
12 847 0.536137465950 Henry Cohn, 2025, needs more optimization.
12 848 0.536193363348 Henry Cohn, 2026, needs more optimization.
12 849 0.536375325961 Henry Cohn, 2025, needs more optimization.
12 850 0.536428797392 Henry Cohn, 2025, needs more optimization.
12 851 0.536773139831 Henry Cohn, 2025, needs more optimization.
12 852 0.537229578938 Henry Cohn, 2026, needs more optimization.
12 853 0.537417805523 Henry Cohn, 2025, needs more optimization.
12 854 0.537428210480 Henry Cohn, 2025, needs more optimization.
12 855 0.537685598125 Henry Cohn, 2025, needs more optimization.
12 856 0.537757234848 Henry Cohn, 2026, needs more optimization.
12 857 0.537769398303 Henry Cohn, 2025, needs more optimization.
12 858 0.538138295013 Henry Cohn, 2025, needs more optimization.
12 859 0.538181862229 Henry Cohn, 2025, needs more optimization.
12 860 0.538272258203 Henry Cohn, 2026, needs more optimization.
12 861 0.538539463883 Henry Cohn, 2025, needs more optimization.
12 862 0.538792024065 Henry Cohn, 2025, needs more optimization.
12 863 0.538796771157 Henry Cohn, 2025, needs more optimization.
12 864 0.538971165052 Henry Cohn, 2026, needs more optimization.
12 866 0.539105562868 Henry Cohn, 2025, needs more optimization.
12 867 0.539420977833 Henry Cohn, 2025, needs more optimization.
12 868 0.539434575143 Henry Cohn, 2026, needs more optimization.
12 869 0.539482540123 Henry Cohn, 2025, needs more optimization.
12 870 0.539717498639 Henry Cohn, 2025, needs more optimization.
12 871 0.539940914659 Henry Cohn, 2025, needs more optimization.
12 872 0.539941280606 Henry Cohn, 2025, needs more optimization.
12 873 0.539947567768 Henry Cohn, 2025, needs more optimization.
12 874 0.539955507094 Henry Cohn, 2025, needs more optimization.
12 875 0.540538080203 Henry Cohn, 2025, needs more optimization.
12 876 0.540539657177 Henry Cohn, 2026, needs more optimization.
12 877 0.540555424019 Henry Cohn, 2025, needs more optimization.
12 878 0.540636337698 Henry Cohn, 2025, needs more optimization.
12 880 0.541219192725 Henry Cohn, 2026, needs more optimization.
12 881 0.541333676122 Henry Cohn, 2025, needs more optimization.
12 882 0.541344755738 Henry Cohn, 2025, needs more optimization.
12 883 0.541721423484 Henry Cohn, 2025, needs more optimization.
12 884 0.541997865472 Henry Cohn, 2026, needs more optimization.
12 885 0.542045952338 Henry Cohn, 2025, needs more optimization.
12 886 0.542067645904 Henry Cohn, 2025, needs more optimization.
12 887 0.542107382042 Henry Cohn, 2025, needs more optimization.
12 888 0.542472081129 Henry Cohn, 2026, needs more optimization.
12 890 0.542504515333 Henry Cohn, 2025, needs more optimization.
12 891 0.542716966071 Henry Cohn, 2025, needs more optimization.
12 892 0.542782152692 Henry Cohn, 2026, needs more optimization.
12 893 0.543207711787 Henry Cohn, 2025, needs more optimization.
12 894 0.543456141381 Henry Cohn, 2025, needs more optimization.
12 895 0.543497043904 Henry Cohn, 2025, needs more optimization.
12 896 0.543547492757 Henry Cohn, 2026, needs more optimization.
12 897 0.543893308049 Henry Cohn, 2025, needs more optimization.
12 898 0.543900823672 Henry Cohn, 2025, needs more optimization.
12 899 0.543919874490 Henry Cohn, 2025, needs more optimization.
12 900 0.543925544989 Henry Cohn, 2026, needs more optimization.
12 901 0.544322418996 Henry Cohn, 2025, needs more optimization.
12 902 0.544381181124 Henry Cohn, 2025, needs more optimization.
12 903 0.544406792234 Henry Cohn, 2025, needs more optimization.
12 904 0.544629845122 Henry Cohn, 2026, needs more optimization.
12 905 0.544667069990 Henry Cohn, 2025, needs more optimization.
12 906 0.544835386880 Henry Cohn, 2025, needs more optimization.
12 907 0.544886413273 Henry Cohn, 2025, needs more optimization.
12 908 0.545184695362 Henry Cohn, 2026, needs more optimization.
12 909 0.545209362200 Henry Cohn, 2025, needs more optimization.
12 910 0.545443246726 Henry Cohn, 2025, needs more optimization.
12 911 0.545448662084 Henry Cohn, 2025, needs more optimization.
12 912 0.545451555011 Henry Cohn, 2026, needs more optimization.
12 913 0.545474162688 Henry Cohn, 2025, needs more optimization.
12 914 0.545743622651 Henry Cohn, 2025, needs more optimization.
12 915 0.545773407652 Henry Cohn, 2025, needs more optimization.
12 916 0.546071039392 Henry Cohn, 2026, needs more optimization.
12 917 0.546077480849 Henry Cohn, 2025, needs more optimization.
12 918 0.546206448972 Henry Cohn, 2025, needs more optimization.
12 919 0.546624962329 Henry Cohn, 2025, needs more optimization.
12 920 0.546633602871 Henry Cohn, 2026, needs more optimization.
12 922 0.546650091319 Henry Cohn, 2025, needs more optimization.
12 923 0.546900657476 Henry Cohn, 2025, needs more optimization.
12 924 0.546995106625 Henry Cohn, 2026, needs more optimization.
12 925 0.547040891382 Henry Cohn, 2025, needs more optimization.
12 926 0.547192185250 Henry Cohn, 2025, needs more optimization.
12 927 0.547367953498 Henry Cohn, 2025, needs more optimization.
12 928 0.547395204939 Henry Cohn, 2026, needs more optimization.
12 929 0.547610209902 Henry Cohn, 2025, needs more optimization.
12 930 0.547618519561 Henry Cohn, 2025, needs more optimization.
12 931 0.547621635609 Henry Cohn, 2025, needs more optimization.
12 932 0.547983489649 Henry Cohn, 2026, needs more optimization.
12 933 0.548166345572 Henry Cohn, 2025, needs more optimization.
12 934 0.548174455525 Henry Cohn, 2025, needs more optimization.
12 935 0.548275056468 Henry Cohn, 2025, needs more optimization.
12 936 0.548438182116 Henry Cohn, 2026, needs more optimization.
12 937 0.548764637739 Henry Cohn, 2025, needs more optimization.
12 938 0.548961812841 Henry Cohn, 2025, needs more optimization.
12 940 0.548989417186 Henry Cohn, 2026, needs more optimization.
12 941 0.549040207156 Henry Cohn, 2025, needs more optimization.
12 942 0.549057147014 Henry Cohn, 2025, needs more optimization.
12 943 0.549450802383 Henry Cohn, 2025, needs more optimization.
12 944 0.549474745499 Henry Cohn, 2026, needs more optimization.
12 945 0.549570476958 Henry Cohn, 2025, needs more optimization.
12 946 0.549705467723 Henry Cohn, 2025, needs more optimization.
12 947 0.549729950762 Henry Cohn, 2025, needs more optimization.
12 948 0.549763578707 Henry Cohn, 2026, needs more optimization.
12 949 0.550020640206 Henry Cohn, 2025, needs more optimization.
12 950 0.550032390490 Henry Cohn, 2025, needs more optimization.
12 951 0.550085460365 Henry Cohn, 2025, needs more optimization.
12 952 0.550572418929 Henry Cohn, 2026, needs more optimization.
12 953 0.550646986647 Henry Cohn, 2025, needs more optimization.
12 954 0.550660472225 Henry Cohn, 2025, needs more optimization.
12 955 0.550675209105 Henry Cohn, 2025, needs more optimization.
12 956 0.550681015515 Henry Cohn, 2026, needs more optimization.
12 957 0.551058568831 Henry Cohn, 2025, needs more optimization.
12 958 0.551087058267 Henry Cohn, 2025, needs more optimization.
12 959 0.551092152756 Henry Cohn, 2025, needs more optimization.
12 960 0.551241431542 Henry Cohn, 2026, needs more optimization.
12 961 0.551280867106 Henry Cohn, 2025, needs more optimization.
12 962 0.551289731610 Henry Cohn, 2025, needs more optimization.
12 963 0.551568055693 Henry Cohn, 2025, needs more optimization.
12 964 0.551614803955 Henry Cohn, 2026, needs more optimization.
12 965 0.551627297606 Henry Cohn, 2025, needs more optimization.
12 966 0.551884930095 Henry Cohn, 2025, needs more optimization.
12 967 0.551889366792 Henry Cohn, 2025, needs more optimization.
12 968 0.551963913130 Henry Cohn, 2026, needs more optimization.
12 969 0.552326081648 Henry Cohn, 2025, needs more optimization.
12 970 0.552372096589 Henry Cohn, 2025, needs more optimization.
12 971 0.552378734126 Henry Cohn, 2025, needs more optimization.
12 972 0.552387393943 Henry Cohn, 2026, needs more optimization.
12 973 0.552552617952 Henry Cohn, 2025, needs more optimization.
12 974 0.552605780398 Henry Cohn, 2025, needs more optimization.
12 975 0.552630771016 Henry Cohn, 2025, needs more optimization.
12 976 0.552926775811 Henry Cohn, 2026, needs more optimization.
12 977 0.552941763697 Henry Cohn, 2025, needs more optimization.
12 978 0.553177368105 Henry Cohn, 2025, needs more optimization.
12 979 0.553188460071 Henry Cohn, 2025, needs more optimization.
12 980 0.553236896900 Henry Cohn, 2026, needs more optimization.
12 981 0.553540138207 Henry Cohn, 2025, needs more optimization.
12 982 0.553621608199 Henry Cohn, 2025, needs more optimization.
12 983 0.553797096864 Henry Cohn, 2025, needs more optimization.
12 984 0.553797650615 Henry Cohn, 2026, needs more optimization.
12 985 0.553803963339 Henry Cohn, 2025, needs more optimization.
12 986 0.554034050778 Henry Cohn, 2025, needs more optimization.
12 1024 0.555555555556 Subcode of a code of size 1144 from T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
9⁢x−5
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 0.089954419243 Henry Cohn, 2025.
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 0.184601884691 Henry Cohn, 2025.
13 61 0.189390971051 Henry Cohn, 2025.
13 62 0.189939244395 Henry Cohn, 2026.
13 63 0.193375545604 Henry Cohn, 2026.
13 64 0.194866298502 Henry Cohn, 2026, needs more optimization.
13 65 0.198942835052 Henry Cohn, 2026, needs more optimization.
13 66 0.201501809764 Henry Cohn, 2026, needs more optimization.
13 67 0.204060485677 Henry Cohn, 2026, needs more optimization.
13 68 0.207255152666 Henry Cohn, 2026, needs more optimization.
13 69 0.208427075365 Henry Cohn, 2025.
13 70 0.210764468531 Henry Cohn, 2026, needs more optimization.
13 71 0.212574330623 Henry Cohn, 2025.
13 72 0.214183844238 Henry Cohn, 2025.
13 73 0.216144836248 Henry Cohn, 2026, needs more optimization.
13 74 0.218072317405 Henry Cohn, 2026, needs more optimization.
13 75 0.219802379115 Henry Cohn, 2026, needs more optimization.
13 76 0.222090009062 Henry Cohn, 2026, needs more optimization.
13 77 0.224126205886 Henry Cohn, 2026, needs more optimization.
13 78 0.226253189158 Henry Cohn, 2026, needs more optimization.
13 79 0.228139500326 Henry Cohn, 2026, needs more optimization.
13 80 0.230720127190 Henry Cohn, 2026, needs more optimization.
13 81 0.232720216127 Henry Cohn, 2024, needs more optimization.
13 82 0.234416735243 Henry Cohn, 2026, needs more optimization.
13 83 0.236606625074 Henry Cohn, 2026, needs more optimization.
13 84 0.238167605203 Henry Cohn, 2026, needs more optimization.
13 85 0.240418979845 Henry Cohn, 2025, needs more optimization.
13 86 0.241749995486 Henry Cohn, 2026, needs more optimization.
13 87 0.243732895627 Henry Cohn, 2026, needs more optimization.
13 88 0.245463352882 Henry Cohn, 2026, needs more optimization.
13 89 0.247238849279 Henry Cohn, 2025, needs more optimization.
13 90 0.248473502762 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, needs more optimization.
13 107 0.258117042194 Henry Cohn, 2026, needs more optimization.
13 108 0.258372350014 Henry Cohn, 2026, needs more optimization.
13 109 0.259501019452 Henry Cohn, 2026, needs more optimization.
13 110 0.259654335458 Henry Cohn, 2026, needs more optimization.
13 111 0.259786920363 Henry Cohn, 2026, needs more optimization.
13 112 0.261427288349 Henry Cohn, 2026, needs more optimization.
13 113 0.263326655725 Henry Cohn, 2026, needs more optimization.
13 114 0.263627757025 Henry Cohn, 2026, needs more optimization.
13 115 0.264623765023 Henry Cohn, 2026, needs more optimization.
13 116 0.267844584869 Henry Cohn, 2026, needs more optimization.
13 117 0.270063758395 Henry Cohn, 2026, needs more optimization.
13 118 0.273015660057 Henry Cohn, 2026, needs more optimization.
13 119 0.275889133748 Henry Cohn, 2026, needs more optimization.
13 120 0.279414787328 Henry Cohn, 2026, needs more optimization.
13 121 0.280540725634 Henry Cohn, 2026, needs more optimization.
13 122 0.282199212303 Henry Cohn, 2026, needs more optimization.
13 123 0.283973352608 Henry Cohn, 2026, needs more optimization.
13 124 0.285952479277 Henry Cohn, 2026, needs more optimization.
13 125 0.287376207941 Henry Cohn, 2026, needs more optimization.
13 126 0.288695220856 Henry Cohn, 2026, needs more optimization.
13 127 0.289523715693 Henry Cohn, 2026, needs more optimization.
13 128 0.289858584248 Henry Cohn, 2026, needs more optimization.
13 129 0.291495303857 Henry Cohn, 2026, needs more optimization.
13 130 0.293843012498 Henry Cohn, 2026, needs more optimization.
13 131 0.295196826693 Henry Cohn, 2026, needs more optimization.
13 132 0.295591236152 Henry Cohn, 2026, needs more optimization.
13 133 0.296194262039 Henry Cohn, 2026, needs more optimization.
13 134 0.296743931233 Henry Cohn, 2026, needs more optimization.
13 135 0.297341933857 Henry Cohn, 2026, needs more optimization.
13 136 0.297894334369 Henry Cohn, 2026, needs more optimization.
13 137 0.298576042885 Henry Cohn, 2026, needs more optimization.
13 138 0.299081144304 Henry Cohn, 2026, needs more optimization.
13 139 0.299687011114 Henry Cohn, 2026, needs more optimization.
13 140 0.300908754186 Henry Cohn, 2026, needs more optimization.
13 141 0.301689305501 Henry Cohn, 2026, needs more optimization.
13 142 0.302925871736 Henry Cohn, 2026, needs more optimization.
13 143 0.303773806996 Henry Cohn, 2026, needs more optimization.
13 144 0.304463200254 Henry Cohn, 2026, needs more optimization.
13 145 0.305392473349 Henry Cohn, 2026, needs more optimization.
13 146 0.305614169346 Henry Cohn, 2026, needs more optimization.
13 147 0.306625964850 Henry Cohn, 2026, needs more optimization.
13 148 0.307110904588 Henry Cohn, 2026, needs more optimization.
13 149 0.307504290603 Henry Cohn, 2026, needs more optimization.
13 150 0.307922556959 Henry Cohn, 2026, needs more optimization.
13 151 0.308453427346 Henry Cohn, 2026, needs more optimization.
13 152 0.308914649721 Henry Cohn, 2026, needs more optimization.
13 153 0.309482096033 Henry Cohn, 2026, needs more optimization.
13 154 0.309938961052 Henry Cohn, 2026, needs more optimization.
13 155 0.310326722390 Henry Cohn, 2026, needs more optimization.
13 156 0.310935197046 Henry Cohn, 2026, needs more optimization.
13 157 0.311482221567 Henry Cohn, 2026, needs more optimization.
13 158 0.311996148756 Henry Cohn, 2026, needs more optimization.
13 159 0.312790591292 Henry Cohn, 2026, needs more optimization.
13 160 0.313545104228 Henry Cohn, 2026, needs more optimization.
13 161 0.314230360763 Henry Cohn, 2026, needs more optimization.
13 162 0.314704972181 Henry Cohn, 2026, needs more optimization.
13 163 0.315167164749 Henry Cohn, 2026, needs more optimization.
13 164 0.315644794463 Henry Cohn, 2026, needs more optimization.
13 165 0.316671838208 Henry Cohn, 2026, needs more optimization.
13 166 0.317335152614 Henry Cohn, 2026, needs more optimization.
13 167 0.318089608224 Henry Cohn, 2026, needs more optimization.
13 168 0.318769142130 Henry Cohn, 2026, needs more optimization.
13 169 0.319340929813 Henry Cohn, 2026, needs more optimization.
13 170 0.319645942716 Henry Cohn, 2026, needs more optimization.
13 171 0.320750947556 Henry Cohn, 2026, needs more optimization.
13 172 0.321193448576 Henry Cohn, 2026, needs more optimization.
13 173 0.322341074304 Henry Cohn, 2026, needs more optimization.
13 174 0.323239803310 Henry Cohn, 2026, needs more optimization.
13 175 0.323517379531 Henry Cohn, 2026, needs more optimization.
13 176 0.323795600860 Henry Cohn, 2026, needs more optimization.
13 177 0.323942425896 Henry Cohn, 2026, needs more optimization.
13 178 0.324146805911 Henry Cohn, 2026, needs more optimization.
13 179 0.325113173311 Henry Cohn, 2026, needs more optimization.
13 180 0.325324848862 Henry Cohn, 2026, needs more optimization.
13 181 0.325621101822 Henry Cohn, 2026, needs more optimization.
13 182 0.326380248280 Henry Cohn, 2026, needs more optimization.
13 183 0.326675940167 Henry Cohn, 2026, needs more optimization.
13 184 0.326698656330 Henry Cohn, 2026, needs more optimization.
13 185 0.326958619498 Henry Cohn, 2026, needs more optimization.
13 186 0.327192685058 Henry Cohn, 2026, needs more optimization.
13 187 0.327372123369 Henry Cohn, 2026, needs more optimization.
13 189 0.327693303407 Henry Cohn, 2026, needs more optimization.
13 190 0.327698070477 Henry Cohn, 2026, needs more optimization.
13 191 0.327972386777 Henry Cohn, 2026, needs more optimization.
13 192 0.328218632145 Henry Cohn, 2026, needs more optimization.
13 193 0.328363911057 Henry Cohn, 2026, needs more optimization.
13 194 0.328476784139 Henry Cohn, 2026, needs more optimization.
13 195 0.328527706166 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 0.350470979699 Henry Cohn, 2025, needs more optimization.
13 210 0.351606658611 Henry Cohn, 2026, needs more optimization.
13 211 0.352321713080 Henry Cohn, 2026, needs more optimization.
13 212 0.353149905905 Henry Cohn, 2026, needs more optimization.
13 213 0.353925063398 Henry Cohn, 2026, needs more optimization.
13 214 0.354503680985 Henry Cohn, 2026, needs more optimization.
13 215 0.355465817859 Henry Cohn, 2026, needs more optimization.
13 216 0.355852066326 Henry Cohn, 2026, needs more optimization.
13 217 0.357469493565 Henry Cohn, 2026, needs more optimization.
13 218 0.357962439825 Henry Cohn, 2026, needs more optimization.
13 219 0.358139862720 Henry Cohn, 2026, needs more optimization.
13 220 0.358999772657 Henry Cohn, 2026, needs more optimization.
13 221 0.360166540430 Henry Cohn, 2026, needs more optimization.
13 222 0.360502750571 Henry Cohn, 2026, needs more optimization.
13 223 0.361611702841 Henry Cohn, 2026, needs more optimization.
13 224 0.362529805331 Henry Cohn, 2026, needs more optimization.
13 225 0.363393181712 Henry Cohn, 2026, needs more optimization.
13 226 0.364090413813 Henry Cohn, 2025, needs more optimization.
13 227 0.364776488046 Henry Cohn, 2026, needs more optimization.
13 228 0.365909317869 Henry Cohn, 2026, needs more optimization.
13 229 0.366391180286 Henry Cohn, 2026, needs more optimization.
13 230 0.367230208524 Henry Cohn, 2026, needs more optimization.
13 231 0.368177190533 Henry Cohn, 2026, needs more optimization.
13 232 0.368769845255 Henry Cohn, 2026, needs more optimization.
13 233 0.369252005489 Henry Cohn, 2026, needs more optimization.
13 234 0.370100528165 Henry Cohn, 2026, needs more optimization.
13 235 0.371116522727 Henry Cohn, 2026, needs more optimization.
13 236 0.371630810741 Henry Cohn, 2026, needs more optimization.
13 237 0.372131340429 Henry Cohn, 2026, needs more optimization.
13 238 0.373146357646 Henry Cohn, 2026, needs more optimization.
13 239 0.373752895200 Henry Cohn, 2026, needs more optimization.
13 240 0.374256685918 Henry Cohn, 2026, needs more optimization.
13 241 0.374844419047 Henry Cohn, 2026, needs more optimization.
13 242 0.375700008443 Henry Cohn, 2026, needs more optimization.
13 243 0.376317697659 Henry Cohn, 2026, needs more optimization.
13 244 0.376709523739 Henry Cohn, 2026, needs more optimization.
13 245 0.377755026511 Henry Cohn, 2026, needs more optimization.
13 246 0.378290566681 Henry Cohn, 2026, needs more optimization.
13 247 0.378891825919 Henry Cohn, 2026, needs more optimization.
13 248 0.379384317543 Henry Cohn, 2026, needs more optimization.
13 249 0.380098148874 Henry Cohn, 2026, needs more optimization.
13 250 0.380786089999 Henry Cohn, 2026, needs more optimization.
13 251 0.381491823702 Henry Cohn, 2026, needs more optimization.
13 252 0.381963272515 Henry Cohn, 2024, needs more optimization.
13 253 0.382864339660 Henry Cohn, 2026, needs more optimization.
13 254 0.383277389646 Henry Cohn, 2026, needs more optimization.
13 255 0.384387375524 Henry Cohn, 2026, needs more optimization.
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
13 336 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 0.417891478892 Henry Cohn, 2025, needs more optimization.
13 338 0.418441080028 Henry Cohn, 2025, needs more optimization.
13 339 0.418737825194 Henry Cohn, 2025, needs more optimization.
13 340 0.418875769127 Henry Cohn, 2025, needs more optimization.
13 341 0.419419034847 Henry Cohn, 2025, needs more optimization.
13 342 0.420049026491 Henry Cohn, 2025, needs more optimization.
13 343 0.420070225222 Henry Cohn, 2025, needs more optimization.
13 344 0.420389870109 Henry Cohn, 2026, needs more optimization.
13 345 0.420581365637 Henry Cohn, 2025, needs more optimization.
13 346 0.420704154424 Henry Cohn, 2025, needs more optimization.
13 347 0.421102107698 Henry Cohn, 2025, needs more optimization.
13 348 0.421545309541 Henry Cohn, 2025, needs more optimization.
13 349 0.421907425104 Henry Cohn, 2025, needs more optimization.
13 350 0.422008380280 Henry Cohn, 2025, needs more optimization.
13 351 0.422575939533 Henry Cohn, 2025, needs more optimization.
13 352 0.422858125025 Henry Cohn, 2026, needs more optimization.
13 353 0.423230257051 Henry Cohn, 2025, needs more optimization.
13 354 0.423743822805 Henry Cohn, 2025, needs more optimization.
13 355 0.424058260598 Henry Cohn, 2025, needs more optimization.
13 356 0.424147835466 Henry Cohn, 2025, needs more optimization.
13 357 0.424432715559 Henry Cohn, 2025, needs more optimization.
13 358 0.424991924513 Henry Cohn, 2025, needs more optimization.
13 359 0.425356584705 Henry Cohn, 2025, needs more optimization.
13 360 0.425473600075 Henry Cohn, 2026, needs more optimization.
13 361 0.426053892700 Henry Cohn, 2025, needs more optimization.
13 363 0.426403543342 Henry Cohn, 2025, needs more optimization.
13 364 0.426678284544 Henry Cohn, 2025, needs more optimization.
13 365 0.427322675493 Henry Cohn, 2025, 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
13 578 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 0.465672455233 Henry Cohn, 2025, needs more optimization.
13 580 0.465789763135 Henry Cohn, 2026, needs more optimization.
13 581 0.465955526650 Henry Cohn, 2025, needs more optimization.
13 582 0.466342901539 Henry Cohn, 2026, needs more optimization.
13 584 0.466530373366 Henry Cohn, 2026, needs more optimization.
13 585 0.466832748141 Henry Cohn, 2025, needs more optimization.
13 586 0.467549101040 Henry Cohn, 2025, needs more optimization.
13 588 0.467574032999 Henry Cohn, 2026, needs more optimization.
13 592 0.467711301366 Henry Cohn, 2026, needs more optimization.
13 596 0.467769086876 Henry Cohn, 2026, needs more optimization.
13 597 0.470122617375 Henry Cohn, 2025, needs more optimization.
13 598 0.470135903308 Henry Cohn, 2025, needs more optimization.
13 599 0.470605232123 Henry Cohn, 2026, needs more optimization.
13 600 0.470770397994 Henry Cohn, 2026, needs more optimization.
13 601 0.471026039091 Henry Cohn, 2025, needs more optimization.
13 602 0.472796352342 Henry Cohn, 2025, needs more optimization.
13 603 0.473262426000 Henry Cohn, 2025, needs more optimization.
13 604 0.473278998215 Henry Cohn, 2026, needs more optimization.
13 605 0.473324558816 Henry Cohn, 2025, needs more optimization.
13 606 0.473522802978 Henry Cohn, 2025, needs more optimization.
13 608 0.473604551063 Henry Cohn, 2026, needs more optimization.
13 609 0.473627679841 Henry Cohn, 2025, needs more optimization.
13 610 0.473665833105 Henry Cohn, 2025, needs more optimization.
13 611 0.473739534858 Henry Cohn, 2025, needs more optimization.
13 612 0.473965827048 Henry Cohn, 2026, needs more optimization.
13 613 0.474406686573 Henry Cohn, 2025, needs more optimization.
13 614 0.474476481362 Henry Cohn, 2025, needs more optimization.
13 615 0.474494086062 Henry Cohn, 2025, needs more optimization.
13 616 0.474905852839 Henry Cohn, 2026, needs more optimization.
13 617 0.474918963482 Henry Cohn, 2025, needs more optimization.
13 618 0.474967584162 Henry Cohn, 2025, needs more optimization.
13 619 0.475383863231 Henry Cohn, 2025, needs more optimization.
13 620 0.475415073774 Henry Cohn, 2026, needs more optimization.
13 621 0.475458135871 Henry Cohn, 2025, needs more optimization.
13 622 0.475534670877 Henry Cohn, 2025, needs more optimization.
13 623 0.475564411116 Henry Cohn, 2025, needs more optimization.
13 624 0.475772458391 Henry Cohn, 2025, needs more optimization.
13 625 0.476105619632 Henry Cohn, 2025, needs more optimization.
13 626 0.476125930108 Henry Cohn, 2025, needs more optimization.
13 627 0.476133672282 Henry Cohn, 2025, needs more optimization.
13 628 0.476274391676 Henry Cohn, 2026, needs more optimization.
13 629 0.476497765410 Henry Cohn, 2025, needs more optimization.
13 630 0.476682055609 Henry Cohn, 2025, needs more optimization.
13 632 0.476753462685 Henry Cohn, 2026, needs more optimization.
13 633 0.476779642724 Henry Cohn, 2025, needs more optimization.
13 634 0.476863611299 Henry Cohn, 2025, needs more optimization.
13 635 0.477164338899 Henry Cohn, 2025, needs more optimization.
13 636 0.477264749703 Henry Cohn, 2026, needs more optimization.
13 637 0.477285852944 Henry Cohn, 2025, needs more optimization.
13 638 0.477612729804 Henry Cohn, 2025, needs more optimization.
13 639 0.477701773044 Henry Cohn, 2025, needs more optimization.
13 640 0.477865043264 Henry Cohn, 2026, needs more optimization.
13 641 0.477876519895 Henry Cohn, 2025, needs more optimization.
13 642 0.477880331706 Henry Cohn, 2025, needs more optimization.
13 644 0.478030845536 Henry Cohn, 2026, needs more optimization.
13 645 0.478368394521 Henry Cohn, 2025, needs more optimization.
13 646 0.478412887584 Henry Cohn, 2025, needs more optimization.
13 647 0.478492404615 Henry Cohn, 2025, needs more optimization.
13 648 0.478503335799 Henry Cohn, 2026, needs more optimization.
13 649 0.478509908716 Henry Cohn, 2025, needs more optimization.
13 650 0.478832290317 Henry Cohn, 2025, needs more optimization.
13 651 0.478838229297 Henry Cohn, 2025, needs more optimization.
13 652 0.478856464367 Henry Cohn, 2026, needs more optimization.
13 653 0.479050421989 Henry Cohn, 2025, needs more optimization.
13 654 0.479071333898 Henry Cohn, 2025, needs more optimization.
13 655 0.479603675125 Henry Cohn, 2025, needs more optimization.
13 656 0.479613974451 Henry Cohn, 2026, needs more optimization.
13 657 0.479687023902 Henry Cohn, 2025, needs more optimization.
13 658 0.479704383217 Henry Cohn, 2025, needs more optimization.
13 659 0.479730979245 Henry Cohn, 2025, needs more optimization.
13 660 0.480347440524 Henry Cohn, 2026, needs more optimization.
13 661 0.480364890268 Henry Cohn, 2025, needs more optimization.
13 662 0.480375210672 Henry Cohn, 2025, needs more optimization.
13 663 0.480405879307 Henry Cohn, 2025, needs more optimization.
13 664 0.480454278236 Henry Cohn, 2026, needs more optimization.
13 665 0.480771700158 Henry Cohn, 2025, needs more optimization.
13 666 0.480815251640 Henry Cohn, 2025, needs more optimization.
13 667 0.480821848300 Henry Cohn, 2025, needs more optimization.
13 668 0.480831213922 Henry Cohn, 2026, needs more optimization.
13 670 0.480891611906 Henry Cohn, 2025, needs more optimization.
13 672 0.481273438735 Henry Cohn, 2025, needs more optimization.
13 673 0.481283021102 Henry Cohn, 2025, needs more optimization.
13 674 0.481286722824 Henry Cohn, 2025, needs more optimization.
13 675 0.481644119395 Henry Cohn, 2025, needs more optimization.
13 676 0.481799113049 Henry Cohn, 2026, needs more optimization.
13 677 0.481830390467 Henry Cohn, 2025, needs more optimization.
13 678 0.481839212161 Henry Cohn, 2025, needs more optimization.
13 679 0.482152300430 Henry Cohn, 2025, needs more optimization.
13 680 0.482154819163 Henry Cohn, 2026, needs more optimization.
13 681 0.482169815140 Henry Cohn, 2025, needs more optimization.
13 682 0.482447772105 Henry Cohn, 2025, needs more optimization.
13 684 0.482480693519 Henry Cohn, 2026, needs more optimization.
13 685 0.482658262037 Henry Cohn, 2025, needs more optimization.
13 687 0.482727338345 Henry Cohn, 2025, needs more optimization.
13 688 0.482904616258 Henry Cohn, 2026, needs more optimization.
13 690 0.482950436988 Henry Cohn, 2025, needs more optimization.
13 691 0.483009366512 Henry Cohn, 2025, needs more optimization.
13 692 0.483662493176 Henry Cohn, 2026, needs more optimization.
13 693 0.483691006742 Henry Cohn, 2025, needs more optimization.
13 694 0.483730398335 Henry Cohn, 2025, needs more optimization.
13 695 0.483792803740 Henry Cohn, 2025, needs more optimization.
13 696 0.483798522832 Henry Cohn, 2026, needs more optimization.
13 697 0.483911175969 Henry Cohn, 2025, needs more optimization.
13 698 0.484152354313 Henry Cohn, 2025, needs more optimization.
13 699 0.484204749320 Henry Cohn, 2025, needs more optimization.
13 700 0.484227609270 Henry Cohn, 2026, needs more optimization.
13 701 0.484248420249 Henry Cohn, 2025, needs more optimization.
13 702 0.484296547674 Henry Cohn, 2025, needs more optimization.
13 703 0.484305418348 Henry Cohn, 2025, needs more optimization.
13 704 0.484321914872 Henry Cohn, 2026, needs more optimization.
13 705 0.484447011111 Henry Cohn, 2025, needs more optimization.
13 706 0.484679433637 Henry Cohn, 2025, needs more optimization.
13 707 0.484760353386 Henry Cohn, 2025, needs more optimization.
13 708 0.484898375649 Henry Cohn, 2026, needs more optimization.
13 710 0.484952826874 Henry Cohn, 2025, needs more optimization.
13 712 0.484987569503 Henry Cohn, 2026, needs more optimization.
13 713 0.485222047626 Henry Cohn, 2025, needs more optimization.
13 714 0.485290800683 Henry Cohn, 2025, needs more optimization.
13 715 0.485403154566 Henry Cohn, 2025, needs more optimization.
13 716 0.485451228042 Henry Cohn, 2026, needs more optimization.
13 717 0.485463210063 Henry Cohn, 2025, needs more optimization.
13 718 0.485467615749 Henry Cohn, 2025, needs more optimization.
13 719 0.485468162774 Henry Cohn, 2025, needs more optimization.
13 720 0.485489349759 Henry Cohn, 2026, needs more optimization.
13 721 0.485591204459 Henry Cohn, 2025, needs more optimization.
13 722 0.485628456057 Henry Cohn, 2025, needs more optimization.
13 723 0.485669629147 Henry Cohn, 2025, needs more optimization.
13 724 0.486214777807 Henry Cohn, 2026, needs more optimization.
13 726 0.486279750394 Henry Cohn, 2025, needs more optimization.
13 728 0.486315569030 Henry Cohn, 2026, needs more optimization.
13 729 0.486343174788 Henry Cohn, 2025, needs more optimization.
13 730 0.486353841057 Henry Cohn, 2025, needs more optimization.
13 732 0.486398271121 Henry Cohn, 2026, needs more optimization.
13 733 0.486424756451 Henry Cohn, 2025, needs more optimization.
13 734 0.486492245340 Henry Cohn, 2025, needs more optimization.
13 735 0.486528687498 Henry Cohn, 2025, needs more optimization.
13 736 0.486541827480 Henry Cohn, 2026, needs more optimization.
13 737 0.486610781541 Henry Cohn, 2025, needs more optimization.
13 738 0.486650314938 Henry Cohn, 2025, needs more optimization.
13 739 0.486674807439 Henry Cohn, 2025, needs more optimization.
13 740 0.486747665413 Henry Cohn, 2026, needs more optimization.
13 741 0.486774481368 Henry Cohn, 2025, needs more optimization.
13 742 0.486790725017 Henry Cohn, 2025, needs more optimization.
13 744 0.486809080246 Henry Cohn, 2026, needs more optimization.
13 745 0.486832029598 Henry Cohn, 2025, needs more optimization.
13 746 0.486894373071 Henry Cohn, 2025, needs more optimization.
13 747 0.486995072672 Henry Cohn, 2025, needs more optimization.
13 748 0.487288300144 Henry Cohn, 2026, needs more optimization.
13 749 0.487297499593 Henry Cohn, 2025, needs more optimization.
13 750 0.487330450141 Henry Cohn, 2025, needs more optimization.
13 751 0.487380839577 Henry Cohn, 2025, needs more optimization.
13 752 0.487382031309 Henry Cohn, 2026, needs more optimization.
13 753 0.487396589409 Henry Cohn, 2025, needs more optimization.
13 754 0.487399549613 Henry Cohn, 2025, needs more optimization.
13 755 0.487502436563 Henry Cohn, 2025, needs more optimization.
13 756 0.487564772802 Henry Cohn, 2026, needs more optimization.
13 757 0.487742083046 Henry Cohn, 2026, needs more optimization.
13 758 0.487816480596 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 0.180989672412 Henry Cohn, 2026.
14 73 0.184685922154 Henry Cohn, 2026, needs more optimization.
14 75 0.185110498567 Henry Cohn, 2026, needs more optimization.
14 76 0.189888419708 Henry Cohn, 2026, needs more optimization.
14 77 0.192044340418 Henry Cohn, 2026, needs more optimization.
14 78 0.192681299289 Henry Cohn, 2026, needs more optimization.
14 79 0.194319485351 Henry Cohn, 2026, needs more optimization.
14 80 0.195567913043 Henry Cohn, 2026, needs more optimization.
14 81 0.198109586451 Henry Cohn, 2026, needs more optimization.
14 83 0.198343911513 Henry Cohn, 2026, needs more optimization.
14 84 0.198352242654 Henry Cohn, 2026, needs more optimization.
14 85 0.198385543226 Henry Cohn, 2026, needs more optimization.
14 86 0.198455824071 Henry Cohn, 2026, needs more optimization.
14 87 0.198500556742 Henry Cohn, 2026, needs more optimization.
14 88 0.198573231108 Henry Cohn, 2026, needs more optimization.
14 89 0.198677263321 Henry Cohn, 2026, needs more optimization.
14 90 0.198771953024 Henry Cohn, 2026, needs more optimization.
14 91 0.198843416031 Henry Cohn, 2026, needs more optimization.
14 92 0.208457898342 Henry Cohn, 2026, needs more optimization.
14 93 0.212930218599 Henry Cohn, 2026, needs more optimization.
14 94 0.213929020886 Henry Cohn, 2026, needs more optimization.
14 95 0.217145618324 Henry Cohn, 2026, needs more optimization.
14 96 0.217581736905 Henry Cohn, 2026, needs more optimization.
14 97 0.217987275841 Henry Cohn, 2026, needs more optimization.
14 98 0.219808790643 Henry Cohn, 2026, needs more optimization.
14 99 0.222120043573 Henry Cohn, 2026, needs more optimization.
14 100 0.223728320054 Henry Cohn, 2026, needs more optimization.
14 101 0.225621017991 Henry Cohn, 2026, needs more optimization.
14 102 0.228336206045 Henry Cohn, 2026, needs more optimization.
14 112 0.229910395528 Henry Cohn, 2026, needs more optimization.
14 113 0.234903720985 Henry Cohn, 2026, needs more optimization.
14 114 0.237369497279 Henry Cohn, 2026, needs more optimization.
14 115 0.239325281760 Henry Cohn, 2026, needs more optimization.
14 116 0.240935156065 Henry Cohn, 2026, needs more optimization.
14 117 0.242371728845 Henry Cohn, 2026, needs more optimization.
14 118 0.244115274965 Henry Cohn, 2026, needs more optimization.
14 119 0.244941008540 Henry Cohn, 2026, needs more optimization.
14 120 0.246542776600 Henry Cohn, 2026, needs more optimization.
14 121 0.247804837635 Henry Cohn, 2026, needs more optimization.
14 122 0.249222342079 Henry Cohn, 2026, needs more optimization.
14 123 0.250379704445 Henry Cohn, 2026, needs more optimization.
14 124 0.251250707332 Henry Cohn, 2026, needs more optimization.
14 125 0.252289325846 Henry Cohn, 2026, needs more optimization.
14 126 0.253313260997 Henry Cohn, 2026, needs more optimization.
14 127 0.254061789773 Henry Cohn, 2026, needs more optimization.
14 128 0.254664010994 Henry Cohn, 2026, needs more optimization.
14 129 0.255355902029 Henry Cohn, 2026, needs more optimization.
14 130 0.256043761691 Henry Cohn, 2026, needs more optimization.
14 131 0.259574413142 Henry Cohn, 2026, needs more optimization.
14 132 0.261696058723 Henry Cohn, 2026, needs more optimization.
14 133 0.262945587611 Henry Cohn, 2026, needs more optimization.
14 134 0.264542191163 Henry Cohn, 2026, needs more optimization.
14 135 0.265838743456 Henry Cohn, 2026, needs more optimization.
14 136 0.267053245625 Henry Cohn, 2026, needs more optimization.
14 137 0.268606116799 Henry Cohn, 2026, needs more optimization.
14 139 0.269360822448 Henry Cohn, 2026, needs more optimization.
14 140 0.269363489591 Henry Cohn, 2026, needs more optimization.
14 141 0.269364654408 Henry Cohn, 2026, needs more optimization.
14 142 0.269374503095 Henry Cohn, 2026, needs more optimization.
14 143 0.269376035730 Henry Cohn, 2026, needs more optimization.
14 144 0.269378796345 Henry Cohn, 2026, needs more optimization.
14 145 0.269385310491 Henry Cohn, 2026, needs more optimization.
14 146 0.269391870899 Henry Cohn, 2026, needs more optimization.
14 147 0.269406679942 Henry Cohn, 2026, needs more optimization.
14 148 0.269436221839 Henry Cohn, 2026, needs more optimization.
14 149 0.269471439877 Henry Cohn, 2026, needs more optimization.
14 150 0.269516324117 Henry Cohn, 2026, needs more optimization.
14 152 0.269752269749 Henry Cohn, 2026, needs more optimization.
14 153 0.273185531227 Henry Cohn, 2026, needs more optimization.
14 154 0.273861278753 Henry Cohn, 2026.
40⁢x2−3
14 156 0.283473354757 Henry Cohn, 2024.
112⁢x2−9
14 157 0.292107146253 Henry Cohn, 2026, needs more optimization.
14 158 0.296453766736 Henry Cohn, 2026, needs more optimization.
14 159 0.297358724217 Henry Cohn, 2026, needs more optimization.
14 160 0.298235893165 Henry Cohn, 2026, needs more optimization.
14 161 0.299219714474 Henry Cohn, 2026, needs more optimization.
14 162 0.300174858927 Henry Cohn, 2026, needs more optimization.
14 163 0.300990663412 Henry Cohn, 2026, needs more optimization.
14 164 0.301631955583 Henry Cohn, 2026, needs more optimization.
14 165 0.302313005813 Henry Cohn, 2026, needs more optimization.
14 166 0.302523056003 Henry Cohn, 2026, needs more optimization.
14 167 0.302967699990 Henry Cohn, 2026, needs more optimization.
14 168 0.303312543886 Henry Cohn, 2026, needs more optimization.
14 169 0.303835817371 Henry Cohn, 2026, needs more optimization.
14 170 0.304593224212 Henry Cohn, 2026, needs more optimization.
14 171 0.309917098390 Henry Cohn, 2026, needs more optimization.
14 172 0.310239995335 Henry Cohn, 2025, needs more optimization.
14 173 0.310637785532 Henry Cohn, 2026, needs more optimization.
14 174 0.311480233175 Henry Cohn, 2026, needs more optimization.
14 175 0.312037841328 Henry Cohn, 2026, needs more optimization.
14 176 0.312207977892 Henry Cohn, 2026, needs more optimization.
14 177 0.312436085073 Henry Cohn, 2026, needs more optimization.
14 178 0.313207837449 Henry Cohn, 2026, needs more optimization.
14 179 0.314230764795 Henry Cohn, 2026, needs more optimization.
14 180 0.314682268521 Henry Cohn, 2026, needs more optimization.
14 181 0.315123945367 Henry Cohn, 2026, needs more optimization.
14 182 0.315928139605 Henry Cohn, 2026, needs more optimization.
14 183 0.316268309238 Henry Cohn, 2026, needs more optimization.
14 184 0.316387449508 Henry Cohn, 2026, needs more optimization.
14 185 0.316550432851 Henry Cohn, 2026, needs more optimization.
14 186 0.317786234423 Henry Cohn, 2026, needs more optimization.
14 210 0.318181818182 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
22⁢x−7
14 211 0.325237190232 Henry Cohn, 2026, needs more optimization.
14 212 0.325353631742 Henry Cohn, 2026, needs more optimization.
14 213 0.325515740918 Henry Cohn, 2026, needs more optimization.
14 214 0.325780837160 Henry Cohn, 2026, needs more optimization.
14 215 0.325810730681 Henry Cohn, 2026, needs more optimization.
14 216 0.326010926112 Henry Cohn, 2026, needs more optimization.
14 217 0.326489146448 Henry Cohn, 2026, needs more optimization.
14 218 0.326717861229 Henry Cohn, 2026, needs more optimization.
14 219 0.326732346212 Henry Cohn, 2026, needs more optimization.
14 220 0.326911196612 Henry Cohn, 2026, needs more optimization.
14 221 0.326918787317 Henry Cohn, 2026, needs more optimization.
14 222 0.326986105033 Henry Cohn, 2026, needs more optimization.
14 223 0.327071206132 Henry Cohn, 2026, needs more optimization.
14 224 0.327203925862 Henry Cohn, 2026, needs more optimization.
14 225 0.327570966121 Henry Cohn, 2026, needs more optimization.
14 226 0.327594408743 Henry Cohn, 2026, needs more optimization.
14 227 0.328079378435 Henry Cohn, 2026, needs more optimization.
14 228 0.328436320574 Henry Cohn, 2026, needs more optimization.
14 229 0.328589621977 Henry Cohn, 2026, needs more optimization.
14 230 0.328969557149 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. T. Zhaowei, 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
14 254 0.348228091414 Henry Cohn, 2026, needs more optimization.
14 255 0.349093446821 Henry Cohn, 2026, needs more optimization.
14 256 0.349099317126 Henry Cohn, 2026, needs more optimization.
14 257 0.349146546868 Henry Cohn, 2026, needs more optimization.
14 258 0.349429822708 Henry Cohn, 2026, needs more optimization.
14 259 0.349609234861 Henry Cohn, 2026, needs more optimization.
14 260 0.349697776015 Henry Cohn, 2026, needs more optimization.
14 261 0.350017604419 Henry Cohn, 2026, needs more optimization.
14 262 0.350101683506 Henry Cohn, 2026, needs more optimization.
14 263 0.350138048688 Henry Cohn, 2026, needs more optimization.
14 264 0.351678846576 Henry Cohn, 2026, needs more optimization.
14 265 0.351707619775 Henry Cohn, 2026, needs more optimization.
14 266 0.351731136767 Henry Cohn, 2026, needs more optimization.
14 267 0.351757022154 Henry Cohn, 2026, needs more optimization.
14 268 0.351839126165 Henry Cohn, 2026, needs more optimization.
14 269 0.352076312504 Henry Cohn, 2026, needs more optimization.
14 270 0.352265343868 Henry Cohn, 2026, needs more optimization.
14 272 0.352365891070 Henry Cohn, 2026, needs more optimization.
14 273 0.352694160387 Henry Cohn, 2026, needs more optimization.
14 274 0.352877344477 Henry Cohn, 2026, needs more optimization.
14 276 0.353102325072 Henry Cohn, 2026, needs more optimization.
14 277 0.353234413318 Henry Cohn, 2026, needs more optimization.
14 278 0.353906292766 Henry Cohn, 2026, needs more optimization.
14 279 0.353919363230 Henry Cohn, 2026, needs more optimization.
14 281 0.354089834130 Henry Cohn, 2026, needs more optimization.
14 282 0.354222114054 Henry Cohn, 2026, needs more optimization.
14 283 0.354275349136 Henry Cohn, 2026, needs more optimization.
14 284 0.354437016909 Henry Cohn, 2026, needs more optimization.
14 285 0.354629938736 Henry Cohn, 2026, needs more optimization.
14 286 0.354659214912 Henry Cohn, 2026, needs more optimization.
14 287 0.354678598213 Henry Cohn, 2026, needs more optimization.
14 288 0.354698270662 Henry Cohn, 2026, needs more optimization.
14 289 0.354709739187 Henry Cohn, 2026, needs more optimization.
14 290 0.354720959468 Henry Cohn, 2026, needs more optimization.
14 291 0.354837309695 Henry Cohn, 2026, needs more optimization.
14 292 0.355114823627 Henry Cohn, 2026, needs more optimization.
14 293 0.355270184236 Henry Cohn, 2026, needs more optimization.
14 294 0.355368455636 Henry Cohn, 2026, needs more optimization.
14 295 0.355369705102 Henry Cohn, 2026, needs more optimization.
14 296 0.355372895389 Henry Cohn, 2026, needs more optimization.
14 300 0.355377450170 Henry Cohn, 2026, needs more optimization.
14 304 0.355592458266 Henry Cohn, 2026, needs more optimization.
14 306 0.355595026220 Henry Cohn, 2026, needs more optimization.
14 307 0.355596245382 Henry Cohn, 2026, needs more optimization.
14 310 0.355596344014 Henry Cohn, 2026, needs more optimization.
14 317 0.355596615854 Henry Cohn, 2026, needs more optimization.
14 318 0.355598619036 Henry Cohn, 2026, needs more optimization.
14 320 0.355598733128 Henry Cohn, 2026, needs more optimization.
14 321 0.355603161787 Henry Cohn, 2026, needs more optimization.
14 322 0.355607105198 Henry Cohn, 2026, needs more optimization.
14 323 0.355613225545 Henry Cohn, 2026, needs more optimization.
14 325 0.355616443419 Henry Cohn, 2026, needs more optimization.
14 327 0.355620633097 Henry Cohn, 2026, needs more optimization.
14 328 0.355620672265 Henry Cohn, 2026, needs more optimization.
14 329 0.355623601673 Henry Cohn, 2026, needs more optimization.
14 330 0.355626910653 Henry Cohn, 2026, needs more optimization.
14 331 0.355647861564 Henry Cohn, 2026, needs more optimization.
14 332 0.355721461595 Henry Cohn, 2026, needs more optimization.
14 333 0.356491665492 Henry Cohn, 2026, needs more optimization.
14 335 0.356523872657 Henry Cohn, 2026, needs more optimization.
14 336 0.356530903868 Henry Cohn, 2026, needs more optimization.
14 337 0.356729335160 Henry Cohn, 2026, needs more optimization.
14 338 0.356783585587 Henry Cohn, 2026, needs more optimization.
14 339 0.358507191076 Henry Cohn, 2026, needs more optimization.
14 340 0.360048220156 Henry Cohn, 2026, needs more optimization.
14 341 0.360721335636 Henry Cohn, 2026, needs more optimization.
14 343 0.367824826104 Henry Cohn, 2026, needs more optimization.
14 344 0.368268128693 Henry Cohn, 2026, needs more optimization.
14 345 0.368689125461 Henry Cohn, 2026, needs more optimization.
14 350 0.369160447936 Henry Cohn, 2026, needs more optimization.
14 351 0.369397909736 Henry Cohn, 2026, needs more optimization.
14 352 0.370682642393 Henry Cohn, 2026, needs more optimization.
14 360 0.378369530745 Henry Cohn, 2026, needs more optimization.
14 364 0.378545858307 Henry Cohn, 2026, needs more optimization.
14 365 0.379505399137 Henry Cohn, 2026, needs more optimization.
14 368 0.379518558288 Henry Cohn, 2026, needs more optimization.
14 369 0.379588636561 Henry Cohn, 2026, needs more optimization.
14 370 0.379617042154 Henry Cohn, 2026, needs more optimization.
14 371 0.379702649736 Henry Cohn, 2026, needs more optimization.
14 376 0.379736746844 Henry Cohn, 2026, needs more optimization.
14 384 0.382719113175 Henry Cohn, 2026, needs more optimization.
14 386 0.383144972193 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
14 492 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
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 0.429784647320 Henry Cohn, 2026, needs more optimization.
14 602 0.430091119011 Henry Cohn, 2025, needs more optimization.
14 603 0.430255500551 Henry Cohn, 2025, needs more optimization.
14 604 0.430605377846 Henry Cohn, 2026, needs more optimization.
14 605 0.431095901490 Henry Cohn, 2025, needs more optimization.
14 606 0.431192286990 Henry Cohn, 2025, needs more optimization.
14 607 0.431236397848 Henry Cohn, 2025, needs more optimization.
14 608 0.431365482112 Henry Cohn, 2026, needs more optimization.
14 609 0.431552382817 Henry Cohn, 2025, needs more optimization.
14 610 0.431669143554 Henry Cohn, 2026, needs more optimization.
14 611 0.431687232253 Henry Cohn, 2025, needs more optimization.
14 612 0.432192772355 Henry Cohn, 2026, needs more optimization.
14 614 0.432432822618 Henry Cohn, 2025, needs more optimization.
14 616 0.432898752936 Henry Cohn, 2026, needs more optimization.
14 618 0.433020999307 Henry Cohn, 2025, needs more optimization.
14 620 0.433039391703 Henry Cohn, 2026, needs more optimization.
14 621 0.433126440825 Henry Cohn, 2025, needs more optimization.
14 624 0.433145754655 Henry Cohn, 2026, needs more optimization.
14 625 0.433243537011 Henry Cohn, 2025, needs more optimization.
14 626 0.433282562279 Henry Cohn, 2025, needs more optimization.
14 627 0.433311094830 Henry Cohn, 2025, needs more optimization.
14 628 0.433563716319 Henry Cohn, 2026, needs more optimization.
14 630 0.433668758998 Henry Cohn, 2025, needs more optimization.
14 632 0.433688204409 Henry Cohn, 2026, needs more optimization.
14 634 0.433779719638 Henry Cohn, 2025, needs more optimization.
14 636 0.433832897674 Henry Cohn, 2026, needs more optimization.
14 637 0.433915481050 Henry Cohn, 2025, needs more optimization.
14 638 0.433959497508 Henry Cohn, 2025, needs more optimization.
14 639 0.433963466338 Henry Cohn, 2025, needs more optimization.
14 640 0.434234535028 Henry Cohn, 2026, needs more optimization.
14 641 0.434243537160 Henry Cohn, 2025, needs more optimization.
14 642 0.434246541036 Henry Cohn, 2025, needs more optimization.
14 644 0.451502692839 Henry Cohn, 2026, needs more optimization.
14 646 0.451526932364 Henry Cohn, 2025, needs more optimization.
14 648 0.451555266873 Henry Cohn, 2026, needs more optimization.
14 649 0.451565788068 Henry Cohn, 2025, needs more optimization.
14 652 0.451683741627 Henry Cohn, 2026, needs more optimization.
14 654 0.451699556322 Henry Cohn, 2025, needs more optimization.
14 656 0.451788208457 Henry Cohn, 2026, needs more optimization.
14 660 0.452033205431 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 0.454721351053 Henry Cohn, 2026, needs more optimization.
14 898 0.454843787060 Henry Cohn, 2026, needs more optimization.
14 899 0.454870853392 Henry Cohn, 2026, needs more optimization.
14 900 0.454887890162 Henry Cohn, 2026, needs more optimization.
14 901 0.454931070240 Henry Cohn, 2026, needs more optimization.
14 902 0.454973664103 Henry Cohn, 2025, needs more optimization.
14 903 0.454999625082 Henry Cohn, 2026, needs more optimization.
14 904 0.455055416212 Henry Cohn, 2026, needs more optimization.
14 905 0.455117451163 Henry Cohn, 2025, needs more optimization.
14 908 0.455121613794 Henry Cohn, 2026, needs more optimization.
14 909 0.455165284846 Henry Cohn, 2025, needs more optimization.
14 910 0.455181904176 Henry Cohn, 2025, needs more optimization.
14 912 0.455187226387 Henry Cohn, 2026, needs more optimization.
14 913 0.455215189225 Henry Cohn, 2025, needs more optimization.
14 914 0.455229290474 Henry Cohn, 2025, needs more optimization.
14 916 0.455249105039 Henry Cohn, 2026, needs more optimization.
14 917 0.455285139780 Henry Cohn, 2025, needs more optimization.
14 918 0.455312697587 Henry Cohn, 2025, needs more optimization.
14 920 0.455326887293 Henry Cohn, 2026, needs more optimization.
14 921 0.455361343330 Henry Cohn, 2025, needs more optimization.
14 922 0.455368216747 Henry Cohn, 2025, needs more optimization.
14 923 0.455372029754 Henry Cohn, 2025, needs more optimization.
14 924 0.492313427682 Henry Cohn, 2026, needs more optimization.
14 925 0.492327194287 Henry Cohn, 2025, needs more optimization.
14 926 0.492446494583 Henry Cohn, 2025, needs more optimization.
14 927 0.492666262172 Henry Cohn, 2025, needs more optimization.
14 928 0.492676366579 Henry Cohn, 2026, needs more optimization.
14 929 0.492692208983 Henry Cohn, 2025, needs more optimization.
14 930 0.492975622881 Henry Cohn, 2025, needs more optimization.
14 931 0.493017067245 Henry Cohn, 2025, needs more optimization.
14 932 0.493028038540 Henry Cohn, 2026, needs more optimization.
14 933 0.493099194502 Henry Cohn, 2025, needs more optimization.
14 934 0.493424999986 Henry Cohn, 2025, needs more optimization.
14 935 0.493436866895 Henry Cohn, 2025, needs more optimization.
14 936 0.493474884160 Henry Cohn, 2026, needs more optimization.
14 937 0.493641027705 Henry Cohn, 2025, needs more optimization.
14 938 0.493697769727 Henry Cohn, 2025, needs more optimization.
14 939 0.493706887962 Henry Cohn, 2025, needs more optimization.
14 940 0.493962683689 Henry Cohn, 2026, needs more optimization.
14 941 0.493974355695 Henry Cohn, 2025, needs more optimization.
14 943 0.494147583322 Henry Cohn, 2025, needs more optimization.
14 944 0.494409198434 Henry Cohn, 2026, needs more optimization.
14 945 0.494441938719 Henry Cohn, 2025, needs more optimization.
14 946 0.494456422769 Henry Cohn, 2025, needs more optimization.
14 947 0.494688575887 Henry Cohn, 2025, needs more optimization.
14 948 0.494703928253 Henry Cohn, 2026, needs more optimization.
14 949 0.494749973807 Henry Cohn, 2025, needs more optimization.
14 950 0.495012728768 Henry Cohn, 2025, needs more optimization.
14 951 0.495023039759 Henry Cohn, 2025, needs more optimization.
14 952 0.495023447217 Henry Cohn, 2026, needs more optimization.
14 953 0.495031085664 Henry Cohn, 2025, needs more optimization.
14 954 0.495147935962 Henry Cohn, 2025, needs more optimization.
14 956 0.495168651929 Henry Cohn, 2026, needs more optimization.
14 957 0.495376527378 Henry Cohn, 2025, needs more optimization.
14 958 0.495386570918 Henry Cohn, 2025, needs more optimization.
14 960 0.495657184832 Henry Cohn, 2026, needs more optimization.
14 961 0.495765560894 Henry Cohn, 2025, needs more optimization.
14 963 0.496056693148 Henry Cohn, 2025, needs more optimization.
14 964 0.496130338879 Henry Cohn, 2026, needs more optimization.
14 965 0.496348709997 Henry Cohn, 2025, needs more optimization.
14 966 0.496371443162 Henry Cohn, 2025, needs more optimization.
14 967 0.496389317457 Henry Cohn, 2025, needs more optimization.
14 968 0.496389619657 Henry Cohn, 2026, needs more optimization.
14 969 0.496658700984 Henry Cohn, 2025, needs more optimization.
14 970 0.496665185326 Henry Cohn, 2025, needs more optimization.
14 971 0.496922774268 Henry Cohn, 2025, needs more optimization.
14 972 0.496975899538 Henry Cohn, 2026, needs more optimization.
14 973 0.497000563595 Henry Cohn, 2025, needs more optimization.
14 974 0.497087302693 Henry Cohn, 2025, needs more optimization.
14 975 0.497289348022 Henry Cohn, 2025, needs more optimization.
14 976 0.497304672293 Henry Cohn, 2026, needs more optimization.
14 977 0.497364578162 Henry Cohn, 2025, needs more optimization.
14 978 0.497607125645 Henry Cohn, 2025, needs more optimization.
14 979 0.497654773739 Henry Cohn, 2025, needs more optimization.
14 980 0.497677114082 Henry Cohn, 2026, needs more optimization.
14 981 0.497751573565 Henry Cohn, 2025, needs more optimization.
14 982 0.497991350964 Henry Cohn, 2025, needs more optimization.
14 983 0.498011822506 Henry Cohn, 2025, needs more optimization.
14 984 0.498020685452 Henry Cohn, 2026, needs more optimization.
14 985 0.498029179824 Henry Cohn, 2025, needs more optimization.
14 986 0.498291451097 Henry Cohn, 2025, needs more optimization.
14 987 0.498476341963 Henry Cohn, 2025, needs more optimization.
14 988 0.498541834310 Henry Cohn, 2026, needs more optimization.
14 989 0.498578439165 Henry Cohn, 2025, needs more optimization.
14 990 0.498764331870 Henry Cohn, 2025, needs more optimization.
14 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
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 0.105767188891 Henry Cohn, 2023.
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 0.129619175385 Henry Cohn, 2025, needs more optimization.
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 71 0.166512948843 Henry Cohn, 2025.
15 72 0.166656830714 Henry Cohn, 2026, needs more optimization.
15 73 0.166704540358 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 0.186858652304 Henry Cohn, 2026, needs more optimization.
15 95 0.187145879513 Henry Cohn, 2026, needs more optimization.
15 96 0.188201821306 Henry Cohn, 2026, needs more optimization.
15 99 0.188682094168 Henry Cohn, 2026, needs more optimization.
15 100 0.189764266343 Henry Cohn, 2026, needs more optimization.
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 0.209693852061 Henry Cohn, 2026, needs more optimization.
15 130 0.216744767943 Henry Cohn, 2026, needs more optimization.
15 131 0.219841453500 Henry Cohn, 2026, needs more optimization.
15 132 0.221699429606 Henry Cohn, 2026, needs more optimization.
15 133 0.223240086287 Henry Cohn, 2026, needs more optimization.
15 134 0.226013010231 Henry Cohn, 2026, needs more optimization.
15 136 0.226153149527 Henry Cohn, 2026, needs more optimization.
15 137 0.226940232582 Henry Cohn, 2026, needs more optimization.
15 142 0.227160244717 Henry Cohn, 2026, needs more optimization.
15 143 0.232905190060 Henry Cohn, 2026, needs more optimization.
15 144 0.236623814027 Henry Cohn, 2025, needs more optimization.
15 145 0.238726765702 Henry Cohn, 2026, needs more optimization.
15 146 0.238734657627 Henry Cohn, 2026, needs more optimization.
15 147 0.238762616069 Henry Cohn, 2026, needs more optimization.
15 150 0.239576060692 Henry Cohn, 2026, needs more optimization.
15 151 0.244768075596 Henry Cohn, 2026, needs more optimization.
15 152 0.245263477965 Henry Cohn, 2026, needs more optimization.
15 153 0.245510293392 Henry Cohn, 2026, needs more optimization.
15 154 0.249413184522 Henry Cohn, 2026, needs more optimization.
15 156 0.25 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
4⁢x−1
15 157 0.251119981017 Henry Cohn, 2026, needs more optimization.
15 158 0.254972169331 Henry Cohn, 2026, needs more optimization.
15 159 0.261528226184 Henry Cohn, 2026, needs more optimization.
15 160 0.265646614406 Henry Cohn, 2026, needs more optimization.
15 161 0.266154825516 Henry Cohn, 2026, needs more optimization.
15 162 0.266681337986 Henry Cohn, 2026, needs more optimization.
15 163 0.267648162676 Henry Cohn, 2026, needs more optimization.
15 164 0.268173483055 Henry Cohn, 2026, needs more optimization.
15 165 0.268884803023 Henry Cohn, 2026, needs more optimization.
15 166 0.269184929405 Henry Cohn, 2026, needs more optimization.
15 167 0.269567634279 Henry Cohn, 2026, needs more optimization.
15 168 0.269752871240 Henry Cohn, 2026, needs more optimization.
15 170 0.269752871241 Henry Cohn, 2026, needs more optimization.
15 171 0.290193867269 Henry Cohn, 2026, needs more optimization.
15 172 0.290799188525 Henry Cohn, 2025, needs more optimization.
15 173 0.291821581929 Henry Cohn, 2026, needs more optimization.
15 174 0.292732786097 Henry Cohn, 2026, needs more optimization.
15 175 0.293430486142 Henry Cohn, 2025, needs more optimization.
15 179 0.294129514920 Henry Cohn, 2026, needs more optimization.
15 180 0.294134359793 Henry Cohn, 2026, needs more optimization.
15 183 0.294140471840 Henry Cohn, 2026, needs more optimization.
15 184 0.294141511408 Henry Cohn, 2026, needs more optimization.
15 186 0.294142301815 Henry Cohn, 2026, needs more optimization.
15 187 0.294145453578 Henry Cohn, 2026, needs more optimization.
15 188 0.294194462005 Henry Cohn, 2026, needs more optimization.
15 189 0.294267022009 Henry Cohn, 2026, needs more optimization.
15 190 0.294325835544 Henry Cohn, 2026, needs more optimization.
15 192 0.294328177668 Henry Cohn, 2026, needs more optimization.
15 193 0.294577808916 Henry Cohn, 2026, needs more optimization.
15 195 0.298915338211 Henry Cohn, 2026, needs more optimization.
15 196 0.300775957005 Henry Cohn, 2026, needs more optimization.
15 240 0.304347826087 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
23⁢x−7
15 256 0.304347826087 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.
23⁢x−7
15 257 0.304907913664 Henry Cohn, 2026, needs more optimization.
15 258 0.305116738245 Henry Cohn, 2026, needs more optimization.
15 259 0.306602551551 Henry Cohn, 2026, needs more optimization.
15 263 0.309536394471 Henry Cohn, 2026, needs more optimization.
15 264 0.310172221735 Henry Cohn, 2026, needs more optimization.
15 265 0.321180427261 Henry Cohn, 2026, needs more optimization.
15 266 0.321432314178 Henry Cohn, 2026, needs more optimization.
15 267 0.321760306814 Henry Cohn, 2026, needs more optimization.
15 268 0.322013813399 Henry Cohn, 2026, needs more optimization.
15 269 0.322229695435 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 0.339370412683 Henry Cohn, 2026, needs more optimization.
15 322 0.340377089292 Henry Cohn, 2026, needs more optimization.
15 323 0.353686979309 Henry Cohn, 2026, needs more optimization.
15 325 0.354517119657 Henry Cohn, 2026, needs more optimization.
15 326 0.354530545782 Henry Cohn, 2026, needs more optimization.
15 328 0.354566984239 Henry Cohn, 2026, needs more optimization.
15 329 0.354604194827 Henry Cohn, 2026, needs more optimization.
15 330 0.354632594790 Henry Cohn, 2026, needs more optimization.
15 331 0.354649136399 Henry Cohn, 2026, needs more optimization.
15 332 0.354713668777 Henry Cohn, 2026, needs more optimization.
15 333 0.354719040551 Henry Cohn, 2026, needs more optimization.
15 336 0.354741888911 Henry Cohn, 2026, needs more optimization.
15 337 0.354826816308 Henry Cohn, 2026, needs more optimization.
15 338 0.355259895838 Henry Cohn, 2026, needs more optimization.
15 339 0.355266702254 Henry Cohn, 2026, needs more optimization.
15 340 0.355276802388 Henry Cohn, 2026, needs more optimization.
15 341 0.355290388162 Henry Cohn, 2026, needs more optimization.
15 342 0.355290659496 Henry Cohn, 2026, needs more optimization.
15 344 0.355309909755 Henry Cohn, 2026, needs more optimization.
15 346 0.355346604838 Henry Cohn, 2026, needs more optimization.
15 347 0.355351162570 Henry Cohn, 2026, needs more optimization.
15 348 0.355364193306 Henry Cohn, 2026, needs more optimization.
15 352 0.355493648494 Henry Cohn, 2026, needs more optimization.
15 353 0.355525152696 Henry Cohn, 2026, needs more optimization.
15 355 0.355533284258 Henry Cohn, 2026, needs more optimization.
15 356 0.355545845211 Henry Cohn, 2026, needs more optimization.
15 358 0.355550069943 Henry Cohn, 2026, needs more optimization.
15 359 0.355600275452 Henry Cohn, 2026, needs more optimization.
15 360 0.355602110975 Henry Cohn, 2026, needs more optimization.
15 361 0.355610820517 Henry Cohn, 2026, needs more optimization.
15 362 0.355618827570 Henry Cohn, 2026, needs more optimization.
15 363 0.355650983568 Henry Cohn, 2026, needs more optimization.
15 364 0.355659351583 Henry Cohn, 2026, needs more optimization.
15 365 0.355680342401 Henry Cohn, 2026, needs more optimization.
15 366 0.355710147631 Henry Cohn, 2026, needs more optimization.
15 367 0.355716028864 Henry Cohn, 2026, needs more optimization.
15 368 0.355726879627 Henry Cohn, 2026, needs more optimization.
15 369 0.355772992600 Henry Cohn, 2026, needs more optimization.
15 370 0.355849158957 Henry Cohn, 2026, needs more optimization.
15 371 0.355865550171 Henry Cohn, 2026, needs more optimization.
15 372 0.355910801874 Henry Cohn, 2026, needs more optimization.
15 373 0.356896924733 Henry Cohn, 2026, needs more optimization.
15 374 0.357213563423 Henry Cohn, 2026, needs more optimization.
15 375 0.357327127633 Henry Cohn, 2026, needs more optimization.
15 376 0.359572438356 Henry Cohn, 2026, needs more optimization.
15 377 0.359692245708 Henry Cohn, 2026, needs more optimization.
15 378 0.359761801743 Henry Cohn, 2026, needs more optimization.
15 379 0.360848677125 Henry Cohn, 2026, needs more optimization.
15 380 0.360874420911 Henry Cohn, 2026, needs more optimization.
15 381 0.361027875254 Henry Cohn, 2026, needs more optimization.
15 382 0.361107627164 Henry Cohn, 2026, needs more optimization.
15 383 0.361793558670 Henry Cohn, 2026, needs more optimization.
15 384 0.362898403048 Henry Cohn, 2026, needs more optimization.
15 385 0.363400396726 Henry Cohn, 2026, needs more optimization.
15 386 0.364162589879 Henry Cohn, 2026, needs more optimization.
15 388 0.365896664560 Henry Cohn, 2026, needs more optimization.
15 389 0.384420108204 Henry Cohn, 2025, needs more optimization.
15 390 0.384918541898 Henry Cohn, 2025, needs more optimization.
15 391 0.385074975412 Henry Cohn, 2026, needs more optimization.
15 392 0.385592066086 Henry Cohn, 2026, needs more optimization.
15 393 0.385697573797 Henry Cohn, 2025, needs more optimization.
15 394 0.385984331138 Henry Cohn, 2025, needs more optimization.
15 395 0.386225226866 Henry Cohn, 2025, needs more optimization.
15 396 0.386618130105 Henry Cohn, 2025, needs more optimization.
15 397 0.387116282587 Henry Cohn, 2025, needs more optimization.
15 398 0.387172791615 Henry Cohn, 2025, needs more optimization.
15 399 0.387606636643 Henry Cohn, 2025, needs more optimization.
15 400 0.387878096356 Henry Cohn, 2026, needs more optimization.
15 401 0.387891088276 Henry Cohn, 2026, needs more optimization.
15 402 0.388339855674 Henry Cohn, 2025, needs more optimization.
15 403 0.388757758623 Henry Cohn, 2025, needs more optimization.
15 404 0.388762229801 Henry Cohn, 2025, needs more optimization.
15 405 0.388931907229 Henry Cohn, 2026, needs more optimization.
15 406 0.389252002498 Henry Cohn, 2026, needs more optimization.
15 407 0.389817861267 Henry Cohn, 2025, needs more optimization.
15 408 0.389821569051 Henry Cohn, 2026, needs more optimization.
15 409 0.390093941582 Henry Cohn, 2025, needs more optimization.
15 410 0.390221832356 Henry Cohn, 2025, needs more optimization.
15 411 0.390425306732 Henry Cohn, 2025, needs more optimization.
15 412 0.390749867913 Henry Cohn, 2025, needs more optimization.
15 413 0.391420636625 Henry Cohn, 2025, needs more optimization.
15 414 0.391448228914 Henry Cohn, 2026, needs more optimization.
15 415 0.391481727130 Henry Cohn, 2026, needs more optimization.
15 416 0.391883380232 Henry Cohn, 2026, needs more optimization.
15 424 0.391884909262 Henry Cohn, 2026, needs more optimization.
15 432 0.391885825686 Henry Cohn, 2026, needs more optimization.
15 433 0.391904247888 Henry Cohn, 2025, needs more optimization.
15 440 0.391910082861 Henry Cohn, 2026, needs more optimization.
15 442 0.391915123600 Henry Cohn, 2025, needs more optimization.
15 443 0.391960592920 Henry Cohn, 2026, needs more optimization.
15 444 0.391965011895 Henry Cohn, 2026, needs more optimization.
15 448 0.391969898330 Henry Cohn, 2026, needs more optimization.
15 449 0.391974552177 Henry Cohn, 2026, needs more optimization.
15 451 0.391982342905 Henry Cohn, 2026, needs more optimization.
15 452 0.392005226466 Henry Cohn, 2026, needs more optimization.
15 453 0.392010208274 Henry Cohn, 2026, needs more optimization.
15 456 0.392017018253 Henry Cohn, 2026, needs more optimization.
15 458 0.392020856406 Henry Cohn, 2026, needs more optimization.
15 459 0.392023857282 Henry Cohn, 2026, needs more optimization.
15 462 0.392041602720 Henry Cohn, 2026, needs more optimization.
15 464 0.392065844463 Henry Cohn, 2026, needs more optimization.
15 465 0.392134371424 Henry Cohn, 2026, needs more optimization.
15 466 0.392165142082 Henry Cohn, 2026, needs more optimization.
15 467 0.392689042234 Henry Cohn, 2026, needs more optimization.
15 470 0.392707676584 Henry Cohn, 2026, needs more optimization.
15 471 0.392759590039 Henry Cohn, 2026, needs more optimization.
15 472 0.392830095296 Henry Cohn, 2026, needs more optimization.
15 473 0.392851877606 Henry Cohn, 2026, needs more optimization.
15 474 0.393154346772 Henry Cohn, 2026, needs more optimization.
15 475 0.393157298956 Henry Cohn, 2026, needs more optimization.
15 476 0.393197710439 Henry Cohn, 2026, needs more optimization.
15 477 0.393294692202 Henry Cohn, 2026, needs more optimization.
15 478 0.393443890839 Henry Cohn, 2026, needs more optimization.
15 479 0.393468087110 Henry Cohn, 2026, needs more optimization.
15 480 0.393710218068 Henry Cohn, 2026, needs more optimization.
15 481 0.393785259773 Henry Cohn, 2026, needs more optimization.
15 484 0.393967039706 Henry Cohn, 2026, needs more optimization.
15 485 0.394156496480 Henry Cohn, 2026, needs more optimization.
15 486 0.394316441201 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
15 990 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
15 994 0.454658082460 Henry Cohn, 2026, needs more optimization.
15 995 0.454665617818 Henry Cohn, 2026, needs more optimization.
15 996 0.454665617827 Henry Cohn, 2025, needs more optimization.
15 997 0.454677607825 Henry Cohn, 2026, needs more optimization.
15 999 0.454677607826 Henry Cohn, 2025, needs more optimization.
15 1001 0.454678212405 Henry Cohn, 2025, needs more optimization.
15 1002 0.454734240452 Henry Cohn, 2026, needs more optimization.
15 1004 0.454780412996 Henry Cohn, 2026, needs more optimization.
15 1008 0.454800278479 Henry Cohn, 2026, needs more optimization.
15 1010 0.454831522563 Henry Cohn, 2026, needs more optimization.
15 1011 0.454837749616 Henry Cohn, 2025, needs more optimization.
15 1012 0.454838359249 Henry Cohn, 2026, needs more optimization.
15 1013 0.454845479817 Henry Cohn, 2025, needs more optimization.
15 1016 0.454914333743 Henry Cohn, 2026, needs more optimization.
15 1017 0.454918331317 Henry Cohn, 2025, needs more optimization.
15 1018 0.454923437843 Henry Cohn, 2025, needs more optimization.
15 1020 0.454926265220 Henry Cohn, 2026, needs more optimization.
15 1021 0.454953155035 Henry Cohn, 2025, needs more optimization.
15 1022 0.454958524980 Henry Cohn, 2025, needs more optimization.
15 1023 0.454961053016 Henry Cohn, 2026, needs more optimization.
15 1024 0.454977519070 Henry Cohn, 2026, needs more optimization.
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 53 0.112902421936 Henry Cohn, 2025.
16 54 0.112907159448 Henry Cohn, 2025.
16 55 0.113137877868 Henry Cohn, 2026.
16 58 0.113835450316 Henry Cohn, 2026.
288⁢x2−24⁢x−1
16 59 0.115469803431 Henry Cohn, 2023, needs more optimization.
16 60 0.115470801109 Henry Cohn, 2026, needs more optimization.
16 61 0.119371454413 Henry Cohn, 2025.
16 62 0.125768177302 Henry Cohn, 2025.
16 74 0.127284656799 Henry Cohn, 2023.
156⁢x2−12⁢x−1
16 75 0.142415975160 Henry Cohn, 2025, needs more optimization.
16 76 0.157616857308 Henry Cohn, 2025.
16 77 0.161334829806 Henry Cohn, 2026, needs more optimization.
16 78 0.164417462768 Henry Cohn, 2026, needs more optimization.
16 79 0.167459213726 Henry Cohn, 2026, needs more optimization.
16 80 0.167572018919 Henry Cohn, 2026, needs more optimization.
16 81 0.167749834182 Henry Cohn, 2026, needs more optimization.
16 82 0.167923286051 Henry Cohn, 2026, needs more optimization.
16 83 0.168279430323 Henry Cohn, 2026, needs more optimization.
16 84 0.168596157094 Henry Cohn, 2026, needs more optimization.
16 85 0.168666428099 Henry Cohn, 2025, needs more optimization.
16 88 0.168668499420 Henry Cohn, 2025, needs more optimization.
16 92 0.168684604646 Henry Cohn, 2025, needs more optimization.
16 94 0.168684943107 Henry Cohn, 2025, needs more optimization.
16 96 0.168685705337 Henry Cohn, 2026, needs more optimization.
16 97 0.169880759711 Henry Cohn, 2026, needs more optimization.
16 102 0.170753175474 Henry Cohn, 2026.
128⁢x2−16⁢x−1
16 103 0.174178397918 Henry Cohn, 2026, needs more optimization.
16 104 0.179379122946 Henry Cohn, 2026, needs more optimization.
16 105 0.183420599437 Henry Cohn, 2026, needs more optimization.
16 106 0.185897329735 Henry Cohn, 2025, needs more optimization.
16 107 0.188035693412 Henry Cohn, 2026, needs more optimization.
16 108 0.191388162639 Henry Cohn, 2026, needs more optimization.
16 116 0.192450089730 Henry Cohn, 2026.
27⁢x2−1
16 117 0.198855478458 Henry Cohn, 2026, needs more optimization.
16 118 0.198870263710 Henry Cohn, 2026, needs more optimization.
16 119 0.198900209819 Henry Cohn, 2026, needs more optimization.
16 122 0.199966091100 Henry Cohn, 2025, needs more optimization.
16 124 0.199989165771 Henry Cohn, 2025, needs more optimization.
16 126 0.199994691163 Henry Cohn, 2025, needs more optimization.
16 127 0.199995845425 Henry Cohn, 2025, needs more optimization.
16 130 0.199999918321 Henry Cohn, 2025, needs more optimization.
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 0.204975442665 Henry Cohn, 2026, needs more optimization.
16 161 0.221710856890 Henry Cohn, 2026, needs more optimization.
16 162 0.230449004034 Henry Cohn, 2026, needs more optimization.
16 163 0.233527617435 Henry Cohn, 2026, needs more optimization.
16 164 0.236157628726 Henry Cohn, 2026, needs more optimization.
16 165 0.238151063046 Henry Cohn, 2026, needs more optimization.
16 166 0.239590518972 Henry Cohn, 2026, needs more optimization.
16 167 0.240932114456 Henry Cohn, 2026, needs more optimization.
16 168 0.242199119696 Henry Cohn, 2026, needs more optimization.
16 169 0.243006711157 Henry Cohn, 2026, needs more optimization.
16 170 0.244101840176 Henry Cohn, 2026, needs more optimization.
16 171 0.245114604983 Henry Cohn, 2026, needs more optimization.
16 172 0.245712824923 Henry Cohn, 2026, needs more optimization.
16 173 0.246008048456 Henry Cohn, 2026, needs more optimization.
16 174 0.246394977527 Henry Cohn, 2026, needs more optimization.
16 175 0.246783142655 Henry Cohn, 2026, needs more optimization.
16 176 0.247725000323 Henry Cohn, 2026, needs more optimization.
16 178 0.248074734294 Henry Cohn, 2026, needs more optimization.
16 179 0.248211352858 Henry Cohn, 2026, needs more optimization.
16 180 0.248538777471 Henry Cohn, 2026, needs more optimization.
16 181 0.248728855824 Henry Cohn, 2026, needs more optimization.
16 182 0.249198180783 Henry Cohn, 2026, needs more optimization.
16 183 0.249276453379 Henry Cohn, 2026, needs more optimization.
16 184 0.249337884492 Henry Cohn, 2026, needs more optimization.
16 185 0.249531552007 Henry Cohn, 2026, needs more optimization.
16 186 0.249698724843 Henry Cohn, 2026, needs more optimization.
16 187 0.249784002919 Henry Cohn, 2026, needs more optimization.
16 188 0.249850990152 Henry Cohn, 2026, needs more optimization.
16 189 0.249902134371 Henry Cohn, 2026, needs more optimization.
16 190 0.249913255634 Henry Cohn, 2026, needs more optimization.
16 191 0.249926192853 Henry Cohn, 2026, needs more optimization.
16 192 0.249933787850 Henry Cohn, 2026, needs more optimization.
16 193 0.249935645652 Henry Cohn, 2026, needs more optimization.
16 195 0.249953080310 Henry Cohn, 2026, needs more optimization.
16 196 0.249983903379 Henry Cohn, 2026, needs more optimization.
16 198 0.249999992083 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 0.290824645574 Henry Cohn, 2026, needs more optimization.
16 290 0.320698560822 Henry Cohn, 2026, needs more optimization.
16 291 0.320946615777 Henry Cohn, 2026, needs more optimization.
16 292 0.321609404202 Henry Cohn, 2026, needs more optimization.
16 293 0.321767393150 Henry Cohn, 2026, needs more optimization.
16 294 0.321970387495 Henry Cohn, 2026, needs more optimization.
16 295 0.322672396914 Henry Cohn, 2026, needs more optimization.
16 296 0.323121569619 Henry Cohn, 2026, needs more optimization.
16 297 0.323494114051 Henry Cohn, 2026, needs more optimization.
16 298 0.323789536022 Henry Cohn, 2026, needs more optimization.
16 299 0.324817825608 Henry Cohn, 2026, needs more optimization.
16 300 0.325173897496 Henry Cohn, 2026, needs more optimization.
16 304 0.325250802196 Henry Cohn, 2026, needs more optimization.
16 305 0.325530267005 Henry Cohn, 2026, needs more optimization.
16 306 0.326028590172 Henry Cohn, 2026, needs more optimization.
16 307 0.326132064917 Henry Cohn, 2026, needs more optimization.
16 308 0.326134278070 Henry Cohn, 2026, needs more optimization.
16 310 0.327908654128 Henry Cohn, 2026, needs more optimization.
16 311 0.327940969500 Henry Cohn, 2026, needs more optimization.
16 312 0.328117052249 Henry Cohn, 2026, needs more optimization.
16 315 0.328328223943 Henry Cohn, 2026, needs more optimization.
16 316 0.328490582938 Henry Cohn, 2026, needs more optimization.
16 317 0.328537943491 Henry Cohn, 2026, needs more optimization.
16 318 0.328664788428 Henry Cohn, 2026, needs more optimization.
16 320 0.328848737906 Henry Cohn, 2026, needs more optimization.
16 321 0.329015682800 Henry Cohn, 2026, needs more optimization.
16 322 0.329064083883 Henry Cohn, 2026, needs more optimization.
16 325 0.329147111466 Henry Cohn, 2026, needs more optimization.
16 326 0.329358212193 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 0.391899630247 Henry Cohn, 2025, needs more optimization.
16 514 0.391925212957 Henry Cohn, 2025, needs more optimization.
16 515 0.392184707636 Henry Cohn, 2025, needs more optimization.
16 516 0.392591412926 Henry Cohn, 2026, needs more optimization.
16 517 0.392634267266 Henry Cohn, 2025, needs more optimization.
16 518 0.392722638362 Henry Cohn, 2025, needs more optimization.
16 519 0.392822032060 Henry Cohn, 2025, needs more optimization.
16 520 0.392903207539 Henry Cohn, 2026, needs more optimization.
16 521 0.393133536522 Henry Cohn, 2025, needs more optimization.
16 522 0.393639694745 Henry Cohn, 2025, needs more optimization.
16 523 0.393642909640 Henry Cohn, 2025, needs more optimization.
16 524 0.394010879429 Henry Cohn, 2026, needs more optimization.
16 525 0.394048136884 Henry Cohn, 2025, needs more optimization.
16 526 0.394349206845 Henry Cohn, 2025, needs more optimization.
16 527 0.394364961294 Henry Cohn, 2025, needs more optimization.
16 528 0.394447496751 Henry Cohn, 2026, needs more optimization.
16 529 0.394734533399 Henry Cohn, 2025, needs more optimization.
16 530 0.394973218996 Henry Cohn, 2025, needs more optimization.
16 531 0.395372694593 Henry Cohn, 2025, needs more optimization.
16 532 0.395560759345 Henry Cohn, 2025, needs more optimization.
16 533 0.395856738708 Henry Cohn, 2025, needs more optimization.
16 534 0.395989958872 Henry Cohn, 2025, needs more optimization.
16 535 0.396176179232 Henry Cohn, 2025, needs more optimization.
16 536 0.396325004089 Henry Cohn, 2026, needs more optimization.
16 537 0.396383621089 Henry Cohn, 2025, needs more optimization.
16 538 0.396684273329 Henry Cohn, 2025, needs more optimization.
16 539 0.396705747724 Henry Cohn, 2025, needs more optimization.
16 540 0.397312657536 Henry Cohn, 2026, needs more optimization.
16 541 0.397369983799 Henry Cohn, 2025, needs more optimization.
16 542 0.397417287827 Henry Cohn, 2025, needs more optimization.
16 543 0.397713318899 Henry Cohn, 2025, needs more optimization.
16 544 0.397775330468 Henry Cohn, 2026, needs more optimization.
16 545 0.398404617655 Henry Cohn, 2025, needs more optimization.
16 546 0.398405841058 Henry Cohn, 2025, needs more optimization.
16 547 0.398553798594 Henry Cohn, 2025, needs more optimization.
16 548 0.398573298565 Henry Cohn, 2026, needs more optimization.
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 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 0.055949336674 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 0.100854947492 Henry Cohn, 2026.
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 0.121411101888 Henry Cohn, 2026, needs more optimization.
17 66 0.124823812635 Henry Cohn, 2026, needs more optimization.
17 67 0.127103338533 Henry Cohn, 2026, needs more optimization.
17 68 0.127225907369 Henry Cohn, 2026, needs more optimization.
17 69 0.127253639348 Henry Cohn, 2026, needs more optimization.
17 71 0.127270310008 Henry Cohn, 2025.
17 74 0.127284404862 Henry Cohn, 2025.
17 76 0.127284594471 Henry Cohn, 2025.
17 77 0.127303652500 Henry Cohn, 2025, needs more optimization.
17 78 0.135257083416 Henry Cohn, 2026, needs more optimization.
17 79 0.142565741403 Henry Cohn, 2026, needs more optimization.
17 80 0.148027287454 Henry Cohn, 2026, needs more optimization.
17 81 0.152542230093 Henry Cohn, 2026, needs more optimization.
17 82 0.156555839847 Henry Cohn, 2026, needs more optimization.
17 83 0.160375445397 Henry Cohn, 2026, needs more optimization.
17 84 0.163972509407 Henry Cohn, 2026, needs more optimization.
17 85 0.164063426175 Henry Cohn, 2026, needs more optimization.
17 86 0.165316161126 Henry Cohn, 2026, needs more optimization.
17 87 0.165352418023 Henry Cohn, 2026, needs more optimization.
17 88 0.166746746533 Henry Cohn, 2026, needs more optimization.
17 89 0.166838473395 Henry Cohn, 2026, needs more optimization.
17 90 0.167172864860 Henry Cohn, 2026, needs more optimization.
17 91 0.167321328702 Henry Cohn, 2026, needs more optimization.
17 92 0.167425672414 Henry Cohn, 2025, needs more optimization.
17 93 0.167574284587 Henry Cohn, 2026, needs more optimization.
17 94 0.167903583492 Henry Cohn, 2025, needs more optimization.
17 95 0.168041892502 Henry Cohn, 2026, needs more optimization.
17 96 0.168431850103 Henry Cohn, 2026, needs more optimization.
17 97 0.168538303449 Henry Cohn, 2026, needs more optimization.
17 98 0.168637510209 Henry Cohn, 2026, needs more optimization.
17 99 0.168674435901 Henry Cohn, 2026, needs more optimization.
17 100 0.168686853696 Henry Cohn, 2026, needs more optimization.
17 101 0.168710064760 Henry Cohn, 2026, needs more optimization.
17 104 0.170753175474 Orthogonal union of 102 points in 16 dimensions and 2 points in 1 dimension.
128⁢x2−16⁢x−1
17 105 0.170753914149 Henry Cohn, 2026, needs more optimization.
17 106 0.170757033121 Henry Cohn, 2026, needs more optimization.
17 107 0.170770206969 Henry Cohn, 2026, needs more optimization.
17 108 0.176361170883 Henry Cohn, 2026, needs more optimization.
17 109 0.179937491931 Henry Cohn, 2026, needs more optimization.
17 110 0.182018690389 Henry Cohn, 2026, needs more optimization.
17 111 0.183121687779 Henry Cohn, 2026, needs more optimization.
17 112 0.184651096470 Henry Cohn, 2026, needs more optimization.
17 113 0.185921325349 Henry Cohn, 2026, needs more optimization.
17 114 0.188137979839 Henry Cohn, 2026, needs more optimization.
17 116 0.189009800326 Henry Cohn, 2026, needs more optimization.
17 117 0.189789285555 Henry Cohn, 2026, needs more optimization.
17 118 0.190942723066 Henry Cohn, 2026, needs more optimization.
17 119 0.191925830194 Henry Cohn, 2026, needs more optimization.
17 120 0.193947471168 Henry Cohn, 2026, needs more optimization.
17 121 0.195096735316 Henry Cohn, 2026, needs more optimization.
17 122 0.196705622342 Henry Cohn, 2026, needs more optimization.
17 123 0.196832058862 Henry Cohn, 2026, needs more optimization.
17 124 0.196936839321 Henry Cohn, 2026, needs more optimization.
17 125 0.197288976274 Henry Cohn, 2026, needs more optimization.
17 126 0.197443296154 Henry Cohn, 2026, needs more optimization.
17 127 0.197638499999 Henry Cohn, 2025, needs more optimization.
17 128 0.197728301827 Henry Cohn, 2026, needs more optimization.
17 129 0.198745176169 Henry Cohn, 2026, needs more optimization.
17 130 0.199288775085 Henry Cohn, 2026, needs more optimization.
17 131 0.199317350125 Henry Cohn, 2026, needs more optimization.
17 132 0.199461539788 Henry Cohn, 2026, needs more optimization.
17 133 0.199776658734 Henry Cohn, 2026, needs more optimization.
17 134 0.199868467610 Henry Cohn, 2026, needs more optimization.
17 135 0.199978702167 Henry Cohn, 2026, needs more optimization.
17 136 0.200016383992 Henry Cohn, 2026, needs more optimization.
17 137 0.200445371316 Henry Cohn, 2026, needs more optimization.
17 139 0.202672812477 Henry Cohn, 2026, needs more optimization.
17 140 0.202792043304 Henry Cohn, 2026, needs more optimization.
17 141 0.202845107989 Henry Cohn, 2026, needs more optimization.
17 142 0.202875852017 Henry Cohn, 2026, needs more optimization.
17 143 0.202875947997 Henry Cohn, 2026, needs more optimization.
17 145 0.202899802961 Henry Cohn, 2026, needs more optimization.
17 146 0.202908434583 Henry Cohn, 2026, needs more optimization.
17 161 0.202913709779 Code with 159 points in 16 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.
44⁢x2−4⁢x−1
17 162 0.202913709780 Henry Cohn, 2025.
17 163 0.202942716521 Henry Cohn, 2026, needs more optimization.
17 164 0.202944298950 Henry Cohn, 2026, needs more optimization.
17 165 0.203276668748 Henry Cohn, 2026, needs more optimization.
17 168 0.209702872201 Henry Cohn, 2026, needs more optimization.
17 170 0.214580576922 Henry Cohn, 2026, needs more optimization.
17 176 0.214580578214 Henry Cohn, 2026, needs more optimization.
17 177 0.214580578340 Henry Cohn, 2026, needs more optimization.
17 178 0.217342605330 Henry Cohn, 2025, needs more optimization.
17 179 0.223983213975 Henry Cohn, 2026, needs more optimization.
17 180 0.229988062772 Henry Cohn, 2026, needs more optimization.
17 181 0.231662506549 Henry Cohn, 2026, needs more optimization.
17 182 0.234058110172 Henry Cohn, 2026, needs more optimization.
17 183 0.235395390974 Henry Cohn, 2026, needs more optimization.
17 184 0.237588760041 Henry Cohn, 2026, needs more optimization.
17 185 0.239474773658 Henry Cohn, 2026, needs more optimization.
17 186 0.239616337843 Henry Cohn, 2026, needs more optimization.
17 187 0.240522185788 Henry Cohn, 2026, needs more optimization.
17 188 0.241475938709 Henry Cohn, 2026, needs more optimization.
17 189 0.242753063296 Henry Cohn, 2026, needs more optimization.
17 190 0.242772874011 Henry Cohn, 2026, needs more optimization.
17 191 0.242781400047 Henry Cohn, 2026, needs more optimization.
17 192 0.242809303531 Henry Cohn, 2026, needs more optimization.
17 193 0.242823179953 Henry Cohn, 2026, needs more optimization.
17 194 0.242868329961 Henry Cohn, 2026, needs more optimization.
17 195 0.242930525879 Henry Cohn, 2026, needs more optimization.
17 196 0.246198013684 Henry Cohn, 2026, needs more optimization.
17 197 0.247763202340 Henry Cohn, 2026, needs more optimization.
17 198 0.247900003708 Henry Cohn, 2026, needs more optimization.
17 199 0.247905192883 Henry Cohn, 2026, needs more optimization.
17 200 0.247938138693 Henry Cohn, 2026, needs more optimization.
17 202 0.248234570508 Henry Cohn, 2026, needs more optimization.
17 204 0.249160582025 Henry Cohn, 2026, needs more optimization.
17 206 0.249165363594 Henry Cohn, 2026, needs more optimization.
17 207 0.249178440903 Henry Cohn, 2026, needs more optimization.
17 208 0.249206231519 Henry Cohn, 2026, needs more optimization.
17 209 0.249220099502 Henry Cohn, 2026, needs more optimization.
17 211 0.249259852893 Henry Cohn, 2026, needs more optimization.
17 213 0.249739451440 Henry Cohn, 2026, needs more optimization.
17 219 0.249783030388 Henry Cohn, 2026, needs more optimization.
17 221 0.249985050505 Henry Cohn, 2026, needs more optimization.
17 292 0.25 Henry Cohn, 2026.
4⁢x−1
17 293 0.250107644001 Henry Cohn, 2026, needs more optimization.
17 312 0.261203876774 Henry Cohn, 2026, needs more optimization.
17 320 0.261203876882 Henry Cohn, 2026, needs more optimization.
17 321 0.284194766727 Henry Cohn, 2026, needs more optimization.
17 322 0.296721877706 Henry Cohn, 2026, needs more optimization.
17 323 0.296815508864 Henry Cohn, 2026, needs more optimization.
17 324 0.296833913622 Henry Cohn, 2025, needs more optimization.
17 326 0.300379517850 Henry Cohn, 2026, needs more optimization.
17 328 0.304222259662 Henry Cohn, 2026, needs more optimization.
17 336 0.304638480718 Henry Cohn, 2026, needs more optimization.
17 337 0.304706956370 Henry Cohn, 2026, needs more optimization.
17 338 0.304706956576 Henry Cohn, 2026, needs more optimization.
17 339 0.304749836304 Henry Cohn, 2026, needs more optimization.
17 340 0.312898776278 Henry Cohn, 2026, needs more optimization.
17 342 0.313400491819 Henry Cohn, 2025, needs more optimization.
17 343 0.314841630605 Henry Cohn, 2025, needs more optimization.
17 344 0.314899169141 Henry Cohn, 2026, needs more optimization.
17 345 0.316057223042 Henry Cohn, 2025, needs more optimization.
17 346 0.316118437255 Henry Cohn, 2025, needs more optimization.
17 347 0.317382420133 Henry Cohn, 2025, needs more optimization.
17 348 0.317427213974 Henry Cohn, 2025, needs more optimization.
17 349 0.318631480893 Henry Cohn, 2025, needs more optimization.
17 350 0.318692686611 Henry Cohn, 2025, needs more optimization.
17 351 0.318842570612 Henry Cohn, 2025, needs more optimization.
17 352 0.320276065763 Henry Cohn, 2026, needs more optimization.
17 353 0.320358004020 Henry Cohn, 2025, needs more optimization.
17 354 0.322921276049 Henry Cohn, 2025, needs more optimization.
17 355 0.323240622037 Henry Cohn, 2025, needs more optimization.
17 356 0.324603914100 Henry Cohn, 2025, needs more optimization.
17 357 0.324674347760 Henry Cohn, 2025, needs more optimization.
17 358 0.324677522206 Henry Cohn, 2025, needs more optimization.
17 359 0.325570396391 Henry Cohn, 2025, needs more optimization.
17 360 0.325675052905 Henry Cohn, 2026, needs more optimization.
17 361 0.326299331409 Henry Cohn, 2025, needs more optimization.
17 362 0.326419782843 Henry Cohn, 2025, needs more optimization.
17 363 0.327636641295 Henry Cohn, 2025, needs more optimization.
17 365 0.327661166414 Henry Cohn, 2025, needs more optimization.
17 366 0.328605574205 Henry Cohn, 2025, needs more optimization.
17 367 0.329725269071 Henry Cohn, 2025, needs more optimization.
17 368 0.330432271058 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. T. Zhaowei, 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 0.384386751984 Henry Cohn, 2025, needs more optimization.
17 580 0.384489580965 Henry Cohn, 2026, needs more optimization.
17 581 0.384499164779 Henry Cohn, 2025, needs more optimization.
17 582 0.384685553512 Henry Cohn, 2025, needs more optimization.
17 583 0.384901400690 Henry Cohn, 2025, needs more optimization.
17 584 0.384949959725 Henry Cohn, 2026, needs more optimization.
17 585 0.384966903624 Henry Cohn, 2025, needs more optimization.
17 586 0.385539098190 Henry Cohn, 2025, needs more optimization.
17 587 0.385541637903 Henry Cohn, 2025, needs more optimization.
17 588 0.385564523673 Henry Cohn, 2026, needs more optimization.
17 589 0.385951190150 Henry Cohn, 2025, needs more optimization.
17 590 0.386012719959 Henry Cohn, 2025, needs more optimization.
17 591 0.386020831990 Henry Cohn, 2025, needs more optimization.
17 592 0.386570929069 Henry Cohn, 2026, needs more optimization.
17 593 0.386655880734 Henry Cohn, 2025, needs more optimization.
17 594 0.386664779495 Henry Cohn, 2025, needs more optimization.
17 595 0.386764215489 Henry Cohn, 2025, needs more optimization.
17 596 0.387207370810 Henry Cohn, 2026, needs more optimization.
17 597 0.387277927498 Henry Cohn, 2025, needs more optimization.
17 598 0.387348389025 Henry Cohn, 2025, needs more optimization.
17 599 0.387399697539 Henry Cohn, 2025, needs more optimization.
17 600 0.387673206849 Henry Cohn, 2026, needs more optimization.
17 601 0.387717207601 Henry Cohn, 2025, needs more optimization.
17 602 0.387903020169 Henry Cohn, 2025, needs more optimization.
17 603 0.388274213435 Henry Cohn, 2025, needs more optimization.
17 604 0.388275605376 Henry Cohn, 2026, needs more optimization.
17 605 0.388352213522 Henry Cohn, 2025, needs more optimization.
17 606 0.388634596757 Henry Cohn, 2025, needs more optimization.
17 607 0.388865235140 Henry Cohn, 2025, needs more optimization.
17 608 0.388896952533 Henry Cohn, 2026, needs more optimization.
17 609 0.389131916372 Henry Cohn, 2025, needs more optimization.
17 610 0.389148122644 Henry Cohn, 2025, needs more optimization.
17 611 0.389517822003 Henry Cohn, 2025, needs more optimization.
17 612 0.389542958746 Henry Cohn, 2026, needs more optimization.
17 613 0.389589334878 Henry Cohn, 2025, needs more optimization.
17 614 0.389853435854 Henry Cohn, 2025, needs more optimization.
17 615 0.389911542351 Henry Cohn, 2025, needs more optimization.
17 616 0.390341304547 Henry Cohn, 2026, needs more optimization.
17 617 0.390365724717 Henry Cohn, 2025, needs more optimization.
17 619 0.390490728552 Henry Cohn, 2025, needs more optimization.
17 620 0.390690214187 Henry Cohn, 2026, needs more optimization.
17 621 0.390847575705 Henry Cohn, 2025, needs more optimization.
17 622 0.390850359831 Henry Cohn, 2025, needs more optimization.
17 624 0.391228368680 Henry Cohn, 2026, needs more optimization.
17 625 0.391368332007 Henry Cohn, 2025, needs more optimization.
17 626 0.391433589471 Henry Cohn, 2025, needs more optimization.
17 628 0.391878103269 Henry Cohn, 2025, needs more optimization.
17 629 0.391929328039 Henry Cohn, 2025, needs more optimization.
17 630 0.392005373070 Henry Cohn, 2025, needs more optimization.
17 631 0.392605304895 Henry Cohn, 2025, needs more optimization.
17 632 0.392625871423 Henry Cohn, 2026, needs more optimization.
17 633 0.392644325274 Henry Cohn, 2025, needs more optimization.
17 634 0.392992152076 Henry Cohn, 2025, needs more optimization.
17 635 0.393018103881 Henry Cohn, 2025, needs more optimization.
17 636 0.393036322130 Henry Cohn, 2026, needs more optimization.
17 637 0.393225216195 Henry Cohn, 2025, needs more optimization.
17 638 0.393595469493 Henry Cohn, 2025, needs more optimization.
17 639 0.393615961966 Henry Cohn, 2025, needs more optimization.
17 640 0.393850893355 Henry Cohn, 2026, needs more optimization.
17 641 0.393861933375 Henry Cohn, 2025, needs more optimization.
17 642 0.394141354266 Henry Cohn, 2025, needs more optimization.
17 643 0.394162888867 Henry Cohn, 2025, needs more optimization.
17 644 0.394217615501 Henry Cohn, 2026, needs more optimization.
17 645 0.394374143224 Henry Cohn, 2025, needs more optimization.
17 646 0.394733161798 Henry Cohn, 2025, needs more optimization.
17 647 0.394865721173 Henry Cohn, 2025, needs more optimization.
17 648 0.394885748828 Henry Cohn, 2026, needs more optimization.
17 649 0.395122837140 Henry Cohn, 2025, needs more optimization.
17 650 0.395183309253 Henry Cohn, 2025, needs more optimization.
17 651 0.395207336902 Henry Cohn, 2025, needs more optimization.
17 652 0.395686916140 Henry Cohn, 2026, needs more optimization.
17 653 0.395761077950 Henry Cohn, 2025, needs more optimization.
17 654 0.395813065070 Henry Cohn, 2025, needs more optimization.
17 655 0.395835524001 Henry Cohn, 2025, needs more optimization.
17 656 0.396208971634 Henry Cohn, 2026, needs more optimization.
17 657 0.396236676884 Henry Cohn, 2025, needs more optimization.
17 658 0.396244518720 Henry Cohn, 2025, needs more optimization.
17 659 0.396393049348 Henry Cohn, 2025, needs more optimization.
17 660 0.396650867275 Henry Cohn, 2026, needs more optimization.
17 661 0.396741644621 Henry Cohn, 2025, needs more optimization.
17 662 0.396996114325 Henry Cohn, 2025, needs more optimization.
17 663 0.397022110102 Henry Cohn, 2025, needs more optimization.
17 664 0.397062837170 Henry Cohn, 2026, needs more optimization.
17 665 0.397074844999 Henry Cohn, 2025, needs more optimization.
17 666 0.397621121011 Henry Cohn, 2025, needs more optimization.
17 667 0.397922919863 Henry Cohn, 2025, needs more optimization.
17 668 0.397951526077 Henry Cohn, 2026, needs more optimization.
17 669 0.398232768001 Henry Cohn, 2025, needs more optimization.
17 670 0.398269006061 Henry Cohn, 2025, needs more optimization.
17 672 0.398532721303 Henry Cohn, 2026, needs more optimization.
17 673 0.398547114794 Henry Cohn, 2025, needs more optimization.
17 674 0.398836644526 Henry Cohn, 2025, needs more optimization.
17 771 0.4 Orthogonal union of 769 points in 16 dimensions and 2 points in 1 dimension.
5⁢x−2
17 772 0.400015816743 Henry Cohn, 2026, needs more optimization.
17 773 0.400022561896 Henry Cohn, 2025, needs more optimization.
17 774 0.411082037303 Henry Cohn, 2025, needs more optimization.
17 775 0.411084956436 Henry Cohn, 2025, needs more optimization.
17 776 0.411377744053 Henry Cohn, 2026, needs more optimization.
17 777 0.411428319972 Henry Cohn, 2025, needs more optimization.
17 778 0.411465759477 Henry Cohn, 2025, needs more optimization.
17 779 0.411774744978 Henry Cohn, 2025, needs more optimization.
17 780 0.411785311602 Henry Cohn, 2026, needs more optimization.
17 781 0.411850362952 Henry Cohn, 2025, needs more optimization.
17 782 0.412065255713 Henry Cohn, 2025, needs more optimization.
17 783 0.412075730897 Henry Cohn, 2025, needs more optimization.
17 784 0.412301978580 Henry Cohn, 2026, needs more optimization.
17 785 0.412313644287 Henry Cohn, 2025, needs more optimization.
17 786 0.412405029289 Henry Cohn, 2025, needs more optimization.
17 787 0.412785425115 Henry Cohn, 2025, needs more optimization.
17 788 0.412790458138 Henry Cohn, 2026, needs more optimization.
17 789 0.412832246084 Henry Cohn, 2025, needs more optimization.
17 790 0.413139899303 Henry Cohn, 2025, needs more optimization.
17 791 0.413161576394 Henry Cohn, 2025, needs more optimization.
17 792 0.413166606292 Henry Cohn, 2026, needs more optimization.
17 793 0.413204447952 Henry Cohn, 2025, needs more optimization.
17 794 0.413528774002 Henry Cohn, 2025, needs more optimization.
17 795 0.413574430036 Henry Cohn, 2025, needs more optimization.
17 796 0.413607535542 Henry Cohn, 2026, needs more optimization.
17 797 0.413669222131 Henry Cohn, 2025, needs more optimization.
17 798 0.413793012924 Henry Cohn, 2025, needs more optimization.
17 799 0.414137970934 Henry Cohn, 2025, needs more optimization.
17 800 0.414143155809 Henry Cohn, 2026, needs more optimization.
17 801 0.414152368895 Henry Cohn, 2025, needs more optimization.
17 802 0.414200689212 Henry Cohn, 2025, needs more optimization.
17 803 0.414464466595 Henry Cohn, 2025, needs more optimization.
17 804 0.414473289276 Henry Cohn, 2026, needs more optimization.
17 805 0.414492954242 Henry Cohn, 2025, needs more optimization.
17 806 0.414845024033 Henry Cohn, 2025, needs more optimization.
17 807 0.414851426398 Henry Cohn, 2025, needs more optimization.
17 808 0.414867129605 Henry Cohn, 2026, needs more optimization.
17 809 0.414992441054 Henry Cohn, 2025, needs more optimization.
17 810 0.415036760899 Henry Cohn, 2025, needs more optimization.
17 811 0.415046825429 Henry Cohn, 2025, needs more optimization.
17 812 0.415442015846 Henry Cohn, 2026, needs more optimization.
17 813 0.415465093504 Henry Cohn, 2025, needs more optimization.
17 814 0.415495419650 Henry Cohn, 2025, needs more optimization.
17 815 0.415875048118 Henry Cohn, 2025, needs more optimization.
17 816 0.415887573019 Henry Cohn, 2026, needs more optimization.
17 817 0.415907955023 Henry Cohn, 2025, needs more optimization.
17 818 0.416099229085 Henry Cohn, 2025, needs more optimization.
17 819 0.416130794227 Henry Cohn, 2025, needs more optimization.
17 820 0.416336035615 Henry Cohn, 2026, needs more optimization.
17 821 0.416353133665 Henry Cohn, 2025, needs more optimization.
17 822 0.416637782886 Henry Cohn, 2025, needs more optimization.
17 824 0.416650604132 Henry Cohn, 2026, needs more optimization.
17 825 0.416671727325 Henry Cohn, 2025, needs more optimization.
17 826 0.416681014990 Henry Cohn, 2025, needs more optimization.
17 828 0.416907328036 Henry Cohn, 2026, needs more optimization.
17 829 0.417300605071 Henry Cohn, 2025, needs more optimization.
17 830 0.417345311198 Henry Cohn, 2025, needs more optimization.
17 831 0.417405991469 Henry Cohn, 2025, needs more optimization.
17 832 0.417550908223 Henry Cohn, 2026, needs more optimization.
17 833 0.417560049988 Henry Cohn, 2025, needs more optimization.
17 834 0.417569007479 Henry Cohn, 2025, needs more optimization.
17 835 0.417620249090 Henry Cohn, 2025, needs more optimization.
17 836 0.418054361132 Henry Cohn, 2026, needs more optimization.
17 837 0.418079431589 Henry Cohn, 2025, needs more optimization.
17 838 0.418095794158 Henry Cohn, 2025, needs more optimization.
17 839 0.418322507555 Henry Cohn, 2025, needs more optimization.
17 840 0.418326928163 Henry Cohn, 2026, needs more optimization.
17 841 0.418389792343 Henry Cohn, 2025, needs more optimization.
17 842 0.418642942254 Henry Cohn, 2025, needs more optimization.
17 843 0.418647876178 Henry Cohn, 2025, needs more optimization.
17 844 0.418653519023 Henry Cohn, 2026, needs more optimization.
17 845 0.418957287057 Henry Cohn, 2025, needs more optimization.
17 846 0.418961599044 Henry Cohn, 2025, needs more optimization.
17 847 0.419307760198 Henry Cohn, 2025, needs more optimization.
17 848 0.419467135138 Henry Cohn, 2026, needs more optimization.
17 849 0.419485178712 Henry Cohn, 2025, needs more optimization.
17 850 0.419491394476 Henry Cohn, 2025, needs more optimization.
17 851 0.419534995750 Henry Cohn, 2025, needs more optimization.
17 852 0.419783382270 Henry Cohn, 2026, needs more optimization.
17 853 0.419794119142 Henry Cohn, 2025, needs more optimization.
17 854 0.420104707196 Henry Cohn, 2025, needs more optimization.
17 855 0.420173932125 Henry Cohn, 2025, needs more optimization.
17 856 0.420198134879 Henry Cohn, 2026, needs more optimization.
17 857 0.420215461401 Henry Cohn, 2025, needs more optimization.
17 858 0.420223660267 Henry Cohn, 2025, needs more optimization.
17 859 0.420414663543 Henry Cohn, 2025, needs more optimization.
17 860 0.420435622319 Henry Cohn, 2026, needs more optimization.
17 861 0.420694111061 Henry Cohn, 2025, needs more optimization.
17 862 0.420724988241 Henry Cohn, 2025, needs more optimization.
17 863 0.420797260097 Henry Cohn, 2025, needs more optimization.
17 864 0.420800233866 Henry Cohn, 2026, needs more optimization.
17 865 0.420826129155 Henry Cohn, 2025, needs more optimization.
17 866 0.420899129272 Henry Cohn, 2025, needs more optimization.
17 867 0.421194066406 Henry Cohn, 2025, needs more optimization.
17 868 0.421196600618 Henry Cohn, 2026, needs more optimization.
17 869 0.421226830560 Henry Cohn, 2025, needs more optimization.
17 870 0.421316051486 Henry Cohn, 2025, needs more optimization.
17 871 0.421706574960 Henry Cohn, 2025, needs more optimization.
17 872 0.421730751141 Henry Cohn, 2026, needs more optimization.
17 873 0.421877057938 Henry Cohn, 2025, needs more optimization.
17 874 0.421914681374 Henry Cohn, 2025, needs more optimization.
17 875 0.422078665519 Henry Cohn, 2025, needs more optimization.
17 876 0.422266429629 Henry Cohn, 2026, needs more optimization.
17 877 0.422277481212 Henry Cohn, 2025, needs more optimization.
17 878 0.422283773870 Henry Cohn, 2025, needs more optimization.
17 879 0.422661431809 Henry Cohn, 2025, needs more optimization.
17 880 0.422670773039 Henry Cohn, 2026, needs more optimization.
17 881 0.422672563066 Henry Cohn, 2025, needs more optimization.
17 882 0.422678059336 Henry Cohn, 2025, needs more optimization.
17 883 0.422712133944 Henry Cohn, 2025, needs more optimization.
17 884 0.422816554663 Henry Cohn, 2026, needs more optimization.
17 885 0.422882244676 Henry Cohn, 2025, needs more optimization.
17 886 0.423216655541 Henry Cohn, 2025, needs more optimization.
17 887 0.423218411168 Henry Cohn, 2025, needs more optimization.
17 888 0.423271999218 Henry Cohn, 2026, needs more optimization.
17 889 0.423303631557 Henry Cohn, 2025, needs more optimization.
17 890 0.423312536334 Henry Cohn, 2025, needs more optimization.
17 891 0.423466479008 Henry Cohn, 2025, needs more optimization.
17 892 0.423679842703 Henry Cohn, 2026, needs more optimization.
17 893 0.423715198583 Henry Cohn, 2025, needs more optimization.
17 894 0.423753656024 Henry Cohn, 2025, needs more optimization.
17 895 0.423980219720 Henry Cohn, 2025, needs more optimization.
17 896 0.423981096147 Henry Cohn, 2026, needs more optimization.
17 897 0.423997831890 Henry Cohn, 2025, needs more optimization.
17 898 0.424172832392 Henry Cohn, 2025, needs more optimization.
17 899 0.424177966744 Henry Cohn, 2025, needs more optimization.
17 900 0.424179997347 Henry Cohn, 2026, needs more optimization.
17 901 0.424483312926 Henry Cohn, 2025, needs more optimization.
17 902 0.424498392033 Henry Cohn, 2025, needs more optimization.
17 903 0.424624928984 Henry Cohn, 2025, needs more optimization.
17 904 0.424867718417 Henry Cohn, 2026, needs more optimization.
17 905 0.424884184079 Henry Cohn, 2025, needs more optimization.
17 906 0.424940831867 Henry Cohn, 2025, needs more optimization.
17 907 0.425084985086 Henry Cohn, 2025, needs more optimization.
17 908 0.425218804645 Henry Cohn, 2026, needs more optimization.
17 909 0.425236552243 Henry Cohn, 2025, needs more optimization.
17 910 0.425250276918 Henry Cohn, 2025, needs more optimization.
17 911 0.425562235092 Henry Cohn, 2025, needs more optimization.
17 912 0.425567139226 Henry Cohn, 2026, needs more optimization.
17 913 0.425618586570 Henry Cohn, 2025, needs more optimization.
17 914 0.425942743101 Henry Cohn, 2025, needs more optimization.
17 916 0.425974475974 Henry Cohn, 2026, needs more optimization.
17 917 0.426243670802 Henry Cohn, 2025, needs more optimization.
17 918 0.426257386877 Henry Cohn, 2025, needs more optimization.
17 919 0.426325470151 Henry Cohn, 2025, needs more optimization.
17 920 0.426533376500 Henry Cohn, 2026, needs more optimization.
17 921 0.426541193565 Henry Cohn, 2025, needs more optimization.
17 922 0.426721743357 Henry Cohn, 2025, needs more optimization.
17 924 0.426827699525 Henry Cohn, 2026, needs more optimization.
17 925 0.426874837261 Henry Cohn, 2025, needs more optimization.
17 926 0.427237733863 Henry Cohn, 2025, needs more optimization.
17 927 0.427278425952 Henry Cohn, 2025, needs more optimization.
17 928 0.427288884466 Henry Cohn, 2026, needs more optimization.
17 929 0.427302674882 Henry Cohn, 2025, needs more optimization.
17 1024 0.428571428572 Subcode of a code of size 1570 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
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.
18 48 0.074706792917 Henry Cohn, 2024.
18 50 0.078219048073 Henry Cohn, 2025.
368⁢x2−16⁢x−1
18 51 0.084340252912 Henry Cohn, 2025.
18 52 0.084342002724 Henry Cohn, 2025.
18 53 0.084342450321 Henry Cohn, 2025.
18 54 0.084342552633 Henry Cohn, 2025.
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.
18 69 0.101456854890 Henry Cohn, 2024.
176⁢x2−8⁢x−1
18 71 0.107360417204 Henry Cohn, 2026, needs more optimization.
18 72 0.109540130291 Henry Cohn, 2026, needs more optimization.
18 73 0.117134464855 Henry Cohn, 2026, needs more optimization.
18 74 0.121825115439 Henry Cohn, 2026, needs more optimization.
18 76 0.122045983421 Henry Cohn, 2026, needs more optimization.
18 77 0.123493846412 Henry Cohn, 2026, needs more optimization.
18 78 0.125855240709 Henry Cohn, 2026, needs more optimization.
18 80 0.126224060075 Henry Cohn, 2026, needs more optimization.
18 81 0.126904281674 Henry Cohn, 2026, needs more optimization.
18 82 0.127626718472 Henry Cohn, 2026, needs more optimization.
18 83 0.129098845419 Henry Cohn, 2026, needs more optimization.
18 84 0.130581918400 Henry Cohn, 2026, needs more optimization.
18 85 0.132295645174 Henry Cohn, 2026, needs more optimization.
18 86 0.132700084117 Henry Cohn, 2026, needs more optimization.
18 87 0.133675592670 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 0.155249851797 Henry Cohn, 2026, needs more optimization.
18 99 0.165211710795 Henry Cohn, 2026, needs more optimization.
18 100 0.167512412028 Henry Cohn, 2026, needs more optimization.
18 101 0.167586738193 Henry Cohn, 2026, needs more optimization.
18 102 0.168091778641 Henry Cohn, 2026, needs more optimization.
18 103 0.168582537376 Henry Cohn, 2026, needs more optimization.
18 104 0.169042218512 Henry Cohn, 2026, needs more optimization.
18 105 0.169059582863 Henry Cohn, 2026, needs more optimization.
18 106 0.169231003773 Henry Cohn, 2026, needs more optimization.
18 107 0.169525752017 Henry Cohn, 2026, needs more optimization.
18 108 0.170156781318 Henry Cohn, 2026, needs more optimization.
18 109 0.170449701157 Henry Cohn, 2026, needs more optimization.
18 110 0.170632593953 Henry Cohn, 2026, needs more optimization.
18 111 0.170820617686 Henry Cohn, 2026, needs more optimization.
18 112 0.171627564390 Henry Cohn, 2026, needs more optimization.
18 113 0.172991187581 Henry Cohn, 2026, needs more optimization.
18 114 0.175540853941 Henry Cohn, 2026, needs more optimization.
18 115 0.177868596063 Henry Cohn, 2026, needs more optimization.
18 116 0.179458482342 Henry Cohn, 2026, needs more optimization.
18 117 0.181388785750 Henry Cohn, 2026, needs more optimization.
18 118 0.183022569146 Henry Cohn, 2026, needs more optimization.
18 119 0.185088015247 Henry Cohn, 2026, needs more optimization.
18 120 0.185217299571 Henry Cohn, 2026, needs more optimization.
18 121 0.186200976847 Henry Cohn, 2026, needs more optimization.
18 122 0.187488969208 Henry Cohn, 2026, needs more optimization.
18 130 0.189193290536 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 0.193070622518 Henry Cohn, 2026, needs more optimization.
18 134 0.193721012479 Henry Cohn, 2026, needs more optimization.
18 135 0.194298502179 Henry Cohn, 2026, needs more optimization.
18 136 0.194623027040 Henry Cohn, 2026, needs more optimization.
18 137 0.194954694296 Henry Cohn, 2026, needs more optimization.
18 138 0.195230307880 Henry Cohn, 2026, needs more optimization.
18 140 0.195281232521 Henry Cohn, 2026, needs more optimization.
18 144 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
18 146 0.200557378588 Henry Cohn, 2026, needs more optimization.
18 149 0.200752258293 Henry Cohn, 2026, needs more optimization.
18 150 0.200758654098 Henry Cohn, 2026, needs more optimization.
18 151 0.200897711229 Henry Cohn, 2026, needs more optimization.
18 152 0.200988279873 Henry Cohn, 2026, needs more optimization.
18 153 0.201281668170 Henry Cohn, 2026, needs more optimization.
18 155 0.201456188190 Henry Cohn, 2026, needs more optimization.
18 156 0.201525857472 Henry Cohn, 2026, needs more optimization.
18 159 0.201643956418 Henry Cohn, 2026, needs more optimization.
18 160 0.201738601286 Henry Cohn, 2026, needs more optimization.
18 161 0.202315871229 Henry Cohn, 2026, needs more optimization.
18 162 0.202388101186 Henry Cohn, 2026, needs more optimization.
18 163 0.202407086318 Henry Cohn, 2026, needs more optimization.
18 164 0.202802024093 Henry Cohn, 2026, needs more optimization.
18 165 0.202887592111 Henry Cohn, 2026, needs more optimization.
18 166 0.202909246056 Henry Cohn, 2026, needs more optimization.
18 167 0.202919368239 Henry Cohn, 2026, needs more optimization.
18 168 0.202922327663 Henry Cohn, 2026, needs more optimization.
18 170 0.202929236638 Henry Cohn, 2026, needs more optimization.
18 171 0.203189812067 Henry Cohn, 2026, needs more optimization.
18 172 0.205664632718 Henry Cohn, 2026, needs more optimization.
18 173 0.208783630556 Henry Cohn, 2026, needs more optimization.
18 174 0.211500751430 Henry Cohn, 2026, needs more optimization.
18 178 0.214580578214 Orthogonal union of 176 points in 17 dimensions and 2 points in 1 dimension.
18 179 0.214580578340 Orthogonal union of 177 points in 17 dimensions and 2 points in 1 dimension.
18 181 0.214617982337 Henry Cohn, 2026, needs more optimization.
18 205 0.224489795919 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.
49⁢x−11
18 206 0.230077130359 Henry Cohn, 2026, needs more optimization.
18 207 0.230089311201 Henry Cohn, 2026, needs more optimization.
18 208 0.232334349852 Henry Cohn, 2026, needs more optimization.
18 209 0.232361428065 Henry Cohn, 2026, needs more optimization.
18 210 0.233280166296 Henry Cohn, 2026, needs more optimization.
18 211 0.233292284982 Henry Cohn, 2026, needs more optimization.
18 212 0.233345215476 Henry Cohn, 2026, needs more optimization.
18 213 0.235310561702 Henry Cohn, 2026, needs more optimization.
18 214 0.235632503571 Henry Cohn, 2026, needs more optimization.
18 215 0.239681444021 Henry Cohn, 2026, needs more optimization.
18 216 0.239731578563 Henry Cohn, 2026, needs more optimization.
18 217 0.240265983562 Henry Cohn, 2026, needs more optimization.
18 218 0.240383112398 Henry Cohn, 2026, needs more optimization.
18 219 0.241089233585 Henry Cohn, 2026, needs more optimization.
18 220 0.241117521283 Henry Cohn, 2026, needs more optimization.
18 221 0.241242932871 Henry Cohn, 2026, needs more optimization.
18 222 0.241411122360 Henry Cohn, 2026, needs more optimization.
18 223 0.241509392725 Henry Cohn, 2026, needs more optimization.
18 224 0.242447660058 Henry Cohn, 2026, needs more optimization.
18 225 0.242796211427 Henry Cohn, 2026, needs more optimization.
18 226 0.243104238993 Henry Cohn, 2026, needs more optimization.
18 227 0.243307521849 Henry Cohn, 2026, needs more optimization.
18 228 0.243310871003 Henry Cohn, 2026, needs more optimization.
18 229 0.243466866615 Henry Cohn, 2026, needs more optimization.
18 230 0.244122957874 Henry Cohn, 2026, needs more optimization.
18 231 0.244159247927 Henry Cohn, 2026, needs more optimization.
18 232 0.244197973463 Henry Cohn, 2026, needs more optimization.
18 256 0.246437044504 Henry Cohn, 2026, needs more optimization.
18 257 0.246787981720 Henry Cohn, 2025, needs more optimization.
18 260 0.247104074684 Henry Cohn, 2025, needs more optimization.
18 261 0.247126454539 Henry Cohn, 2026, needs more optimization.
18 262 0.247159741095 Henry Cohn, 2025, needs more optimization.
18 263 0.247191335203 Henry Cohn, 2025, needs more optimization.
18 264 0.247212300667 Henry Cohn, 2025, needs more optimization.
18 265 0.247289888703 Henry Cohn, 2025, needs more optimization.
18 266 0.247360813446 Henry Cohn, 2025, needs more optimization.
18 267 0.247394795521 Henry Cohn, 2025, needs more optimization.
18 268 0.247489610910 Henry Cohn, 2025, needs more optimization.
18 269 0.247492387801 Henry Cohn, 2025, needs more optimization.
18 270 0.247510978203 Henry Cohn, 2025, needs more optimization.
18 271 0.247554974434 Henry Cohn, 2026, needs more optimization.
18 272 0.247588413101 Henry Cohn, 2025, needs more optimization.
18 273 0.247601988251 Henry Cohn, 2025, needs more optimization.
18 274 0.247610943409 Henry Cohn, 2025, needs more optimization.
18 276 0.247661604596 Henry Cohn, 2025, needs more optimization.
18 277 0.247714163483 Henry Cohn, 2025, needs more optimization.
18 278 0.247740576377 Henry Cohn, 2025, needs more optimization.
18 280 0.247754588482 Henry Cohn, 2025, needs more optimization.
18 282 0.247830057904 Henry Cohn, 2026, needs more optimization.
18 286 0.247864612414 Henry Cohn, 2026, needs more optimization.
18 287 0.248707750538 Henry Cohn, 2026, needs more optimization.
18 288 0.248892043394 Henry Cohn, 2026, needs more optimization.
18 289 0.248943124800 Henry Cohn, 2025, needs more optimization.
18 290 0.249341399134 Henry Cohn, 2026, needs more optimization.
18 291 0.249410609573 Henry Cohn, 2026, needs more optimization.
18 292 0.249507024422 Henry Cohn, 2025, needs more optimization.
18 296 0.25 Henry Cohn, 2026.
4⁢x−1
18 300 0.250104964694 Henry Cohn, 2026, needs more optimization.
18 301 0.250104964716 Henry Cohn, 2025, needs more optimization.
18 302 0.250123060329 Henry Cohn, 2025, needs more optimization.
18 303 0.251311867492 Henry Cohn, 2026, needs more optimization.
18 304 0.259265953487 Henry Cohn, 2026, needs more optimization.
18 305 0.259369064427 Henry Cohn, 2025, needs more optimization.
18 307 0.259439567247 Henry Cohn, 2025, needs more optimization.
18 312 0.260092303960 Henry Cohn, 2026, needs more optimization.
18 316 0.260233277600 Henry Cohn, 2025, needs more optimization.
18 318 0.260464842805 Henry Cohn, 2025, needs more optimization.
18 319 0.260531286407 Henry Cohn, 2025, needs more optimization.
18 320 0.261111039640 Henry Cohn, 2026, needs more optimization.
18 322 0.261203876882 Orthogonal union of 320 points in 17 dimensions and 2 points in 1 dimension.
18 323 0.261552196966 Henry Cohn, 2026, needs more optimization.
18 364 0.296296296297 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
27⁢x−8
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 0.298586129437 Henry Cohn, 2025, needs more optimization.
18 482 0.300581695675 Henry Cohn, 2025, needs more optimization.
18 483 0.301586559090 Henry Cohn, 2025, 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
18 867 0.357142857143 Henry Cohn, 2025, by modifying a construction from C. Ma, T. T. Zhaowei, 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 0.386504377977 Henry Cohn, 2026, needs more optimization.
18 876 0.386721050350 Henry Cohn, 2026, needs more optimization.
18 884 0.386923690267 Henry Cohn, 2026, needs more optimization.
18 892 0.387349972483 Henry Cohn, 2026, needs more optimization.
18 900 0.387819990221 Henry Cohn, 2026, needs more optimization.
18 908 0.388358564157 Henry Cohn, 2026, needs more optimization.
18 916 0.388712514668 Henry Cohn, 2026, needs more optimization.
18 918 0.389421806449 Henry Cohn, 2026, needs more optimization.
18 924 0.389421806821 Henry Cohn, 2026, needs more optimization.
18 932 0.389824088284 Henry Cohn, 2026, needs more optimization.
18 940 0.390329807464 Henry Cohn, 2026, needs more optimization.
18 948 0.390832601346 Henry Cohn, 2026, needs more optimization.
18 956 0.391377812500 Henry Cohn, 2026, needs more optimization.
18 964 0.391962673688 Henry Cohn, 2026, needs more optimization.
18 972 0.392525281181 Henry Cohn, 2026, needs more optimization.
18 980 0.393240630442 Henry Cohn, 2026, needs more optimization.
18 984 0.393867167590 Henry Cohn, 2026, needs more optimization.
18 988 0.393961422830 Henry Cohn, 2026, needs more optimization.
18 992 0.394831928428 Henry Cohn, 2026, needs more optimization.
18 996 0.395047828358 Henry Cohn, 2026, needs more optimization.
18 997 0.395938146558 Henry Cohn, 2026, needs more optimization.
18 1024 0.4 Henry Cohn, 2025, subcode of a code of size 1156 obtained by modifying a construction from C. Ma, T. T. Zhaowei, 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
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 0.077608632538 Henry Cohn, 2026, needs more optimization.
19 53 0.080493593475 Henry Cohn, 2026, needs more optimization.
19 54 0.081692292171 Henry Cohn, 2025.
19 55 0.082178889828 Henry Cohn, 2025.
19 56 0.083233613341 Henry Cohn, 2026, needs more optimization.
19 57 0.084818962260 Henry Cohn, 2025.
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 0.101319957448 Henry Cohn, 2026, needs more optimization.
19 70 0.101392647883 Henry Cohn, 2025, needs more optimization.
19 71 0.101456853396 Henry Cohn, 2025, needs more optimization.
19 72 0.102183670655 Henry Cohn, 2026, needs more optimization.
19 73 0.102201317334 Henry Cohn, 2026.
311⁢x2−22⁢x−1
19 74 0.104261701003 Henry Cohn, 2026, needs more optimization.
19 75 0.107816370386 Henry Cohn, 2026, needs more optimization.
19 76 0.111567748620 Henry Cohn, 2026, needs more optimization.
19 77 0.112842766161 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 0.132272376899 Henry Cohn, 2026, needs more optimization.
19 92 0.134883034236 Henry Cohn, 2026, needs more optimization.
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 0.153836524069 Henry Cohn, 2026, needs more optimization.
19 105 0.155558023696 Henry Cohn, 2026, needs more optimization.
19 106 0.155560107315 Henry Cohn, 2026, needs more optimization.
19 107 0.155579742659 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 0.168802199664 Henry Cohn, 2026, needs more optimization.
19 134 0.174620105379 Henry Cohn, 2026, needs more optimization.
19 136 0.177874973980 Henry Cohn, 2026, needs more optimization.
19 137 0.177881904481 Henry Cohn, 2026, needs more optimization.
19 138 0.177905918343 Henry Cohn, 2026, needs more optimization.
19 139 0.178042822743 Henry Cohn, 2026, needs more optimization.
19 140 0.178189492333 Henry Cohn, 2026, needs more optimization.
19 141 0.178377871257 Henry Cohn, 2026, needs more optimization.
19 142 0.178808771337 Henry Cohn, 2026, needs more optimization.
19 143 0.179258507628 Henry Cohn, 2026, needs more optimization.
19 144 0.179754356322 Henry Cohn, 2026, needs more optimization.
19 145 0.180769687081 Henry Cohn, 2026, needs more optimization.
19 146 0.181640065382 Henry Cohn, 2026, needs more optimization.
19 147 0.182658088986 Henry Cohn, 2026, needs more optimization.
19 148 0.183369175231 Henry Cohn, 2026, needs more optimization.
19 149 0.183926724816 Henry Cohn, 2026, needs more optimization.
19 150 0.184646543856 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
19 192 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 0.203357317364 Henry Cohn, 2026, needs more optimization.
19 194 0.205922584173 Henry Cohn, 2026, needs more optimization.
19 195 0.207129181968 Henry Cohn, 2026, needs more optimization.
19 196 0.208049605574 Henry Cohn, 2026, needs more optimization.
19 197 0.208710456590 Henry Cohn, 2026, needs more optimization.
19 198 0.209833111196 Henry Cohn, 2026, needs more optimization.
19 199 0.210704058071 Henry Cohn, 2026, needs more optimization.
19 200 0.210982588277 Henry Cohn, 2026, needs more optimization.
19 201 0.211549532983 Henry Cohn, 2026, needs more optimization.
19 202 0.212965119630 Henry Cohn, 2026, needs more optimization.
19 203 0.213178977488 Henry Cohn, 2026, needs more optimization.
19 204 0.214895645558 Henry Cohn, 2025, needs more optimization.
19 205 0.215123722974 Henry Cohn, 2026, needs more optimization.
19 206 0.216034012878 Henry Cohn, 2025, needs more optimization.
19 207 0.216052401231 Henry Cohn, 2025, needs more optimization.
19 208 0.216212192509 Henry Cohn, 2025, needs more optimization.
19 209 0.218045539010 Henry Cohn, 2025, needs more optimization.
19 210 0.218431698944 Henry Cohn, 2025, needs more optimization.
19 211 0.218440680920 Henry Cohn, 2025, needs more optimization.
19 212 0.218485283387 Henry Cohn, 2026, needs more optimization.
19 213 0.219212673776 Henry Cohn, 2025, needs more optimization.
19 214 0.219765378982 Henry Cohn, 2026, needs more optimization.
19 215 0.220216906106 Henry Cohn, 2026, needs more optimization.
19 216 0.220547755759 Henry Cohn, 2026, needs more optimization.
19 240 0.230769230770 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
13⁢x−3
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
19 291 0.238519274309 Henry Cohn, 2026, needs more optimization.
19 292 0.243289905986 Henry Cohn, 2026, needs more optimization.
19 293 0.244127472826 Henry Cohn, 2026, needs more optimization.
19 294 0.245709904195 Henry Cohn, 2026, needs more optimization.
19 297 0.246500410186 Henry Cohn, 2026, needs more optimization.
19 298 0.248395767298 Henry Cohn, 2026, needs more optimization.
19 299 0.248551711591 Henry Cohn, 2026, needs more optimization.
19 300 0.248945053229 Henry Cohn, 2026, needs more optimization.
19 301 0.249978686033 Henry Cohn, 2026, needs more optimization.
19 304 0.249991047942 Henry Cohn, 2026, needs more optimization.
19 307 0.249994992895 Henry Cohn, 2026, needs more optimization.
19 308 0.249999378534 Henry Cohn, 2026, needs more optimization.
19 310 0.250005325886 Henry Cohn, 2026, needs more optimization.
19 312 0.250025250933 Henry Cohn, 2026, needs more optimization.
19 314 0.250027040456 Henry Cohn, 2026, needs more optimization.
19 318 0.250041457295 Henry Cohn, 2026, needs more optimization.
19 321 0.250043209609 Henry Cohn, 2026, needs more optimization.
19 322 0.250097646993 Henry Cohn, 2026, needs more optimization.
19 323 0.250124054478 Henry Cohn, 2026, needs more optimization.
19 324 0.250805365176 Henry Cohn, 2026, needs more optimization.
19 325 0.251181376933 Henry Cohn, 2026, needs more optimization.
19 328 0.287402439925 Henry Cohn, 2026, needs more optimization.
19 344 0.287466109704 Henry Cohn, 2026, needs more optimization.
19 360 0.287730492456 Henry Cohn, 2026, needs more optimization.
19 368 0.288046074744 Henry Cohn, 2026, needs more optimization.
19 376 0.288078500644 Henry Cohn, 2026, needs more optimization.
19 384 0.288768382513 Henry Cohn, 2026, needs more optimization.
19 392 0.289460464596 Henry Cohn, 2026, needs more optimization.
19 400 0.290310710074 Henry Cohn, 2026, needs more optimization.
19 408 0.290719405993 Henry Cohn, 2026, needs more optimization.
19 415 0.291690435834 Henry Cohn, 2026, needs more optimization.
19 485 0.296296296297 Henry Cohn, 2025.
27⁢x−8
19 560 0.304347826087 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
23⁢x−7
19 576 0.304347826087 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.
23⁢x−7
19 577 0.304507931848 Henry Cohn, 2026, needs more optimization.
19 578 0.304559376332 Henry Cohn, 2026, needs more optimization.
19 579 0.304610478353 Henry Cohn, 2026, needs more optimization.
19 580 0.304616094668 Henry Cohn, 2026, needs more optimization.
19 581 0.304638247229 Henry Cohn, 2026, needs more optimization.
19 582 0.304674048208 Henry Cohn, 2026, needs more optimization.
19 584 0.304688572506 Henry Cohn, 2026, needs more optimization.
19 585 0.304712559975 Henry Cohn, 2026, needs more optimization.
19 586 0.304732933650 Henry Cohn, 2026, needs more optimization.
19 588 0.304747554025 Henry Cohn, 2026, needs more optimization.
19 589 0.304768584912 Henry Cohn, 2026, needs more optimization.
19 590 0.304798319072 Henry Cohn, 2026, needs more optimization.
19 591 0.304807267890 Henry Cohn, 2026, needs more optimization.
19 592 0.304816887679 Henry Cohn, 2026, needs more optimization.
19 593 0.304850036313 Henry Cohn, 2025, needs more optimization.
19 594 0.304870068483 Henry Cohn, 2025, needs more optimization.
19 596 0.304882572546 Henry Cohn, 2026, needs more optimization.
19 597 0.304904010177 Henry Cohn, 2025, needs more optimization.
19 598 0.304914905451 Henry Cohn, 2025, needs more optimization.
19 600 0.304924768823 Henry Cohn, 2026, needs more optimization.
19 604 0.304954995080 Henry Cohn, 2026, needs more optimization.
19 605 0.304998577549 Henry Cohn, 2025, needs more optimization.
19 606 0.305007916218 Henry Cohn, 2026, needs more optimization.
19 607 0.305008902041 Henry Cohn, 2025, needs more optimization.
19 608 0.305013451984 Henry Cohn, 2026, needs more optimization.
19 609 0.305031662932 Henry Cohn, 2025, needs more optimization.
19 612 0.305031675525 Henry Cohn, 2026, needs more optimization.
19 613 0.305048594759 Henry Cohn, 2025, needs more optimization.
19 616 0.305050192359 Henry Cohn, 2026, needs more optimization.
19 617 0.305068555187 Henry Cohn, 2025, needs more optimization.
19 620 0.305081347021 Henry Cohn, 2026, needs more optimization.
19 624 0.305097417134 Henry Cohn, 2026, needs more optimization.
19 625 0.305114170876 Henry Cohn, 2025, needs more optimization.
19 628 0.305119407750 Henry Cohn, 2026, needs more optimization.
19 629 0.305137259572 Henry Cohn, 2025, needs more optimization.
19 630 0.305143351492 Henry Cohn, 2025, needs more optimization.
19 632 0.305145919737 Henry Cohn, 2026, needs more optimization.
19 633 0.305160018914 Henry Cohn, 2025, needs more optimization.
19 636 0.305161817320 Henry Cohn, 2026, needs more optimization.
19 640 0.305175574270 Henry Cohn, 2026, needs more optimization.
19 644 0.309227966944 Henry Cohn, 2026, needs more optimization.
19 646 0.309904355337 Henry Cohn, 2025, needs more optimization.
19 648 0.311072646970 Henry Cohn, 2026, needs more optimization.
19 649 0.312098563188 Henry Cohn, 2026, needs more optimization.
19 650 0.312098563493 Henry Cohn, 2026, needs more optimization.
19 651 0.312098563747 Henry Cohn, 2025, needs more optimization.
19 652 0.312302448986 Henry Cohn, 2026, needs more optimization.
19 656 0.313222186607 Henry Cohn, 2026, needs more optimization.
19 660 0.314243955461 Henry Cohn, 2026, needs more optimization.
19 664 0.315048124686 Henry Cohn, 2026, needs more optimization.
19 666 0.315489930454 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 0.339605417332 Henry Cohn, 2025, needs more optimization.
19 898 0.341453472442 Henry Cohn, 2025, needs more optimization.
19 899 0.342826411178 Henry Cohn, 2025, needs more optimization.
19 900 0.344190688570 Henry Cohn, 2026, needs more optimization.
19 901 0.345826645384 Henry Cohn, 2025, needs more optimization.
19 902 0.346308168967 Henry Cohn, 2025, needs more optimization.
19 903 0.347200185233 Henry Cohn, 2025, needs more optimization.
19 904 0.347511723865 Henry Cohn, 2026, needs more optimization.
19 905 0.348090774308 Henry Cohn, 2025, needs more optimization.
19 906 0.348507475092 Henry Cohn, 2025, needs more optimization.
19 907 0.349125653486 Henry Cohn, 2025, needs more optimization.
19 908 0.349379233183 Henry Cohn, 2026, needs more optimization.
19 909 0.349790733491 Henry Cohn, 2026, needs more optimization.
19 910 0.350137049274 Henry Cohn, 2025, needs more optimization.
19 911 0.350202781234 Henry Cohn, 2025, needs more optimization.
19 912 0.350921071750 Henry Cohn, 2026, needs more optimization.
19 913 0.351034600979 Henry Cohn, 2025, needs more optimization.
19 914 0.351442708251 Henry Cohn, 2025, needs more optimization.
19 915 0.351545937935 Henry Cohn, 2025, needs more optimization.
19 1024 0.368421052632 N. J. A. Sloane, S. M. Reddy, and C.-L. Chen, New binary codes, IEEE Trans. Inform. Theory 18 (1972), 503–510, doi:10.1109/tit.1972.1054833.
19⁢x−7
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, needs more optimization.
20 65 0.087640553690 Henry Cohn, 2026, needs more optimization.
20 66 0.089690435161 Henry Cohn, 2026.
330⁢x2+15⁢x−4
20 67 0.095918298180 Henry Cohn, 2026, needs more optimization.
20 68 0.097744099611 Henry Cohn, 2025, needs more optimization.
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 84 0.112895349963 Henry Cohn, 2025, needs more optimization.
20 85 0.112902505500 Henry Cohn, 2025, 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 0.121893958182 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 0.136915269074 Henry Cohn, 2026, needs more optimization.
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 0.145853791081 Henry Cohn, 2026, needs more optimization.
20 125 0.147670835581 Henry Cohn, 2026, needs more optimization.
20 126 0.149831609589 Henry Cohn, 2026, needs more optimization.
20 127 0.150090306704 Henry Cohn, 2026, needs more optimization.
20 128 0.150091864275 Henry Cohn, 2026, needs more optimization.
20 129 0.150493370176 Henry Cohn, 2026, needs more optimization.
20 130 0.150610322438 Henry Cohn, 2026, needs more optimization.
20 132 0.150697836383 Henry Cohn, 2026, needs more optimization.
20 133 0.151453018405 Henry Cohn, 2026, needs more optimization.
20 135 0.151505609414 Henry Cohn, 2026, needs more optimization.
20 136 0.151506098385 Henry Cohn, 2026, needs more optimization.
20 137 0.153216502836 Henry Cohn, 2026, needs more optimization.
20 138 0.154490499210 Henry Cohn, 2026, needs more optimization.
20 139 0.155171111582 Henry Cohn, 2026, needs more optimization.
20 140 0.156027125137 Henry Cohn, 2026, needs more optimization.
20 141 0.157502608513 Henry Cohn, 2025, needs more optimization.
20 142 0.161809087537 Henry Cohn, 2026, needs more optimization.
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
20 176 0.189208372942 Henry Cohn, 2026, needs more optimization.
20 177 0.189211418624 Henry Cohn, 2026, needs more optimization.
20 178 0.191919191920 Orthogonal union of 176 points in 19 dimensions and 2 points in 1 dimension.
99⁢x−19
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
20 262 0.208386801326 Henry Cohn, 2026, needs more optimization.
20 263 0.208856371119 Henry Cohn, 2026, needs more optimization.
20 264 0.208862423530 Henry Cohn, 2026, needs more optimization.
20 265 0.215340499599 Henry Cohn, 2026, needs more optimization.
20 266 0.218839013131 Henry Cohn, 2026, needs more optimization.
20 267 0.218843434758 Henry Cohn, 2026, needs more optimization.
20 268 0.218846700962 Henry Cohn, 2026, needs more optimization.
20 269 0.218893426482 Henry Cohn, 2026, needs more optimization.
20 270 0.218896677981 Henry Cohn, 2026, needs more optimization.
20 271 0.218907991187 Henry Cohn, 2026, needs more optimization.
20 272 0.218911333577 Henry Cohn, 2026, needs more optimization.
20 273 0.218913094158 Henry Cohn, 2026, needs more optimization.
20 274 0.218917980505 Henry Cohn, 2026, needs more optimization.
20 275 0.218926740860 Henry Cohn, 2026, needs more optimization.
20 276 0.218928153358 Henry Cohn, 2026, needs more optimization.
20 277 0.218933485739 Henry Cohn, 2026, needs more optimization.
20 278 0.218935918304 Henry Cohn, 2026, needs more optimization.
20 279 0.218938293587 Henry Cohn, 2026, needs more optimization.
20 294 0.220695461526 Henry Cohn, 2024, 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
20 378 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
20 405 0.25 C. Ma, T. T. Zhaowei, 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 0.262180653313 Henry Cohn, 2026, needs more optimization.
20 473 0.266666666667 Henry Cohn, 2025.
15⁢x−4
20 474 0.269878877064 Henry Cohn, 2026, needs more optimization.
20 475 0.271304137415 Henry Cohn, 2025, needs more optimization.
20 476 0.272622512553 Henry Cohn, 2026, needs more optimization.
20 477 0.273459280230 Henry Cohn, 2025, needs more optimization.
20 478 0.274387603276 Henry Cohn, 2025, needs more optimization.
20 479 0.275200367871 Henry Cohn, 2025, needs more optimization.
20 480 0.275966924004 Henry Cohn, 2026, needs more optimization.
20 488 0.276469909920 Henry Cohn, 2026, needs more optimization.
20 492 0.278204522843 Henry Cohn, 2026, needs more optimization.
20 496 0.278298282200 Henry Cohn, 2026, needs more optimization.
20 497 0.281336900131 Henry Cohn, 2025, needs more optimization.
20 498 0.281346725928 Henry Cohn, 2026, needs more optimization.
20 499 0.281346754647 Henry Cohn, 2025, needs more optimization.
20 500 0.281348261555 Henry Cohn, 2025, needs more optimization.
20 503 0.281393107933 Henry Cohn, 2025, needs more optimization.
20 504 0.283650277827 Henry Cohn, 2026, needs more optimization.
20 508 0.285343377207 Henry Cohn, 2026, needs more optimization.
20 511 0.285651857828 Henry Cohn, 2025, needs more optimization.
20 516 0.288364124534 Henry Cohn, 2026, needs more optimization.
20 520 0.288372970609 Henry Cohn, 2026, needs more optimization.
20 521 0.289404389705 Henry Cohn, 2026, needs more optimization.
20 544 0.289726812929 Henry Cohn, 2026, needs more optimization.
20 548 0.289726813349 Henry Cohn, 2026, needs more optimization.
20 549 0.289734511943 Henry Cohn, 2025, needs more optimization.
20 550 0.289735107894 Henry Cohn, 2025, needs more optimization.
20 552 0.289765170476 Henry Cohn, 2026, needs more optimization.
20 673 0.304347826087 Henry Cohn, 2025.
23⁢x−7
20 676 0.304396956509 Henry Cohn, 2025, needs more optimization.
20 678 0.304400569629 Henry Cohn, 2025, needs more optimization.
20 679 0.304412508599 Henry Cohn, 2025, needs more optimization.
20 896 0.311475409837 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
61⁢x−19
20 897 0.312190960644 Henry Cohn, 2025, needs more optimization.
20 898 0.312370616820 Henry Cohn, 2025, needs more optimization.
20 899 0.312531816974 Henry Cohn, 2025, needs more optimization.
20 900 0.312540011762 Henry Cohn, 2026, needs more optimization.
20 901 0.312720092892 Henry Cohn, 2025, needs more optimization.
20 902 0.312863895819 Henry Cohn, 2025, needs more optimization.
20 903 0.312959756948 Henry Cohn, 2025, needs more optimization.
20 904 0.312985013976 Henry Cohn, 2026, needs more optimization.
20 905 0.313030006626 Henry Cohn, 2025, needs more optimization.
20 906 0.313153437504 Henry Cohn, 2025, needs more optimization.
20 907 0.313177804356 Henry Cohn, 2025, needs more optimization.
20 908 0.313269275702 Henry Cohn, 2026, needs more optimization.
20 909 0.313319621737 Henry Cohn, 2025, needs more optimization.
20 910 0.313383064338 Henry Cohn, 2026, needs more optimization.
20 911 0.313437876546 Henry Cohn, 2025, needs more optimization.
20 912 0.313458851296 Henry Cohn, 2026, needs more optimization.
20 913 0.313515019568 Henry Cohn, 2025, needs more optimization.
20 914 0.313600475015 Henry Cohn, 2025, needs more optimization.
20 915 0.313687412324 Henry Cohn, 2025, needs more optimization.
20 916 0.313689185245 Henry Cohn, 2026, needs more optimization.
20 917 0.313742181219 Henry Cohn, 2025, needs more optimization.
20 918 0.313787799243 Henry Cohn, 2025, needs more optimization.
20 920 0.313821753717 Henry Cohn, 2026, needs more optimization.
20 921 0.313871643206 Henry Cohn, 2025, needs more optimization.
20 924 0.313896470232 Henry Cohn, 2026, needs more optimization.
20 925 0.313926649291 Henry Cohn, 2025, needs more optimization.
20 926 0.313959334833 Henry Cohn, 2025, needs more optimization.
20 928 0.313987096650 Henry Cohn, 2026, needs more optimization.
20 929 0.314045700687 Henry Cohn, 2025, needs more optimization.
20 930 0.314080492810 Henry Cohn, 2025, needs more optimization.
20 932 0.314105414716 Henry Cohn, 2026, needs more optimization.
20 936 0.314148192896 Henry Cohn, 2026, needs more optimization.
20 937 0.314183050926 Henry Cohn, 2025, needs more optimization.
20 938 0.314194097610 Henry Cohn, 2025, needs more optimization.
20 939 0.314212488531 Henry Cohn, 2025, needs more optimization.
20 940 0.314247841153 Henry Cohn, 2026, needs more optimization.
20 941 0.314288358360 Henry Cohn, 2025, needs more optimization.
20 942 0.314299297491 Henry Cohn, 2025, needs more optimization.
20 944 0.314310558267 Henry Cohn, 2026, needs more optimization.
20 945 0.314343744037 Henry Cohn, 2025, needs more optimization.
20 946 0.314357771839 Henry Cohn, 2025, needs more optimization.
20 947 0.314377623395 Henry Cohn, 2025, needs more optimization.
20 948 0.314389395166 Henry Cohn, 2026, needs more optimization.
20 949 0.314424194227 Henry Cohn, 2025, needs more optimization.
20 950 0.314444907491 Henry Cohn, 2025, needs more optimization.
20 952 0.314458294723 Henry Cohn, 2026, needs more optimization.
20 953 0.314484691487 Henry Cohn, 2025, needs more optimization.
20 954 0.314517046991 Henry Cohn, 2025, needs more optimization.
20 955 0.314549253350 Henry Cohn, 2025, needs more optimization.
20 956 0.314553955096 Henry Cohn, 2026, needs more optimization.
20 957 0.314584476667 Henry Cohn, 2025, needs more optimization.
20 958 0.314597847655 Henry Cohn, 2025, needs more optimization.
20 960 0.314608007053 Henry Cohn, 2026, needs more optimization.
20 961 0.314636423852 Henry Cohn, 2025, needs more optimization.
20 964 0.314653666340 Henry Cohn, 2026, needs more optimization.
20 965 0.314673974781 Henry Cohn, 2025, needs more optimization.
20 966 0.314685551082 Henry Cohn, 2025, needs more optimization.
20 968 0.314691494481 Henry Cohn, 2026, needs more optimization.
20 969 0.314709699248 Henry Cohn, 2025, needs more optimization.
20 970 0.314715303236 Henry Cohn, 2025, needs more optimization.
20 972 0.316635841942 Henry Cohn, 2026, needs more optimization.
20 976 0.316637268930 Henry Cohn, 2026, needs more optimization.
20 977 0.316731825153 Henry Cohn, 2025, needs more optimization.
20 978 0.317372002201 Henry Cohn, 2025, needs more optimization.
20 980 0.318163805803 Henry Cohn, 2026, needs more optimization.
20 984 0.318183545207 Henry Cohn, 2026, needs more optimization.
20 988 0.318200273204 Henry Cohn, 2026, needs more optimization.
20 989 0.318314238796 Henry Cohn, 2025, needs more optimization.
20 990 0.318564063560 Henry Cohn, 2025, needs more optimization.
20 991 0.319493547827 Henry Cohn, 2025, needs more optimization.
20 992 0.319662706947 Henry Cohn, 2026, needs more optimization.
20 994 0.320469116056 Henry Cohn, 2025, needs more optimization.
20 996 0.321277826314 Henry Cohn, 2026, needs more optimization.
20 998 0.321933292999 Henry Cohn, 2025, needs more optimization.
20 1000 0.322171034334 Henry Cohn, 2026, needs more optimization.
20 1002 0.322236055657 Henry Cohn, 2025, needs more optimization.
20 1004 0.323142177678 Henry Cohn, 2026, needs more optimization.
20 1006 0.323165149636 Henry Cohn, 2025, needs more optimization.
20 1008 0.323233914732 Henry Cohn, 2026, needs more optimization.
20 1010 0.323564675377 Henry Cohn, 2025, needs more optimization.
20 1012 0.323933408162 Henry Cohn, 2026, needs more optimization.
20 1015 0.323956619698 Henry Cohn, 2025, needs more optimization.
20 1016 0.324031372969 Henry Cohn, 2026, needs more optimization.
20 1017 0.324054978602 Henry Cohn, 2025, needs more optimization.
20 1020 0.324162583394 Henry Cohn, 2026, needs more optimization.
20 1022 0.324326602715 Henry Cohn, 2025, needs more optimization.
20 1024 0.324776552083 Henry Cohn, 2026, needs more optimization.
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 0.062643510087 Henry Cohn, 2023.
21 53 0.066665620363 Henry Cohn, 2025.
21 54 0.066665850459 Henry Cohn, 2025.
21 55 0.066666409280 Henry Cohn, 2025, needs more optimization.
21 56 0.066666653891 Henry Cohn, 2025, needs more optimization.
21 57 0.066666662289 Henry Cohn, 2025, needs more optimization.
21 58 0.066666666337 Henry Cohn, 2025, 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.
21 65 0.081966984796 Henry Cohn, 2025, needs more optimization.
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 0.093247656079 Henry Cohn, 2026, needs more optimization.
21 81 0.093297851019 Henry Cohn, 2026, needs more optimization.
21 82 0.093297851020 Henry Cohn, 2026, needs more optimization.
21 83 0.095616261318 Henry Cohn, 2026, needs more optimization.
21 84 0.096120290871 Henry Cohn, 2026, needs more optimization.
21 85 0.097851719730 Henry Cohn, 2026.
84⁢x2+2⁢x−1
21 86 0.104649382570 Henry Cohn, 2026, needs more optimization.
21 87 0.107536754349 Henry Cohn, 2026, needs more optimization.
21 88 0.108040226878 Henry Cohn, 2026, needs more optimization.
21 89 0.108846463758 Henry Cohn, 2026, needs more optimization.
21 90 0.110085419958 Henry Cohn, 2026, needs more optimization.
21 91 0.110089945291 Henry Cohn, 2026, needs more optimization.
21 92 0.110758056129 Henry Cohn, 2026, needs more optimization.
21 93 0.110772296541 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 0.127363959723 Henry Cohn, 2026, needs more optimization.
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
21 122 0.139354052717 Henry Cohn, 2026, needs more optimization.
21 123 0.139446357525 Henry Cohn, 2026, needs more optimization.
21 124 0.140535785430 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 0.153926281049 Henry Cohn, 2026, needs more optimization.
21 164 0.160794343577 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
21 210 0.189189189190 Kissing configuration of 529 points in 22 dimensions from T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
37⁢x−7
21 225 0.189189189190 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.
37⁢x−7
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
21 336 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
21 345 0.230818230927 Henry Cohn, 2026, needs more optimization.
21 353 0.230819078355 Henry Cohn, 2026, needs more optimization.
21 371 0.230820117549 Henry Cohn, 2026, needs more optimization.
21 374 0.230820493211 Henry Cohn, 2026, needs more optimization.
21 375 0.230828419531 Henry Cohn, 2026, needs more optimization.
21 380 0.230829007825 Henry Cohn, 2026, needs more optimization.
21 381 0.230829256256 Henry Cohn, 2026, needs more optimization.
21 388 0.230893614344 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
21 660 0.266666666667 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
15⁢x−4
21 716 0.272727272728 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
11⁢x−3
21 1024 0.311475409837 Henry Cohn, 2025.
61⁢x−19
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 0.041709010751 Henry Cohn, 2026.
22 47 0.046962270332 Henry Cohn, 2026.
22 48 0.047524915294 Henry Cohn, 2025, continuous family of codes without rattlers.
64⁢x2+18⁢x−1
22 49 0.047603596837 Henry Cohn, 2025, needs more optimization.
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 0.064359647827 Henry Cohn, 2026, needs more optimization.
22 57 0.066657147970 Henry Cohn, 2026, needs more optimization.
22 59 0.066664590405 Henry Cohn, 2026, needs more optimization.
22 60 0.066664720886 Henry Cohn, 2026, needs more optimization.
22 61 0.069653549396 Henry Cohn, 2026, needs more optimization.
22 62 0.071738103734 Henry Cohn, 2026, needs more optimization.
22 64 0.076920313939 Henry Cohn, 2025, needs more optimization.
22 65 0.076924075556 Henry Cohn, 2026, needs more optimization.
22 66 0.078264461355 Henry Cohn, 2026, needs more optimization.
22 67 0.079295799194 Henry Cohn, 2026, needs more optimization.
22 68 0.080927905689 Henry Cohn, 2026, needs more optimization.
22 69 0.083048702406 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 0.083333305431 Henry Cohn, 2025, 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 0.086876541555 Henry Cohn, 2026, needs more optimization.
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 0.109433688341 Henry Cohn, 2026, needs more optimization.
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 0.121319631346 Henry Cohn, 2026, needs more optimization.
22 117 0.122811460191 Henry Cohn, 2026, needs more optimization.
22 118 0.130947195767 Henry Cohn, 2026, needs more optimization.
22 121 0.131782945737 Code with 119 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.
129⁢x−17
22 126 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, 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.
37⁢x−5
22 142 0.135581434330 Henry Cohn, 2026, needs more optimization.
22 143 0.138392916073 Henry Cohn, 2026, needs more optimization.
22 144 0.139626978577 Henry Cohn, 2026, needs more optimization.
22 164 0.142857142858 Code with 162 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.
7⁢x−1
22 166 0.142857633906 Henry Cohn, 2026, needs more optimization.
22 167 0.150694419400 Henry Cohn, 2026, needs more optimization.
22 168 0.155185176796 Henry Cohn, 2026, needs more optimization.
22 169 0.159348029498 Henry Cohn, 2026, needs more optimization.
22 170 0.160025551291 Henry Cohn, 2026, needs more optimization.
22 200 0.161904761905 Code with 198 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.
105⁢x−17
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
22 338 0.2 Code with 336 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.
5⁢x−1
22 424 0.209817070715 Henry Cohn, 2026, needs more optimization.
22 428 0.209819210970 Henry Cohn, 2026, needs more optimization.
22 429 0.209819211160 Henry Cohn, 2026, needs more optimization.
22 430 0.209819211247 Henry Cohn, 2026, needs more optimization.
22 432 0.212433779378 Henry Cohn, 2026, needs more optimization.
22 433 0.212503875731 Henry Cohn, 2026, needs more optimization.
22 434 0.212569976110 Henry Cohn, 2026, needs more optimization.
22 435 0.212589878460 Henry Cohn, 2026, needs more optimization.
22 436 0.212591059582 Henry Cohn, 2026, needs more optimization.
22 437 0.212635538515 Henry Cohn, 2026, needs more optimization.
22 451 0.212654836504 Henry Cohn, 2026, needs more optimization.
22 484 0.229650348229 Henry Cohn, 2026, needs more optimization.
22 485 0.229651854557 Henry Cohn, 2026, needs more optimization.
22 504 0.229926564994 Henry Cohn, 2026, needs more optimization.
22 505 0.229927684818 Henry Cohn, 2025, needs more optimization.
22 506 0.231141363150 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
22 891* 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 0.047373578446 Henry Cohn, 2026, needs more optimization.
23 52 0.047490059118 Henry Cohn, 2026, needs more optimization.
23 53 0.047609748527 Henry Cohn, 2024, needs more optimization.
23 54 0.047609798559 Henry Cohn, 2024, needs more optimization.
23 55 0.055674420072 Henry Cohn, 2024.
23 56 0.057275984127 Henry Cohn, 2025.
23 57 0.061655029733 Ilmari Vahteristo, 2026.
23 58 0.064546893895 Henry Cohn, 2026, needs more optimization.
23 59 0.066400113954 Henry Cohn, 2026, needs more optimization.
23 60 0.066578533763 Henry Cohn, 2026, needs more optimization.
23 61 0.066599568077 Henry Cohn, 2025, needs more optimization.
23 62 0.066599790838 Henry Cohn, 2025, needs more optimization.
23 63 0.067273702694 Henry Cohn, 2026, needs more optimization.
23 64 0.069716146537 Henry Cohn, 2026, needs more optimization.
23 65 0.073685156024 Henry Cohn, 2026, needs more optimization.
23 66 0.076868373578 Henry Cohn, 2026, needs more optimization.
23 67 0.076908850880 Henry Cohn, 2026, needs more optimization.
23 68 0.076926238615 Henry Cohn, 2026, needs more optimization.
23 69 0.077673812170 Henry Cohn, 2026, needs more optimization.
23 70 0.077985696760 Henry Cohn, 2026, needs more optimization.
23 71 0.079646439023 Henry Cohn, 2026, needs more optimization.
23 72 0.080600120909 Henry Cohn, 2026, needs more optimization.
23 73 0.082853645940 Henry Cohn, 2026, needs more optimization.
23 81 0.083333222004 Henry Cohn, 2025, needs more optimization.
23 82 0.083397112292 Henry Cohn, 2026, needs more optimization.
23 83 0.087449050695 Henry Cohn, 2026, needs more optimization.
23 84 0.090623839956 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 0.103889057081 Henry Cohn, 2026, needs more optimization.
23 116 0.111111109788 Henry Cohn, 2025, needs more optimization.
23 117 0.111124873982 Henry Cohn, 2026, needs more optimization.
23 118 0.114841775567 Henry Cohn, 2026, needs more optimization.
23 119 0.118704776821 Henry Cohn, 2026, needs more optimization.
23 120 0.121176526071 Henry Cohn, 2026, needs more optimization.
23 121 0.127680714314 Henry Cohn, 2026, needs more optimization.
23 122 0.130977017878 Henry Cohn, 2026, needs more optimization.
23 123 0.131779371379 Henry Cohn, 2025, needs more optimization.
23 128 0.131782945737 Orthogonal union of 126 points in 22 dimensions and 2 points in 1 dimension.
129⁢x−17
23 129 0.131787572852 Henry Cohn, 2026, needs more optimization.
23 130 0.131807435199 Henry Cohn, 2026, needs more optimization.
23 131 0.132303834122 Henry Cohn, 2026, needs more optimization.
23 132 0.134434136145 Henry Cohn, 2026, needs more optimization.
23 133 0.134939068214 Henry Cohn, 2026, needs more optimization.
23 138 0.135135135136 Code with 136 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.
37⁢x−5
23 143 0.135135135136 Orthogonal union of 141 points in 22 dimensions and 2 points in 1 dimension.
37⁢x−5
23 146 0.135135718818 Henry Cohn, 2026, needs more optimization.
23 147 0.135471094281 Henry Cohn, 2026, needs more optimization.
23 148 0.140082467145 Henry Cohn, 2026, needs more optimization.
23 166 0.142857142858 Code with 164 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.
7⁢x−1
23 167 0.142857143337 Henry Cohn, 2026, needs more optimization.
23 168 0.142857633906 Orthogonal union of 166 points in 22 dimensions and 2 points in 1 dimension.
23 170 0.142865346672 Henry Cohn, 2026, needs more optimization.
23 171 0.159348029498 Orthogonal union of 169 points in 22 dimensions and 2 points in 1 dimension.
23 173 0.160017501690 Henry Cohn, 2026, needs more optimization.
23 174 0.160022059572 Henry Cohn, 2026, needs more optimization.
23 202 0.161904761905 Code with 200 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.
105⁢x−17
23 203 0.161940081728 Henry Cohn, 2026, needs more optimization.
23 205 0.161944690832 Henry Cohn, 2026, needs more optimization.
23 206 0.161949065921 Henry Cohn, 2026, needs more optimization.
23 207 0.162352973274 Henry Cohn, 2026, needs more optimization.
23 277 0.166666666667 Code with 275 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.
6⁢x−1
23 279 0.171408036565 Henry Cohn, 2026, needs more optimization.
23 281 0.181918567390 Henry Cohn, 2026, needs more optimization.
23 283 0.183988535621 Henry Cohn, 2026, needs more optimization.
23 284 0.188519179676 Henry Cohn, 2026, needs more optimization.
23 285 0.188985112883 Henry Cohn, 2026, needs more optimization.
23 286 0.189266323919 Henry Cohn, 2026, needs more optimization.
23 288 0.189442338755 Henry Cohn, 2026, needs more optimization.
23 289 0.189508988656 Henry Cohn, 2026, needs more optimization.
23 291 0.198557992135 Henry Cohn, 2026, needs more optimization.
23 292 0.198580566782 Henry Cohn, 2026, needs more optimization.
23 293 0.199477525427 Henry Cohn, 2026, needs more optimization.
23 294 0.199491986979 Henry Cohn, 2026, needs more optimization.
23 295 0.199495707192 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
23 558 0.238095238096 Orthogonal union of 554 points in 21 dimensions and 4 points in 2 dimensions.
21⁢x−5
23 564 0.242347692504 Henry Cohn, 2026, needs more optimization.
23 568 0.243318196393 Henry Cohn, 2026, needs more optimization.
23 572 0.243350935121 Henry Cohn, 2026, needs more optimization.
23 893 0.25 Orthogonal union of 891 points in 22 dimensions and 2 points in 1 dimension.
4⁢x−1
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 0.047563043071 Henry Cohn, 2024, needs more optimization.
24 57 0.053295300110 Ilmari Vahteristo, 2026.
24 58 0.054403503474 Henry Cohn, 2025.
24 59 0.057903810057 Henry Cohn, 2026.
24 60 0.061570441778 Henry Cohn, 2026, needs more optimization.
24 61 0.064823518342 Henry Cohn, 2026, needs more optimization.
24 62 0.065885709710 Henry Cohn, 2026, needs more optimization.
24 63 0.065889732159 Henry Cohn, 2026, needs more optimization.
24 64 0.065926554739 Henry Cohn, 2026, needs more optimization.
24 65 0.066620540545 Henry Cohn, 2026, needs more optimization.
24 66 0.068188397880 Henry Cohn, 2026, needs more optimization.
24 67 0.071159402406 Henry Cohn, 2026, needs more optimization.
24 68 0.073544410184 Henry Cohn, 2026, needs more optimization.
24 69 0.074868113179 Henry Cohn, 2026, needs more optimization.
24 70 0.076699871521 Henry Cohn, 2026, needs more optimization.
24 71 0.076928741368 Henry Cohn, 2026, needs more optimization.
24 72 0.077524249785 Henry Cohn, 2025, needs more optimization.
24 73 0.077887425403 Henry Cohn, 2026, needs more optimization.
24 74 0.077908692840 Henry Cohn, 2026, needs more optimization.
24 75 0.078600884756 Henry Cohn, 2026, needs more optimization.
24 76 0.078850062000 Henry Cohn, 2026, needs more optimization.
24 77 0.081790897066 Henry Cohn, 2026, needs more optimization.
24 78 0.082774182084 Henry Cohn, 2026, needs more optimization.
24 79 0.083298493258 Henry Cohn, 2026, needs more optimization.
24 80 0.083320095951 Henry Cohn, 2025, needs more optimization.
24 83 0.083320171859 Henry Cohn, 2025, needs more optimization.
24 85 0.083335343915 Henry Cohn, 2026, needs more optimization.
24 86 0.086447948297 Henry Cohn, 2026, needs more optimization.
24 87 0.088167485927 Henry Cohn, 2026, needs more optimization.
24 88 0.089937149505 Henry Cohn, 2026, needs more optimization.
24 89 0.090291024770 Henry Cohn, 2026, needs more optimization.
24 90 0.090743696895 Henry Cohn, 2026, needs more optimization.
24 91 0.090834171392 Henry Cohn, 2026, needs more optimization.
24 92 0.090886623151 Henry Cohn, 2026, needs more optimization.
24 104 0.090909090666 Henry Cohn, 2025, needs more optimization.
24 105 0.091535358779 Henry Cohn, 2026, needs more optimization.
24 106 0.095288691538 Henry Cohn, 2026, needs more optimization.
24 107 0.102478292355 Henry Cohn, 2026, needs more optimization.
24 108 0.105664962686 Henry Cohn, 2026, needs more optimization.
24 118 0.111099565428 Henry Cohn, 2025, needs more optimization.
24 119 0.111113332243 Henry Cohn, 2026, needs more optimization.
24 121 0.111113986191 Henry Cohn, 2026, needs more optimization.
24 122 0.112368306160 Henry Cohn, 2026, needs more optimization.
24 123 0.116180792187 Henry Cohn, 2026, needs more optimization.
24 124 0.117906183525 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
24 130 0.131782945737 Orthogonal union of 126 points in 22 dimensions and 4 points in 2 dimensions.
129⁢x−17
24 131 0.131785059357 Henry Cohn, 2026, needs more optimization.
24 132 0.131785826825 Henry Cohn, 2026, needs more optimization.
24 134 0.131788311295 Henry Cohn, 2026, needs more optimization.
24 135 0.131982938707 Henry Cohn, 2026, needs more optimization.
24 136 0.132748784856 Henry Cohn, 2026, needs more optimization.
24 137 0.132974024906 Henry Cohn, 2026, needs more optimization.
24 138 0.133563563014 Henry Cohn, 2026, needs more optimization.
24 139 0.134487827079 Henry Cohn, 2026, needs more optimization.
24 140 0.134811319929 Henry Cohn, 2026, needs more optimization.
24 141 0.135004691448 Henry Cohn, 2026, needs more optimization.
24 142 0.135091159740 Henry Cohn, 2026, needs more optimization.
24 145 0.135135135136 Orthogonal union of 141 points in 22 dimensions and 4 points in 2 dimensions.
37⁢x−5
24 148 0.135135718818 Orthogonal union of 146 points in 23 dimensions and 2 points in 1 dimension.
24 149 0.135140707003 Henry Cohn, 2026, needs more optimization.
24 150 0.135148555193 Henry Cohn, 2026, needs more optimization.
24 151 0.135709658711 Henry Cohn, 2026, needs more optimization.
24 152 0.137403091837 Henry Cohn, 2026, needs more optimization.
24 153 0.138376488553 Henry Cohn, 2026, needs more optimization.
24 154 0.139936051506 Henry Cohn, 2026, needs more optimization.
24 155 0.141753411501 Henry Cohn, 2026, needs more optimization.
24 167 0.142857140433 Henry Cohn, 2026, needs more optimization.
24 172 0.142857140440 Henry Cohn, 2026, needs more optimization.
24 174 0.142857172719 Henry Cohn, 2026, needs more optimization.
24 175 0.146979690652 Henry Cohn, 2026, needs more optimization.
24 176 0.148579488951 Henry Cohn, 2026, needs more optimization.
24 177 0.148600869869 Henry Cohn, 2026, needs more optimization.
24 178 0.150949826637 Henry Cohn, 2026, needs more optimization.
24 179 0.153553247721 Henry Cohn, 2026, needs more optimization.
24 180 0.155874843016 Henry Cohn, 2026, needs more optimization.
24 181 0.158075494419 Henry Cohn, 2026, needs more optimization.
24 182 0.161844673156 Henry Cohn, 2026, needs more optimization.
24 184 0.161865069644 Henry Cohn, 2026, needs more optimization.
24 204 0.161904761905 Code with 202 points in 23 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.
105⁢x−17
24 212 0.161905140019 Henry Cohn, 2026, needs more optimization.
24 213 0.161972647520 Henry Cohn, 2026, needs more optimization.
24 214 0.162353490528 Henry Cohn, 2026, needs more optimization.
24 215 0.163954256598 Henry Cohn, 2026, needs more optimization.
24 216 0.164339546667 Henry Cohn, 2026, needs more optimization.
24 217 0.165411372093 Henry Cohn, 2026, needs more optimization.
24 218 0.165438883316 Henry Cohn, 2026, needs more optimization.
24 219 0.166044551798 Henry Cohn, 2026, needs more optimization.
24 220 0.166284576697 Henry Cohn, 2026, needs more optimization.
24 221 0.166376811434 Henry Cohn, 2026, needs more optimization.
24 222 0.166579076986 Henry Cohn, 2026, needs more optimization.
24 223 0.166607863008 Henry Cohn, 2026, needs more optimization.
24 224 0.166633668265 Henry Cohn, 2026, needs more optimization.
24 279 0.166666666667 Code with 277 points in 23 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.
6⁢x−1
24 280 0.166725131947 Henry Cohn, 2026, needs more optimization.
24 281 0.166725569662 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
24 330 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
24 554 0.2 Code with 552 points in 23 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.
5⁢x−1
24 561 0.238095238096 Orthogonal union of 554 points in 21 dimensions and 7 points in 3 dimensions.
21⁢x−5
24 564 0.238324345033 Henry Cohn, 2026, needs more optimization.
24 568 0.239006334996 Henry Cohn, 2026, needs more optimization.
24 572 0.240565555318 Henry Cohn, 2026, needs more optimization.
24 574 0.243350935121 Orthogonal union of 572 points in 23 dimensions and 2 points in 1 dimension.
24 580 0.249320155828 Henry Cohn, 2026, needs more optimization.
24 588 0.249628583856 Henry Cohn, 2026, needs more optimization.
24 596 0.249766220796 Henry Cohn, 2026, needs more optimization.
24 600 0.249965036328 Henry Cohn, 2026, needs more optimization.
24 614 0.249999999973 Henry Cohn, 2026, needs more optimization.
24 895 0.25 Orthogonal union of 891 points in 22 dimensions and 4 points in 2 dimensions.
4⁢x−1
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 53 0.045305381447 Henry Cohn, 2025, needs more optimization.
25 54 0.045671054769 Henry Cohn, 2025.
25 55 0.046279562119 Henry Cohn, 2025.
25 56 0.046433703861 Henry Cohn, 2025, needs more optimization.
25 57 0.046863894921 Henry Cohn, 2025.
25 58 0.046863920964 Henry Cohn, 2025.
25 59 0.051394584232 Henry Cohn, 2024.
25 60 0.053010635350 Henry Cohn, 2026, needs more optimization.
25 61 0.056086471401 Henry Cohn, 2026, needs more optimization.
25 62 0.060614782374 Ilmari Vahteristo, 2026.
25 63 0.062412125820 Henry Cohn, 2026, needs more optimization.
25 64 0.064254785157 Henry Cohn, 2026, needs more optimization.
25 65 0.065379647303 Henry Cohn, 2024, needs more optimization.
25 66 0.065382268725 Henry Cohn, 2024, needs more optimization.
25 67 0.066333988857 Henry Cohn, 2026, needs more optimization.
25 68 0.066550363948 Henry Cohn, 2026, needs more optimization.
25 69 0.068868043532 Henry Cohn, 2026, needs more optimization.
25 70 0.071388671489 Henry Cohn, 2026, needs more optimization.
25 71 0.073815015326 Henry Cohn, 2026, needs more optimization.
25 72 0.075613254793 Henry Cohn, 2026, needs more optimization.
25 73 0.076645004518 Henry Cohn, 2026, needs more optimization.
25 74 0.076908492251 Henry Cohn, 2026, needs more optimization.
25 76 0.076951278019 Henry Cohn, 2026, needs more optimization.
25 77 0.077490049713 Henry Cohn, 2026, needs more optimization.
25 78 0.077961000458 Henry Cohn, 2026, needs more optimization.
25 79 0.078566094854 Henry Cohn, 2026, needs more optimization.
25 80 0.081703414373 Henry Cohn, 2026, needs more optimization.
25 81 0.082346328533 Henry Cohn, 2026, needs more optimization.
25 82 0.082748796262 Henry Cohn, 2026, needs more optimization.
25 83 0.083154714342 Henry Cohn, 2026, needs more optimization.
25 84 0.083199942916 Henry Cohn, 2026, needs more optimization.
25 85 0.083277480936 Henry Cohn, 2025, needs more optimization.
25 86 0.083321259228 Henry Cohn, 2026, needs more optimization.
25 87 0.083335343915 Orthogonal union of 85 points in 24 dimensions and 2 points in 1 dimension.
25 88 0.083358400773 Henry Cohn, 2025, needs more optimization.
25 89 0.085256212950 Henry Cohn, 2026, needs more optimization.
25 90 0.087307257636 Henry Cohn, 2025, needs more optimization.
25 91 0.088650490507 Henry Cohn, 2026, needs more optimization.
25 92 0.089333745703 Henry Cohn, 2026, needs more optimization.
25 93 0.090111728617 Henry Cohn, 2026, needs more optimization.
25 94 0.090337394819 Henry Cohn, 2026, needs more optimization.
25 95 0.090484092606 Henry Cohn, 2026, needs more optimization.
25 96 0.090654514283 Henry Cohn, 2026, needs more optimization.
25 97 0.090861831328 Henry Cohn, 2026, needs more optimization.
25 98 0.090899999492 Henry Cohn, 2026, needs more optimization.
25 99 0.090908851575 Henry Cohn, 2026, needs more optimization.
25 106 0.090909090666 Orthogonal union of 104 points in 24 dimensions and 2 points in 1 dimension.
25 107 0.090913623862 Henry Cohn, 2026, needs more optimization.
25 108 0.093169859745 Henry Cohn, 2026, needs more optimization.
25 109 0.096463145655 Henry Cohn, 2026, needs more optimization.
25 110 0.100753584656 Henry Cohn, 2026, needs more optimization.
25 111 0.102982898244 Henry Cohn, 2026, needs more optimization.
25 112 0.106062267865 Henry Cohn, 2026, needs more optimization.
25 114 0.111015805022 Henry Cohn, 2026, needs more optimization.
25 115 0.111045057443 Henry Cohn, 2026, needs more optimization.
25 116 0.111081986649 Henry Cohn, 2026, needs more optimization.
25 117 0.111097245349 Henry Cohn, 2026, needs more optimization.
25 120 0.111099565428 Orthogonal union of 118 points in 24 dimensions and 2 points in 1 dimension.
25 123 0.111109715013 Henry Cohn, 2026, needs more optimization.
25 124 0.111110673751 Henry Cohn, 2026, needs more optimization.
25 125 0.111112955319 Henry Cohn, 2026, needs more optimization.
25 126 0.111209584994 Henry Cohn, 2026, needs more optimization.
25 127 0.114417209624 Henry Cohn, 2026, needs more optimization.
25 128 0.116274255928 Henry Cohn, 2026, needs more optimization.
25 129 0.118373838464 Henry Cohn, 2026, needs more optimization.
25 130 0.120036186929 Henry Cohn, 2026, needs more optimization.
25 131 0.122028078033 Henry Cohn, 2026, needs more optimization.
25 132 0.123583659785 Henry Cohn, 2026, needs more optimization.
25 133 0.125091451058 Henry Cohn, 2026, needs more optimization.
25 134 0.126246822279 Henry Cohn, 2026, needs more optimization.
25 135 0.128300824797 Henry Cohn, 2026, needs more optimization.
25 136 0.130217025523 Henry Cohn, 2026, needs more optimization.
25 137 0.131780744869 Henry Cohn, 2026, needs more optimization.
25 139 0.131800346327 Henry Cohn, 2026, needs more optimization.
25 140 0.131943452580 Henry Cohn, 2026, needs more optimization.
25 141 0.132719877999 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
25 158 0.137812593843 Henry Cohn, 2026, needs more optimization.
25 159 0.140154574954 Henry Cohn, 2026, needs more optimization.
25 160 0.141422346269 Henry Cohn, 2026, needs more optimization.
25 161 0.142221672186 Henry Cohn, 2026, needs more optimization.
25 167 0.142857140433 Orthogonal union of 165 points in 24 dimensions and 2 points in 1 dimension.
25 174 0.142857140440 Orthogonal union of 172 points in 24 dimensions and 2 points in 1 dimension.
25 176 0.142857172719 Orthogonal union of 174 points in 24 dimensions and 2 points in 1 dimension.
25 177 0.142893491541 Henry Cohn, 2026, needs more optimization.
25 178 0.143244061948 Henry Cohn, 2026, needs more optimization.
25 179 0.143288197044 Henry Cohn, 2026, needs more optimization.
25 180 0.143309214752 Henry Cohn, 2026, needs more optimization.
25 181 0.144756609174 Henry Cohn, 2026, needs more optimization.
25 182 0.144758794789 Henry Cohn, 2026, needs more optimization.
25 183 0.148441318554 Henry Cohn, 2026, needs more optimization.
25 184 0.150238991098 Henry Cohn, 2026, needs more optimization.
25 185 0.150256923482 Henry Cohn, 2026, needs more optimization.
25 186 0.150962876902 Henry Cohn, 2026, needs more optimization.
25 187 0.155201050452 Henry Cohn, 2026, needs more optimization.
25 188 0.156207847674 Henry Cohn, 2026, needs more optimization.
25 189 0.158167009276 Henry Cohn, 2026, needs more optimization.
25 190 0.158299793161 Henry Cohn, 2026, needs more optimization.
25 191 0.161331775247 Henry Cohn, 2026, needs more optimization.
25 192 0.161334324025 Henry Cohn, 2026, needs more optimization.
25 194 0.161336177523 Henry Cohn, 2026, needs more optimization.
25 197 0.161760651318 Henry Cohn, 2026, needs more optimization.
25 198 0.161841388986 Henry Cohn, 2026, needs more optimization.
25 199 0.161843961009 Henry Cohn, 2026, needs more optimization.
25 200 0.161850114643 Henry Cohn, 2026, needs more optimization.
25 201 0.161875838409 Henry Cohn, 2026, needs more optimization.
25 206 0.161890055666 Henry Cohn, 2025, needs more optimization.
25 214 0.161905140019 Orthogonal union of 212 points in 24 dimensions and 2 points in 1 dimension.
25 216 0.161914962876 Henry Cohn, 2026, needs more optimization.
25 217 0.161951938624 Henry Cohn, 2026, needs more optimization.
25 219 0.161955693228 Henry Cohn, 2026, needs more optimization.
25 220 0.162247049168 Henry Cohn, 2026, needs more optimization.
25 221 0.164711057096 Henry Cohn, 2026, needs more optimization.
25 224 0.164712759150 Henry Cohn, 2026, needs more optimization.
25 225 0.166607863008 Orthogonal union of 223 points in 24 dimensions and 2 points in 1 dimension.
25 226 0.166633668265 Orthogonal union of 224 points in 24 dimensions and 2 points in 1 dimension.
25 281 0.166666666667 Orthogonal union of 275 points in 22 dimensions and 6 points in 3 dimensions.
6⁢x−1
25 283 0.166712841552 Henry Cohn, 2026, needs more optimization.
25 284 0.179533531202 Henry Cohn, 2026, needs more optimization.
25 287 0.179536387249 Henry Cohn, 2026, needs more optimization.
25 288 0.179746398971 Henry Cohn, 2026, needs more optimization.
25 299 0.181818181819 Orthogonal union of 297 points in 24 dimensions and 2 points in 1 dimension.
11⁢x−2
25 332 0.193548387097 Orthogonal union of 330 points in 24 dimensions and 2 points in 1 dimension.
31⁢x−6
25 556 0.2 Orthogonal union of 552 points in 23 dimensions and 4 points in 2 dimensions.
5⁢x−1
25 566 0.238095238096 Henry Cohn, 2025.
21⁢x−5
25 567 0.238140742993 Henry Cohn, 2025, needs more optimization.
25 568 0.238222097670 Henry Cohn, 2026, needs more optimization.
25 572 0.238225652680 Henry Cohn, 2026, needs more optimization.
25 576 0.238455704035 Henry Cohn, 2026, needs more optimization.
25 580 0.239534136427 Henry Cohn, 2026, needs more optimization.
25 588 0.241805634200 Henry Cohn, 2026, needs more optimization.
25 596 0.244843693358 Henry Cohn, 2026, needs more optimization.
25 600 0.247273777413 Henry Cohn, 2026, needs more optimization.
25 604 0.247283994767 Henry Cohn, 2026, needs more optimization.
25 612 0.248651724434 Henry Cohn, 2026, needs more optimization.
25 616 0.249338895785 Henry Cohn, 2026, needs more optimization.
25 620 0.249373494425 Henry Cohn, 2026, needs more optimization.
25 628 0.249672626512 Henry Cohn, 2026, needs more optimization.
25 632 0.249856248211 Henry Cohn, 2026, needs more optimization.
25 636 0.249889236005 Henry Cohn, 2026, needs more optimization.
25 640 0.249975942437 Henry Cohn, 2026, needs more optimization.
25 642 0.249995385048 Henry Cohn, 2026, needs more optimization.
25 900 0.25 Henry Cohn, 2025.
4⁢x−1
25 901 0.250172215665 Henry Cohn, 2025, needs more optimization.
25 902 0.250174426298 Henry Cohn, 2025, needs more optimization.
25 903 0.250187558714 Henry Cohn, 2025, needs more optimization.
25 904 0.250190030344 Henry Cohn, 2026, needs more optimization.
25 905 0.250195554497 Henry Cohn, 2025, needs more optimization.
25 906 0.250432380411 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 0.035747988474 Henry Cohn, 2024.
26 55 0.044648817329 Henry Cohn, 2026, needs more optimization.
26 56 0.044677228625 Henry Cohn, 2026, needs more optimization.
26 57 0.045162601400 Henry Cohn, 2026.
26 58 0.045550434603 Henry Cohn, 2024.
26 59 0.046163974402 Henry Cohn, 2025.
26 60 0.046470042214 Henry Cohn, 2026, needs more optimization.
26 61 0.049244768381 Ilmari Vahteristo, 2026.
26 62 0.051941453530 Henry Cohn, 2026, needs more optimization.
26 63 0.054447616037 Henry Cohn, 2026, needs more optimization.
26 64 0.057509209262 Henry Cohn, 2026, needs more optimization.
26 65 0.060322599559 Ilmari Vahteristo, 2026.
26 66 0.062271873063 Ilmari Vahteristo, 2026.
26 67 0.063584340933 Henry Cohn, 2026, needs more optimization.
26 68 0.063615584472 Henry Cohn, 2026, needs more optimization.
26 69 0.065701780856 Henry Cohn, 2026, needs more optimization.
26 70 0.065967079947 Henry Cohn, 2026, needs more optimization.
26 71 0.067339220512 Henry Cohn, 2026, needs more optimization.
26 72 0.068772033414 Henry Cohn, 2026, needs more optimization.
26 73 0.071038864128 Henry Cohn, 2026, needs more optimization.
26 74 0.073221175318 Henry Cohn, 2026, needs more optimization.
26 75 0.074494473225 Henry Cohn, 2026, needs more optimization.
26 76 0.075428208864 Henry Cohn, 2026, needs more optimization.
26 77 0.076616811293 Henry Cohn, 2026, needs more optimization.
26 78 0.076890349677 Henry Cohn, 2026, needs more optimization.
26 79 0.076929054841 Henry Cohn, 2026, needs more optimization.
26 80 0.076970913959 Henry Cohn, 2026, needs more optimization.
26 81 0.077860197134 Henry Cohn, 2026, needs more optimization.
26 82 0.078065084116 Henry Cohn, 2026, needs more optimization.
26 83 0.079135982292 Henry Cohn, 2026, needs more optimization.
26 84 0.079428726177 Henry Cohn, 2026, needs more optimization.
26 85 0.082428660070 Henry Cohn, 2026, needs more optimization.
26 86 0.082680160885 Henry Cohn, 2026, needs more optimization.
26 87 0.082901900395 Henry Cohn, 2026, needs more optimization.
26 88 0.083040165820 Henry Cohn, 2026, needs more optimization.
26 89 0.083272866986 Henry Cohn, 2026, needs more optimization.
26 90 0.083325409942 Henry Cohn, 2026, needs more optimization.
26 91 0.083343090219 Henry Cohn, 2026, needs more optimization.
26 92 0.084461145014 Henry Cohn, 2026, needs more optimization.
26 93 0.085583115229 Henry Cohn, 2026, needs more optimization.
26 94 0.086971261642 Henry Cohn, 2026, needs more optimization.
26 95 0.088505181135 Henry Cohn, 2026, needs more optimization.
26 96 0.089256950363 Henry Cohn, 2026, needs more optimization.
26 97 0.089494716291 Henry Cohn, 2026, needs more optimization.
26 98 0.089888755088 Henry Cohn, 2026, needs more optimization.
26 99 0.090359914861 Henry Cohn, 2026, needs more optimization.
26 100 0.090598268022 Henry Cohn, 2026, needs more optimization.
26 101 0.090627382887 Henry Cohn, 2026, needs more optimization.
26 102 0.090802736280 Henry Cohn, 2026, needs more optimization.
26 103 0.090864963821 Henry Cohn, 2026, needs more optimization.
26 104 0.090902256836 Henry Cohn, 2026, needs more optimization.
26 105 0.090907314760 Henry Cohn, 2026, needs more optimization.
26 108 0.090909090666 Orthogonal union of 104 points in 24 dimensions and 4 points in 2 dimensions.
26 109 0.090911118785 Henry Cohn, 2026, needs more optimization.
26 110 0.090916330156 Henry Cohn, 2026, needs more optimization.
26 111 0.091962301617 Henry Cohn, 2026, needs more optimization.
26 112 0.094699820916 Henry Cohn, 2026, needs more optimization.
26 113 0.098024434962 Henry Cohn, 2026, needs more optimization.
26 114 0.101011474714 Henry Cohn, 2026, needs more optimization.
26 119 0.103125332235 Henry Cohn, 2026.
191⁢x2−10⁢x−1
26 120 0.103389121229 Henry Cohn, 2026, needs more optimization.
26 121 0.104420094616 Henry Cohn, 2026, needs more optimization.
26 122 0.106117393680 Henry Cohn, 2026, needs more optimization.
26 123 0.106828773499 Henry Cohn, 2026, needs more optimization.
26 124 0.107368191392 Henry Cohn, 2026, needs more optimization.
26 125 0.108144273465 Henry Cohn, 2026, needs more optimization.
26 126 0.108632867044 Henry Cohn, 2026, needs more optimization.
26 127 0.109260311627 Henry Cohn, 2026, needs more optimization.
26 128 0.111104370546 Henry Cohn, 2026, needs more optimization.
26 129 0.111134275955 Henry Cohn, 2026, needs more optimization.
26 130 0.111135339092 Henry Cohn, 2026, needs more optimization.
26 131 0.111163874604 Henry Cohn, 2026, needs more optimization.
26 132 0.114492372958 Henry Cohn, 2026, needs more optimization.
26 133 0.115303164421 Henry Cohn, 2026, needs more optimization.
26 134 0.116502301293 Henry Cohn, 2026, needs more optimization.
26 135 0.120126797537 Henry Cohn, 2026, needs more optimization.
26 136 0.121250353689 Henry Cohn, 2026, needs more optimization.
26 137 0.123454793143 Henry Cohn, 2026, needs more optimization.
26 138 0.125222723437 Henry Cohn, 2026, needs more optimization.
26 139 0.127316050422 Henry Cohn, 2026, needs more optimization.
26 140 0.128748167883 Henry Cohn, 2026, needs more optimization.
26 141 0.130090148924 Henry Cohn, 2026, needs more optimization.
26 143 0.131677462055 Henry Cohn, 2026, needs more optimization.
26 144 0.131749173554 Henry Cohn, 2026, needs more optimization.
26 145 0.131924904830 Henry Cohn, 2026, needs more optimization.
26 146 0.132356295141 Henry Cohn, 2026, needs more optimization.
26 147 0.132563647050 Henry Cohn, 2026, needs more optimization.
26 148 0.133094846911 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 0.134477328125 Henry Cohn, 2026, needs more optimization.
26 160 0.134766028310 Henry Cohn, 2026, needs more optimization.
26 163 0.136862682914 Henry Cohn, 2026, needs more optimization.
26 164 0.137705162794 Henry Cohn, 2026, needs more optimization.
26 165 0.138801905680 Henry Cohn, 2026, needs more optimization.
26 166 0.140055172927 Henry Cohn, 2026, needs more optimization.
26 167 0.141427556197 Henry Cohn, 2026, needs more optimization.
26 168 0.142224166458 Henry Cohn, 2026, needs more optimization.
26 170 0.142816407359 Henry Cohn, 2026, needs more optimization.
26 171 0.142845030693 Henry Cohn, 2026, needs more optimization.
26 174 0.142848949139 Henry Cohn, 2026, needs more optimization.
26 176 0.142857140440 Orthogonal union of 172 points in 24 dimensions and 4 points in 2 dimensions.
26 178 0.142857172719 Orthogonal union of 174 points in 24 dimensions and 4 points in 2 dimensions.
26 179 0.142862632100 Henry Cohn, 2026, needs more optimization.
26 180 0.142867565216 Henry Cohn, 2026, needs more optimization.
26 181 0.142875069744 Henry Cohn, 2026, needs more optimization.
26 182 0.142886715514 Henry Cohn, 2026, needs more optimization.
26 185 0.142933680729 Henry Cohn, 2026, needs more optimization.
26 186 0.143671187633 Henry Cohn, 2026, needs more optimization.
26 187 0.145137827729 Henry Cohn, 2026, needs more optimization.
26 188 0.145491106769 Henry Cohn, 2026, needs more optimization.
26 189 0.146762402220 Henry Cohn, 2026, needs more optimization.
26 190 0.148056964477 Henry Cohn, 2026, needs more optimization.
26 191 0.149212065856 Henry Cohn, 2026, needs more optimization.
26 192 0.150074064370 Henry Cohn, 2026, needs more optimization.
26 193 0.150195612350 Henry Cohn, 2026, needs more optimization.
26 194 0.152573083967 Henry Cohn, 2026, needs more optimization.
26 195 0.154216418239 Henry Cohn, 2026, needs more optimization.
26 196 0.157310364100 Henry Cohn, 2026, needs more optimization.
26 197 0.158131818566 Henry Cohn, 2026, needs more optimization.
26 198 0.158306003506 Henry Cohn, 2026, needs more optimization.
26 199 0.159339645016 Henry Cohn, 2026, needs more optimization.
26 200 0.160098246872 Henry Cohn, 2026, needs more optimization.
26 201 0.160123998877 Henry Cohn, 2026, needs more optimization.
26 202 0.160969512771 Henry Cohn, 2026, needs more optimization.
26 204 0.161313459390 Henry Cohn, 2026, needs more optimization.
26 205 0.161525413521 Henry Cohn, 2026, needs more optimization.
26 208 0.161559492881 Henry Cohn, 2026, needs more optimization.
26 214 0.161813630738 Henry Cohn, 2026, needs more optimization.
26 221 0.161889890677 Henry Cohn, 2026, needs more optimization.
26 225 0.161911531138 Henry Cohn, 2026, needs more optimization.
26 227 0.161983210773 Henry Cohn, 2026, needs more optimization.
26 228 0.162054821023 Henry Cohn, 2026, needs more optimization.
26 229 0.162405138372 Henry Cohn, 2026, needs more optimization.
26 230 0.162588295291 Henry Cohn, 2026, needs more optimization.
26 231 0.162694975431 Henry Cohn, 2026, needs more optimization.
26 232 0.164613568793 Henry Cohn, 2026, needs more optimization.
26 234 0.164915453186 Henry Cohn, 2026, needs more optimization.
26 235 0.165109450766 Henry Cohn, 2026, needs more optimization.
26 236 0.166472443455 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
26 286 0.179533531202 Orthogonal union of 284 points in 25 dimensions and 2 points in 1 dimension.
26 289 0.179536387249 Orthogonal union of 287 points in 25 dimensions and 2 points in 1 dimension.
26 291 0.179540728357 Henry Cohn, 2026, needs more optimization.
26 292 0.179541108819 Henry Cohn, 2026, needs more optimization.
26 296 0.179551049602 Henry Cohn, 2026, needs more optimization.
26 297 0.179672295545 Henry Cohn, 2026, needs more optimization.
26 298 0.180327752656 Henry Cohn, 2026, needs more optimization.
26 301 0.181818181819 Orthogonal union of 297 points in 24 dimensions and 4 points in 2 dimensions.
11⁢x−2
26 334 0.193548387097 Orthogonal union of 330 points in 24 dimensions and 4 points in 2 dimensions.
31⁢x−6
26 558 0.2 Orthogonal union of 552 points in 23 dimensions and 6 points in 3 dimensions.
5⁢x−1
26 559 0.200074016035 Henry Cohn, 2026, needs more optimization.
26 560 0.200082923136 Henry Cohn, 2025, needs more optimization.
26 562 0.200092912683 Henry Cohn, 2026, needs more optimization.
26 563 0.200101611377 Henry Cohn, 2026, needs more optimization.
26 570 0.238095238096 Orthogonal union of 554 points in 21 dimensions and 16 points in 5 dimensions.
21⁢x−5
26 572 0.238172425447 Henry Cohn, 2026, needs more optimization.
26 576 0.238219624605 Henry Cohn, 2026, needs more optimization.
26 580 0.238307863858 Henry Cohn, 2026, needs more optimization.
26 588 0.238593885182 Henry Cohn, 2026, needs more optimization.
26 596 0.239608145954 Henry Cohn, 2026, needs more optimization.
26 604 0.242894710613 Henry Cohn, 2026, needs more optimization.
26 612 0.245725454066 Henry Cohn, 2026, needs more optimization.
26 620 0.247512109662 Henry Cohn, 2026, needs more optimization.
26 628 0.248468221990 Henry Cohn, 2026, needs more optimization.
26 632 0.249084908179 Henry Cohn, 2026, needs more optimization.
26 635 0.249218339467 Henry Cohn, 2026, needs more optimization.
26 636 0.249218339690 Henry Cohn, 2026, needs more optimization.
26 644 0.249645265443 Henry Cohn, 2026, needs more optimization.
26 652 0.249824023123 Henry Cohn, 2026, needs more optimization.
26 660 0.249913277894 Henry Cohn, 2026, needs more optimization.
26 664 0.249960889164 Henry Cohn, 2026, needs more optimization.
26 666 0.249992105150 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
26 904 0.250129113023 Henry Cohn, 2026, needs more optimization.
26 907 0.250132202205 Henry Cohn, 2025, needs more optimization.
26 908 0.250172640654 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 57 0.043679995742 Henry Cohn, 2024.
27 58 0.044452314700 Henry Cohn, 2025, needs more optimization.
27 59 0.044834667132 Henry Cohn, 2026, needs more optimization.
27 60 0.045477973897 Henry Cohn, 2024, needs more optimization.
27 61 0.045484387668 Henry Cohn, 2024, needs more optimization.
27 62 0.046198040189 Henry Cohn, 2025.
27 63 0.047991049635 Henry Cohn, 2026, needs more optimization.
27 64 0.050812921596 Ilmari Vahteristo, 2026.
27 65 0.054279304766 Ilmari Vahteristo, 2026.
27 66 0.056580679072 Ilmari Vahteristo, 2026.
27 67 0.058509552092 Ilmari Vahteristo, 2026.
27 68 0.060176451205 Ilmari Vahteristo, 2026.
27 69 0.061864367114 Ilmari Vahteristo, 2026.
27 70 0.063020456858 Henry Cohn, 2026, needs more optimization.
27 71 0.064734334003 Henry Cohn, 2026, needs more optimization.
27 72 0.065180354550 Henry Cohn, 2026, needs more optimization.
27 73 0.065970170202 Henry Cohn, 2026, needs more optimization.
27 74 0.066455678003 Henry Cohn, 2026, needs more optimization.
27 75 0.068140390838 Henry Cohn, 2026, needs more optimization.
27 76 0.070143504741 Henry Cohn, 2026, needs more optimization.
27 77 0.072407277927 Henry Cohn, 2026, needs more optimization.
27 78 0.074685407780 Henry Cohn, 2025, needs more optimization.
27 79 0.075388526440 Henry Cohn, 2026, needs more optimization.
27 80 0.076183661282 Henry Cohn, 2026, needs more optimization.
27 81 0.076903197736 Henry Cohn, 2026, needs more optimization.
27 82 0.076914784420 Henry Cohn, 2026, needs more optimization.
27 83 0.077065977390 Henry Cohn, 2026, needs more optimization.
27 84 0.077110338996 Henry Cohn, 2026, needs more optimization.
27 85 0.077413552992 Henry Cohn, 2026, needs more optimization.
27 86 0.077736768150 Henry Cohn, 2026, needs more optimization.
27 87 0.078596822028 Henry Cohn, 2026, needs more optimization.
27 88 0.079208430417 Henry Cohn, 2026, needs more optimization.
27 92 0.080685611688 Henry Cohn, 2026, needs more optimization.
27 93 0.080686333418 Henry Cohn, 2026, needs more optimization.
27 96 0.080689661386 Henry Cohn, 2026, needs more optimization.
27 97 0.080738068610 Henry Cohn, 2026, needs more optimization.
27 98 0.081861525900 Henry Cohn, 2026, needs more optimization.
27 99 0.087657549958 Henry Cohn, 2026, needs more optimization.
27 100 0.088573143124 Henry Cohn, 2026, needs more optimization.
27 101 0.089284624014 Henry Cohn, 2025, needs more optimization.
27 102 0.089876296956 Henry Cohn, 2026, needs more optimization.
27 103 0.090178224354 Henry Cohn, 2026, needs more optimization.
27 104 0.090444555490 Henry Cohn, 2026, needs more optimization.
27 105 0.090552549258 Henry Cohn, 2026, needs more optimization.
27 106 0.090633494174 Henry Cohn, 2026, needs more optimization.
27 107 0.090783999576 Henry Cohn, 2026, needs more optimization.
27 108 0.090790215093 Henry Cohn, 2026, needs more optimization.
27 109 0.090847120956 Henry Cohn, 2026, needs more optimization.
27 110 0.090870650464 Henry Cohn, 2024, needs more optimization.
27 111 0.090900390936 Henry Cohn, 2026, needs more optimization.
27 112 0.090907019693 Henry Cohn, 2026, needs more optimization.
27 113 0.090958539364 Henry Cohn, 2026, needs more optimization.
27 114 0.091623787351 Henry Cohn, 2026, needs more optimization.
27 115 0.093391124521 Henry Cohn, 2026, needs more optimization.
27 116 0.096257658725 Henry Cohn, 2026, needs more optimization.
27 117 0.098876011407 Henry Cohn, 2026, needs more optimization.
27 118 0.101486371476 Henry Cohn, 2026, needs more optimization.
27 121 0.103125332235 Orthogonal union of 119 points in 26 dimensions and 2 points in 1 dimension.
191⁢x2−10⁢x−1
27 123 0.103125332798 Henry Cohn, 2026, needs more optimization.
27 124 0.103125651194 Henry Cohn, 2026, needs more optimization.
27 125 0.103125890679 Henry Cohn, 2026, needs more optimization.
27 126 0.104878726889 Henry Cohn, 2026, needs more optimization.
27 127 0.106667465179 Henry Cohn, 2026, needs more optimization.
27 128 0.107144963945 Henry Cohn, 2026, needs more optimization.
27 129 0.107483786660 Henry Cohn, 2026, needs more optimization.
27 130 0.108488894961 Henry Cohn, 2026, needs more optimization.
27 131 0.109689406485 Henry Cohn, 2026, needs more optimization.
27 132 0.109735632194 Henry Cohn, 2026, needs more optimization.
27 133 0.110916947898 Henry Cohn, 2026, needs more optimization.
27 134 0.111073965210 Henry Cohn, 2026, needs more optimization.
27 135 0.113473209777 Henry Cohn, 2026, needs more optimization.
27 136 0.114173526701 Henry Cohn, 2026, needs more optimization.
27 137 0.115517618396 Henry Cohn, 2026, needs more optimization.
27 138 0.117060595111 Henry Cohn, 2026, needs more optimization.
27 139 0.118365367403 Henry Cohn, 2026, needs more optimization.
27 140 0.119821045450 Henry Cohn, 2026, needs more optimization.
27 141 0.120668521094 Henry Cohn, 2026, needs more optimization.
27 142 0.122869450665 Henry Cohn, 2026, needs more optimization.
27 143 0.124319887132 Henry Cohn, 2026, needs more optimization.
27 144 0.125680618660 Henry Cohn, 2026, needs more optimization.
27 145 0.127113320181 Henry Cohn, 2026, needs more optimization.
27 146 0.128568633358 Henry Cohn, 2026, needs more optimization.
27 147 0.129598837475 Henry Cohn, 2026, needs more optimization.
27 148 0.130764793439 Henry Cohn, 2026, needs more optimization.
27 149 0.132039336500 Henry Cohn, 2026, needs more optimization.
27 150 0.132834409706 Henry Cohn, 2025, needs more optimization.
27 152 0.132962586273 Henry Cohn, 2026, needs more optimization.
27 153 0.133088789941 Henry Cohn, 2026, needs more optimization.
27 154 0.133139567122 Henry Cohn, 2026, needs more optimization.
27 155 0.133200807256 Henry Cohn, 2026, needs more optimization.
27 156 0.133239352820 Henry Cohn, 2026, needs more optimization.
27 157 0.133273021157 Henry Cohn, 2026, needs more optimization.
27 160 0.133281675069 Henry Cohn, 2026, needs more optimization.
27 161 0.133316359293 Henry Cohn, 2026, needs more optimization.
27 162 0.133328342255 Henry Cohn, 2026, needs more optimization.
27 163 0.133542925889 Henry Cohn, 2026, needs more optimization.
27 164 0.134258075788 Henry Cohn, 2026, needs more optimization.
27 165 0.135666932327 Henry Cohn, 2026, needs more optimization.
27 168 0.135708181860 Henry Cohn, 2026, needs more optimization.
27 169 0.136022647391 Henry Cohn, 2026, needs more optimization.
27 170 0.136789049345 Henry Cohn, 2026, needs more optimization.
27 171 0.142162334813 Henry Cohn, 2026, needs more optimization.
27 172 0.142278362134 Henry Cohn, 2026, needs more optimization.
27 173 0.142310634237 Henry Cohn, 2026, needs more optimization.
27 174 0.142352904784 Henry Cohn, 2026, needs more optimization.
27 175 0.142436398597 Henry Cohn, 2026, needs more optimization.
27 176 0.142463353894 Henry Cohn, 2026, needs more optimization.
27 177 0.142493557618 Henry Cohn, 2026, needs more optimization.
27 178 0.142515678753 Henry Cohn, 2026, needs more optimization.
27 179 0.142722110123 Henry Cohn, 2026, needs more optimization.
27 180 0.142727522751 Henry Cohn, 2026, needs more optimization.
27 181 0.142734675260 Henry Cohn, 2026, needs more optimization.
27 182 0.142740256002 Henry Cohn, 2026, needs more optimization.
27 183 0.142747239529 Henry Cohn, 2026, needs more optimization.
27 184 0.142810354581 Henry Cohn, 2026, needs more optimization.
27 185 0.142815957967 Henry Cohn, 2026, needs more optimization.
27 186 0.142818327381 Henry Cohn, 2026, needs more optimization.
27 187 0.142820356559 Henry Cohn, 2026, needs more optimization.
27 188 0.142823757768 Henry Cohn, 2026, needs more optimization.
27 189 0.142826775521 Henry Cohn, 2026, needs more optimization.
27 190 0.142829747582 Henry Cohn, 2026, needs more optimization.
27 191 0.142869012975 Henry Cohn, 2026, needs more optimization.
27 192 0.143076333978 Henry Cohn, 2026, needs more optimization.
27 193 0.143463247360 Henry Cohn, 2026, needs more optimization.
27 194 0.143951734956 Henry Cohn, 2026, needs more optimization.
27 195 0.145469229060 Henry Cohn, 2026, needs more optimization.
27 196 0.146195800191 Henry Cohn, 2026, needs more optimization.
27 197 0.146680515904 Henry Cohn, 2026, needs more optimization.
27 198 0.147574571769 Henry Cohn, 2026, needs more optimization.
27 199 0.148384094301 Henry Cohn, 2026, needs more optimization.
27 200 0.148972318596 Henry Cohn, 2026, needs more optimization.
27 201 0.150007054145 Henry Cohn, 2026, needs more optimization.
27 202 0.153047382197 Henry Cohn, 2026, needs more optimization.
27 203 0.153841531638 Henry Cohn, 2026, needs more optimization.
27 204 0.154381647790 Henry Cohn, 2026, needs more optimization.
27 205 0.154603081441 Henry Cohn, 2026, needs more optimization.
27 206 0.159259395742 Henry Cohn, 2026, needs more optimization.
27 207 0.159424904332 Henry Cohn, 2026, needs more optimization.
27 208 0.159682991607 Henry Cohn, 2026, needs more optimization.
27 209 0.160124978214 Henry Cohn, 2026, needs more optimization.
27 210 0.160674060969 Henry Cohn, 2026, needs more optimization.
27 211 0.160711441072 Henry Cohn, 2026, needs more optimization.
27 212 0.160810028737 Henry Cohn, 2026, needs more optimization.
27 213 0.160881060563 Henry Cohn, 2026, needs more optimization.
27 215 0.160975288060 Henry Cohn, 2026, needs more optimization.
27 216 0.161168769968 Henry Cohn, 2026, needs more optimization.
27 217 0.161447223364 Henry Cohn, 2026, needs more optimization.
27 218 0.161475844513 Henry Cohn, 2026, needs more optimization.
27 219 0.161507556597 Henry Cohn, 2026, needs more optimization.
27 220 0.161567357429 Henry Cohn, 2026, needs more optimization.
27 221 0.161597809935 Henry Cohn, 2026, needs more optimization.
27 222 0.161640899830 Henry Cohn, 2026, needs more optimization.
27 223 0.161716190392 Henry Cohn, 2026, needs more optimization.
27 224 0.161726521527 Henry Cohn, 2026, needs more optimization.
27 225 0.161761903308 Henry Cohn, 2026, needs more optimization.
27 226 0.161766235904 Henry Cohn, 2026, needs more optimization.
27 227 0.161771053879 Henry Cohn, 2026, needs more optimization.
27 228 0.161776510128 Henry Cohn, 2026, needs more optimization.
27 229 0.161784900622 Henry Cohn, 2026, needs more optimization.
27 230 0.161795356459 Henry Cohn, 2026, needs more optimization.
27 231 0.161858738350 Henry Cohn, 2026, needs more optimization.
27 232 0.161888218859 Henry Cohn, 2026, needs more optimization.
27 235 0.161890207420 Henry Cohn, 2026, needs more optimization.
27 237 0.161965564949 Henry Cohn, 2026, needs more optimization.
27 238 0.162440623494 Henry Cohn, 2026, needs more optimization.
27 239 0.162927835686 Henry Cohn, 2026, needs more optimization.
27 240 0.163014821790 Henry Cohn, 2026, needs more optimization.
27 241 0.163345086587 Henry Cohn, 2026, needs more optimization.
27 243 0.163448848811 Henry Cohn, 2026, needs more optimization.
27 245 0.165099354590 Henry Cohn, 2026, needs more optimization.
27 247 0.165171967135 Henry Cohn, 2026, needs more optimization.
27 248 0.165913619392 Henry Cohn, 2026, needs more optimization.
27 287 0.166666666667 Orthogonal union of 275 points in 22 dimensions and 12 points in 5 dimensions.
6⁢x−1
27 288 0.166687947349 Henry Cohn, 2026, needs more optimization.
27 289 0.166696111005 Henry Cohn, 2026, needs more optimization.
27 290 0.179492432689 Henry Cohn, 2026, needs more optimization.
27 291 0.179492839372 Henry Cohn, 2026, needs more optimization.
27 292 0.179493118776 Henry Cohn, 2026, needs more optimization.
27 293 0.179493566291 Henry Cohn, 2026, needs more optimization.
27 294 0.179493965203 Henry Cohn, 2026, needs more optimization.
27 295 0.179494496941 Henry Cohn, 2026, needs more optimization.
27 296 0.179494996359 Henry Cohn, 2026, needs more optimization.
27 297 0.179495688918 Henry Cohn, 2026, needs more optimization.
27 298 0.179496613103 Henry Cohn, 2026, needs more optimization.
27 299 0.179498235412 Henry Cohn, 2026, needs more optimization.
27 300 0.179500637410 Henry Cohn, 2026, needs more optimization.
27 301 0.179572440091 Henry Cohn, 2026, needs more optimization.
27 303 0.181818181819 Orthogonal union of 297 points in 24 dimensions and 6 points in 3 dimensions.
11⁢x−2
27 336 0.193548387097 Orthogonal union of 330 points in 24 dimensions and 6 points in 3 dimensions.
31⁢x−6
27 339 0.199999887471 Henry Cohn, 2026, needs more optimization.
27 340 0.199999985070 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
27 563 0.200069910253 Henry Cohn, 2026, needs more optimization.
27 564 0.200071739851 Henry Cohn, 2025, needs more optimization.
27 566 0.200076155705 Henry Cohn, 2025, needs more optimization.
27 568 0.200135182099 Henry Cohn, 2026, needs more optimization.
27 574 0.238095238096 Orthogonal union of 554 points in 21 dimensions and 20 points in 6 dimensions.
21⁢x−5
27 576 0.238109925296 Henry Cohn, 2026, needs more optimization.
27 577 0.238137087627 Henry Cohn, 2026, needs more optimization.
27 580 0.238142233407 Henry Cohn, 2026, needs more optimization.
27 588 0.238161083887 Henry Cohn, 2026, needs more optimization.
27 596 0.238207206832 Henry Cohn, 2026, needs more optimization.
27 604 0.238399890402 Henry Cohn, 2026, needs more optimization.
27 612 0.239166035658 Henry Cohn, 2026, needs more optimization.
27 620 0.241495642847 Henry Cohn, 2026, needs more optimization.
27 628 0.244293223902 Henry Cohn, 2026, needs more optimization.
27 636 0.246018298720 Henry Cohn, 2026, needs more optimization.
27 644 0.247363798966 Henry Cohn, 2026, needs more optimization.
27 652 0.248274699172 Henry Cohn, 2026, needs more optimization.
27 660 0.248937425811 Henry Cohn, 2026, needs more optimization.
27 668 0.249461567860 Henry Cohn, 2026, needs more optimization.
27 676 0.249707754126 Henry Cohn, 2026, needs more optimization.
27 680 0.249830157413 Henry Cohn, 2026, needs more optimization.
27 684 0.249866421550 Henry Cohn, 2026, needs more optimization.
27 688 0.249941784708 Henry Cohn, 2026, needs more optimization.
27 692 0.249949554902 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
27 908 0.250076752649 Henry Cohn, 2025, needs more optimization.
27 909 0.250084000707 Henry Cohn, 2025, needs more optimization.
27 910 0.250086806348 Henry Cohn, 2025, needs more optimization.
27 912 0.250095826107 Henry Cohn, 2026, needs more optimization.
27 913 0.250099713424 Henry Cohn, 2025, needs more optimization.
27 916 0.250106086370 Henry Cohn, 2026, needs more optimization.
27 917 0.250108530833 Henry Cohn, 2025, needs more optimization.
27 918 0.254738822225 Henry Cohn, 2026, needs more optimization.
27 1024 0.272727272728 Code with 1024 points in 22 dimensions.
11⁢x−3
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 Henry Cohn, 2025.
30⁢x−1
28 59 0.042130667237 Henry Cohn, 2024.
28 60 0.044218259412 Henry Cohn, 2026, needs more optimization.
28 61 0.044427604359 Henry Cohn, 2024, needs more optimization.
28 62 0.044625901428 Henry Cohn, 2024, needs more optimization.
28 63 0.045182176447 Henry Cohn, 2025.
28 64 0.045901657151 Henry Cohn, 2024, needs more optimization.
28 65 0.046145258913 Ilmari Vahteristo, 2026.
28 66 0.047459655819 Henry Cohn, 2026, needs more optimization.
28 67 0.052323638850 Henry Cohn, 2026, needs more optimization.
28 68 0.054470922409 Ilmari Vahteristo, 2026.
28 69 0.056753787692 Ilmari Vahteristo, 2026.
28 70 0.058214949264 Ilmari Vahteristo, 2026.
28 71 0.059766428606 Ilmari Vahteristo, 2026.
28 72 0.061426204796 Ilmari Vahteristo, 2026.
28 73 0.063278585592 Ilmari Vahteristo, 2026.
28 74 0.064151244567 Henry Cohn, 2026, needs more optimization.
28 75 0.064464413105 Henry Cohn, 2026, needs more optimization.
28 76 0.065175455351 Henry Cohn, 2026, needs more optimization.
28 77 0.065946455320 Henry Cohn, 2026, needs more optimization.
28 78 0.067571589868 Henry Cohn, 2026, needs more optimization.
28 79 0.069499875187 Henry Cohn, 2026, needs more optimization.
28 80 0.070926468281 Henry Cohn, 2026, needs more optimization.
28 81 0.073525822534 Henry Cohn, 2026, needs more optimization.
28 82 0.074611025346 Henry Cohn, 2026, needs more optimization.
28 83 0.075254176337 Henry Cohn, 2026, needs more optimization.
28 84 0.076025802568 Henry Cohn, 2026, needs more optimization.
28 85 0.076872370934 Henry Cohn, 2026, needs more optimization.
28 86 0.076923977005 Henry Cohn, 2026, needs more optimization.
28 87 0.076955712598 Henry Cohn, 2026, needs more optimization.
28 88 0.077113470975 Henry Cohn, 2026, needs more optimization.
28 89 0.077467120610 Henry Cohn, 2026, needs more optimization.
28 90 0.077724114982 Henry Cohn, 2026, needs more optimization.
28 91 0.078601510699 Henry Cohn, 2026, needs more optimization.
28 92 0.078830242372 Henry Cohn, 2026, needs more optimization.
28 93 0.079271710144 Henry Cohn, 2026, needs more optimization.
28 94 0.079557626814 Henry Cohn, 2026, needs more optimization.
28 95 0.079928574733 Henry Cohn, 2026, needs more optimization.
28 96 0.080268571925 Henry Cohn, 2026, needs more optimization.
28 97 0.080574990897 Henry Cohn, 2026, needs more optimization.
28 98 0.080620406437 Henry Cohn, 2026, needs more optimization.
28 99 0.080685615344 Henry Cohn, 2026, needs more optimization.
28 100 0.080691901296 Henry Cohn, 2026, needs more optimization.
28 101 0.080797928679 Henry Cohn, 2026, needs more optimization.
28 102 0.083360350094 Henry Cohn, 2026, needs more optimization.
28 103 0.084604797113 Henry Cohn, 2026, needs more optimization.
28 104 0.087202826891 Henry Cohn, 2026, needs more optimization.
28 105 0.088002557923 Henry Cohn, 2026, needs more optimization.
28 106 0.088470797162 Henry Cohn, 2026, needs more optimization.
28 107 0.089395286803 Henry Cohn, 2026, needs more optimization.
28 108 0.089580869149 Henry Cohn, 2026, needs more optimization.
28 109 0.089897939279 Henry Cohn, 2026, needs more optimization.
28 110 0.090255695226 Henry Cohn, 2026, needs more optimization.
28 112 0.090571969089 Henry Cohn, 2026, needs more optimization.
28 113 0.090581506565 Henry Cohn, 2026, needs more optimization.
28 114 0.090757595678 Henry Cohn, 2026, needs more optimization.
28 115 0.090848489913 Henry Cohn, 2026, needs more optimization.
28 116 0.090898347529 Henry Cohn, 2026, needs more optimization.
28 117 0.090940145071 Henry Cohn, 2026, needs more optimization.
28 118 0.091808410424 Henry Cohn, 2026, needs more optimization.
28 119 0.094736990935 Henry Cohn, 2026, needs more optimization.
28 120 0.096286493392 Henry Cohn, 2026, needs more optimization.
28 121 0.098163186868 Henry Cohn, 2026, needs more optimization.
28 122 0.099833837861 Henry Cohn, 2026, needs more optimization.
28 123 0.101818357108 Henry Cohn, 2026, needs more optimization.
28 125 0.103078638343 Henry Cohn, 2026, needs more optimization.
28 127 0.103125377262 Henry Cohn, 2026, needs more optimization.
28 128 0.103126189303 Henry Cohn, 2026, needs more optimization.
28 129 0.103134430085 Henry Cohn, 2026, needs more optimization.
28 130 0.103617981762 Henry Cohn, 2026, needs more optimization.
28 131 0.104465547746 Henry Cohn, 2026, needs more optimization.
28 132 0.105993238672 Henry Cohn, 2026, needs more optimization.
28 133 0.107041147607 Henry Cohn, 2026, needs more optimization.
28 134 0.108139525644 Henry Cohn, 2026, needs more optimization.
28 135 0.109560481177 Henry Cohn, 2026, needs more optimization.
28 136 0.109836220042 Henry Cohn, 2026, needs more optimization.
28 137 0.110512044303 Henry Cohn, 2026, needs more optimization.
28 138 0.111293073189 Henry Cohn, 2026, needs more optimization.
28 139 0.112084993060 Henry Cohn, 2026, needs more optimization.
28 140 0.113425277406 Henry Cohn, 2026, needs more optimization.
28 141 0.114308855606 Henry Cohn, 2026, needs more optimization.
28 142 0.115151001926 Henry Cohn, 2026, needs more optimization.
28 143 0.116332359204 Henry Cohn, 2026, needs more optimization.
28 144 0.117490823219 Henry Cohn, 2026, needs more optimization.
28 145 0.118804586203 Henry Cohn, 2026, needs more optimization.
28 146 0.119866188383 Henry Cohn, 2026, needs more optimization.
28 147 0.120866781562 Henry Cohn, 2026, needs more optimization.
28 148 0.122044345163 Henry Cohn, 2026, needs more optimization.
28 149 0.123283124897 Henry Cohn, 2026, needs more optimization.
28 150 0.124465724270 Henry Cohn, 2026, needs more optimization.
28 151 0.125310821278 Henry Cohn, 2026, needs more optimization.
28 152 0.126335505353 Henry Cohn, 2026, needs more optimization.
28 153 0.127867331423 Henry Cohn, 2026, needs more optimization.
28 154 0.129077007676 Henry Cohn, 2026, needs more optimization.
28 155 0.130243077928 Henry Cohn, 2026, needs more optimization.
28 156 0.131023955203 Henry Cohn, 2026, needs more optimization.
28 157 0.131490147907 Henry Cohn, 2026, needs more optimization.
28 158 0.131648392517 Henry Cohn, 2026, needs more optimization.
28 159 0.131955323298 Henry Cohn, 2026, needs more optimization.
28 160 0.132280463960 Henry Cohn, 2026, needs more optimization.
28 161 0.132427898598 Henry Cohn, 2026, needs more optimization.
28 162 0.132720176996 Henry Cohn, 2026, needs more optimization.
28 163 0.132892915806 Henry Cohn, 2026, needs more optimization.
28 164 0.132945071753 Henry Cohn, 2026, needs more optimization.
28 165 0.133057137561 Henry Cohn, 2026, needs more optimization.
28 166 0.133177322883 Henry Cohn, 2026, needs more optimization.
28 167 0.133239041896 Henry Cohn, 2026, needs more optimization.
28 168 0.133396933855 Henry Cohn, 2026, needs more optimization.
28 169 0.133529412089 Henry Cohn, 2026, needs more optimization.
28 170 0.135708181860 Orthogonal union of 168 points in 27 dimensions and 2 points in 1 dimension.
28 171 0.136022647391 Orthogonal union of 169 points in 27 dimensions and 2 points in 1 dimension.
28 172 0.136789049345 Orthogonal union of 170 points in 27 dimensions and 2 points in 1 dimension.
28 173 0.141184501363 Henry Cohn, 2026, needs more optimization.
28 174 0.141394988066 Henry Cohn, 2026, needs more optimization.
28 175 0.141437511577 Henry Cohn, 2026, needs more optimization.
28 176 0.141571736292 Henry Cohn, 2026, needs more optimization.
28 177 0.141616237491 Henry Cohn, 2026, needs more optimization.
28 178 0.141761447172 Henry Cohn, 2026, needs more optimization.
28 179 0.141855088655 Henry Cohn, 2026, needs more optimization.
28 180 0.141873422464 Henry Cohn, 2026, needs more optimization.
28 181 0.141989770735 Henry Cohn, 2026, needs more optimization.
28 182 0.141997560157 Henry Cohn, 2026, needs more optimization.
28 183 0.142315476259 Henry Cohn, 2026, needs more optimization.
28 184 0.142337499902 Henry Cohn, 2026, needs more optimization.
28 185 0.142359114708 Henry Cohn, 2026, needs more optimization.
28 186 0.142370056586 Henry Cohn, 2026, needs more optimization.
28 187 0.142431035802 Henry Cohn, 2026, needs more optimization.
28 188 0.142526151768 Henry Cohn, 2026, needs more optimization.
28 189 0.142535678372 Henry Cohn, 2026, needs more optimization.
28 190 0.142542094159 Henry Cohn, 2026, needs more optimization.
28 191 0.142550928966 Henry Cohn, 2026, needs more optimization.
28 192 0.142570810396 Henry Cohn, 2026, needs more optimization.
28 193 0.142706931386 Henry Cohn, 2026, needs more optimization.
28 194 0.142741767413 Henry Cohn, 2026, needs more optimization.
28 195 0.142752503589 Henry Cohn, 2026, needs more optimization.
28 196 0.142767752948 Henry Cohn, 2026, needs more optimization.
28 197 0.142849220586 Henry Cohn, 2026, needs more optimization.
28 198 0.142854602233 Henry Cohn, 2026, needs more optimization.
28 199 0.143041492564 Henry Cohn, 2026, needs more optimization.
28 200 0.143384638181 Henry Cohn, 2026, needs more optimization.
28 201 0.143879484424 Henry Cohn, 2026, needs more optimization.
28 202 0.144264140230 Henry Cohn, 2026, needs more optimization.
28 203 0.145128242910 Henry Cohn, 2026, needs more optimization.
28 204 0.145981090303 Henry Cohn, 2026, needs more optimization.
28 205 0.146246337867 Henry Cohn, 2026, needs more optimization.
28 206 0.147829714899 Henry Cohn, 2026, needs more optimization.
28 207 0.148630210050 Henry Cohn, 2026, needs more optimization.
28 209 0.148882443232 Henry Cohn, 2026, needs more optimization.
28 210 0.148958481245 Henry Cohn, 2026, needs more optimization.
28 211 0.149045953846 Henry Cohn, 2026, needs more optimization.
28 212 0.150485820013 Henry Cohn, 2026, needs more optimization.
28 213 0.150576935023 Henry Cohn, 2026, needs more optimization.
28 214 0.153768116470 Henry Cohn, 2026, needs more optimization.
28 215 0.153811576046 Henry Cohn, 2026, needs more optimization.
28 216 0.153987301044 Henry Cohn, 2026, needs more optimization.
28 217 0.154162866703 Henry Cohn, 2026, needs more optimization.
28 218 0.155760690761 Henry Cohn, 2026, needs more optimization.
28 219 0.155880315605 Henry Cohn, 2026, needs more optimization.
28 220 0.157009083578 Henry Cohn, 2026, needs more optimization.
28 221 0.157142801704 Henry Cohn, 2026, needs more optimization.
28 222 0.158046718212 Henry Cohn, 2026, needs more optimization.
28 223 0.160336267452 Henry Cohn, 2026, needs more optimization.
28 224 0.160789746370 Henry Cohn, 2026, needs more optimization.
28 225 0.160848602787 Henry Cohn, 2026, needs more optimization.
28 226 0.160888717937 Henry Cohn, 2026, needs more optimization.
28 227 0.160931661133 Henry Cohn, 2026, needs more optimization.
28 228 0.160968219374 Henry Cohn, 2026, needs more optimization.
28 229 0.161006073936 Henry Cohn, 2026, needs more optimization.
28 230 0.161048780296 Henry Cohn, 2026, needs more optimization.
28 231 0.161087023664 Henry Cohn, 2026, needs more optimization.
28 232 0.161132806026 Henry Cohn, 2026, needs more optimization.
28 233 0.161483563029 Henry Cohn, 2026, needs more optimization.
28 234 0.161509251075 Henry Cohn, 2026, needs more optimization.
28 235 0.161535309467 Henry Cohn, 2026, needs more optimization.
28 236 0.161556789150 Henry Cohn, 2026, needs more optimization.
28 237 0.161591069550 Henry Cohn, 2026, needs more optimization.
28 238 0.161619857688 Henry Cohn, 2026, needs more optimization.
28 241 0.161627723805 Henry Cohn, 2026, needs more optimization.
28 242 0.161735964206 Henry Cohn, 2026, needs more optimization.
28 243 0.161741064087 Henry Cohn, 2026, needs more optimization.
28 244 0.161805154606 Henry Cohn, 2026, needs more optimization.
28 246 0.161805154743 Henry Cohn, 2026, needs more optimization.
28 248 0.161856039522 Henry Cohn, 2026, needs more optimization.
28 249 0.163075265595 Henry Cohn, 2026, needs more optimization.
28 250 0.163850639744 Henry Cohn, 2026, needs more optimization.
28 251 0.164323610767 Henry Cohn, 2026, needs more optimization.
28 256 0.165809729546 Henry Cohn, 2026, needs more optimization.
28 259 0.165956761111 Henry Cohn, 2026, needs more optimization.
28 260 0.166078880574 Henry Cohn, 2026, needs more optimization.
28 261 0.166096002858 Henry Cohn, 2026, needs more optimization.
28 264 0.166136116761 Henry Cohn, 2026, needs more optimization.
28 267 0.166367400121 Henry Cohn, 2026, needs more optimization.
28 290 0.166666666667 Orthogonal union of 275 points in 22 dimensions and 15 points in 6 dimensions.
6⁢x−1
28 291 0.166696111005 Orthogonal union of 289 points in 27 dimensions and 2 points in 1 dimension.
28 292 0.177070882269 Henry Cohn, 2026, needs more optimization.
28 293 0.177434181065 Henry Cohn, 2026, needs more optimization.
28 294 0.179493118776 Orthogonal union of 292 points in 27 dimensions and 2 points in 1 dimension.
28 295 0.179493566291 Orthogonal union of 293 points in 27 dimensions and 2 points in 1 dimension.
28 296 0.179493965203 Orthogonal union of 294 points in 27 dimensions and 2 points in 1 dimension.
28 298 0.179494072201 Henry Cohn, 2026, needs more optimization.
28 299 0.179494792438 Henry Cohn, 2026, needs more optimization.
28 300 0.179495671503 Henry Cohn, 2026, needs more optimization.
28 301 0.179498235412 Orthogonal union of 299 points in 27 dimensions and 2 points in 1 dimension.
28 302 0.179500637410 Orthogonal union of 300 points in 27 dimensions and 2 points in 1 dimension.
28 304 0.179540025559 Henry Cohn, 2026, needs more optimization.
28 305 0.179556400032 Henry Cohn, 2026, needs more optimization.
28 306 0.179721772975 Henry Cohn, 2026, needs more optimization.
28 307 0.181818181819 Orthogonal union of 297 points in 24 dimensions and 10 points in 4 dimensions.
11⁢x−2
28 314 0.193548387073 Henry Cohn, 2026, needs more optimization.
28 338 0.193548387074 Henry Cohn, 2026, needs more optimization.
28 340 0.193548387097 Orthogonal union of 330 points in 24 dimensions and 10 points in 4 dimensions.
31⁢x−6
28 344 0.195656419106 Henry Cohn, 2026, needs more optimization.
28 346 0.196890169495 Henry Cohn, 2026, needs more optimization.
28 350 0.196890169770 Henry Cohn, 2026, needs more optimization.
28 352 0.196890169936 Henry Cohn, 2026, needs more optimization.
28 354 0.199999721954 Henry Cohn, 2026, needs more optimization.
28 356 0.199999849101 Henry Cohn, 2026, needs more optimization.
28 359 0.199999943719 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
28 570 0.200116970684 Henry Cohn, 2026, needs more optimization.
28 572 0.237569013471 Henry Cohn, 2026, needs more optimization.
28 575 0.237590051282 Henry Cohn, 2025, needs more optimization.
28 576 0.237597962608 Henry Cohn, 2026, needs more optimization.
28 578 0.237610957097 Henry Cohn, 2026, needs more optimization.
28 579 0.237628473124 Henry Cohn, 2026, needs more optimization.
28 580 0.237629619918 Henry Cohn, 2026, needs more optimization.
28 581 0.237692814107 Henry Cohn, 2026, needs more optimization.
28 582 0.237714075083 Henry Cohn, 2025, needs more optimization.
28 584 0.237716304844 Henry Cohn, 2026, needs more optimization.
28 588 0.238072292146 Henry Cohn, 2026, needs more optimization.
28 596 0.238101495092 Henry Cohn, 2026, needs more optimization.
28 604 0.238133418950 Henry Cohn, 2026, needs more optimization.
28 612 0.238188262156 Henry Cohn, 2026, needs more optimization.
28 620 0.238395994479 Henry Cohn, 2026, needs more optimization.
28 628 0.239141579031 Henry Cohn, 2026, needs more optimization.
28 632 0.241077615809 Henry Cohn, 2026, needs more optimization.
28 636 0.241508043760 Henry Cohn, 2026, needs more optimization.
28 640 0.244245435854 Henry Cohn, 2026, needs more optimization.
28 644 0.245037071683 Henry Cohn, 2026, needs more optimization.
28 652 0.246038453780 Henry Cohn, 2026, needs more optimization.
28 660 0.246818081010 Henry Cohn, 2026, needs more optimization.
28 668 0.247406464596 Henry Cohn, 2026, needs more optimization.
28 676 0.247953703952 Henry Cohn, 2026, needs more optimization.
28 684 0.248476052699 Henry Cohn, 2026, needs more optimization.
28 692 0.248951633783 Henry Cohn, 2026, needs more optimization.
28 700 0.249320131997 Henry Cohn, 2026, needs more optimization.
28 708 0.249559351332 Henry Cohn, 2026, needs more optimization.
28 712 0.249748810727 Henry Cohn, 2026, needs more optimization.
28 716 0.249755125762 Henry Cohn, 2026, needs more optimization.
28 720 0.249896484306 Henry Cohn, 2026, needs more optimization.
28 724 0.249896901858 Henry Cohn, 2026, needs more optimization.
28 945 0.25 Henry Cohn, 2026.
4⁢x−1
28 1024 0.272727272728 Code with 1024 points in 22 dimensions.
11⁢x−3
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 0.040903059852 Ilmari Vahteristo, 2026.
29 62 0.043374719000 Henry Cohn, 2025.
29 63 0.044360269883 Henry Cohn, 2026, needs more optimization.
29 64 0.044414060128 Henry Cohn, 2026, needs more optimization.
29 65 0.044630891047 Henry Cohn, 2026, needs more optimization.
29 67 0.044635261511 Ilmari Vahteristo, 2026.
29 68 0.046023775811 Henry Cohn, 2026, needs more optimization.
29 69 0.051047738681 Ilmari Vahteristo, 2026.
29 70 0.053128890684 Henry Cohn, 2026, needs more optimization.
29 71 0.054345970478 Ilmari Vahteristo, 2026.
29 72 0.056581472111 Ilmari Vahteristo, 2026.
29 73 0.057727762926 Ilmari Vahteristo, 2026.
29 74 0.059425484827 Ilmari Vahteristo, 2026.
29 75 0.061018195925 Ilmari Vahteristo, 2026.
29 76 0.062685332560 Ilmari Vahteristo, 2026.
29 77 0.063118781133 Henry Cohn, 2026, needs more optimization.
29 78 0.063590302823 Henry Cohn, 2026, needs more optimization.
29 79 0.064177563261 Henry Cohn, 2026, needs more optimization.
29 80 0.065762893017 Henry Cohn, 2026, needs more optimization.
29 81 0.067273877342 Henry Cohn, 2026, needs more optimization.
29 82 0.069115068008 Henry Cohn, 2026, needs more optimization.
29 83 0.070376248868 Henry Cohn, 2026, needs more optimization.
29 84 0.072208409827 Henry Cohn, 2026, needs more optimization.
29 85 0.074098752717 Henry Cohn, 2026, needs more optimization.
29 86 0.074850917418 Henry Cohn, 2026, needs more optimization.
29 87 0.075852862626 Henry Cohn, 2026, needs more optimization.
29 88 0.076404169848 Henry Cohn, 2026, needs more optimization.
29 89 0.076790017627 Henry Cohn, 2026, needs more optimization.
29 90 0.076936477102 Henry Cohn, 2026, needs more optimization.
29 91 0.077298649733 Henry Cohn, 2026, needs more optimization.
29 92 0.077435670533 Henry Cohn, 2026, needs more optimization.
29 93 0.077486820640 Henry Cohn, 2026, needs more optimization.
29 94 0.078105789581 Henry Cohn, 2026, needs more optimization.
29 95 0.078157923990 Henry Cohn, 2026, needs more optimization.
29 96 0.078214160070 Henry Cohn, 2026, needs more optimization.
29 97 0.078845424448 Henry Cohn, 2026, needs more optimization.
29 98 0.078892257318 Henry Cohn, 2026, needs more optimization.
29 99 0.079122379005 Henry Cohn, 2026, needs more optimization.
29 100 0.079584097245 Henry Cohn, 2026, needs more optimization.
29 101 0.080311755250 Henry Cohn, 2026, needs more optimization.
29 102 0.080677419043 Henry Cohn, 2026, needs more optimization.
29 103 0.080693044865 Henry Cohn, 2026, needs more optimization.
29 104 0.080701974372 Henry Cohn, 2026, needs more optimization.
29 105 0.080873763810 Henry Cohn, 2026, needs more optimization.
29 106 0.083875562207 Henry Cohn, 2026, needs more optimization.
29 107 0.085859414589 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 0.089845480291 Henry Cohn, 2026, needs more optimization.
29 114 0.090045393160 Henry Cohn, 2026, needs more optimization.
29 115 0.090240238695 Henry Cohn, 2026, needs more optimization.
29 116 0.090332242852 Henry Cohn, 2026, needs more optimization.
29 117 0.090535515729 Henry Cohn, 2026, needs more optimization.
29 118 0.090731853548 Henry Cohn, 2026, needs more optimization.
29 119 0.090803322292 Henry Cohn, 2026, needs more optimization.
29 120 0.090905545491 Henry Cohn, 2026, needs more optimization.
29 121 0.091234623534 Henry Cohn, 2026, needs more optimization.
29 122 0.092062473859 Henry Cohn, 2026, needs more optimization.
29 123 0.094203726546 Henry Cohn, 2026, needs more optimization.
29 124 0.094349652107 Henry Cohn, 2026, needs more optimization.
29 125 0.096652030111 Henry Cohn, 2026, needs more optimization.
29 126 0.098482942611 Henry Cohn, 2026, needs more optimization.
29 127 0.100208369065 Henry Cohn, 2026, needs more optimization.
29 128 0.101606392114 Henry Cohn, 2026, needs more optimization.
29 130 0.102475146887 Henry Cohn, 2026, needs more optimization.
29 131 0.102838405050 Henry Cohn, 2026, needs more optimization.
29 132 0.102956555422 Henry Cohn, 2026, needs more optimization.
29 133 0.103050492424 Henry Cohn, 2026, needs more optimization.
29 134 0.103063885217 Henry Cohn, 2026, needs more optimization.
29 135 0.103620984871 Henry Cohn, 2026, needs more optimization.
29 136 0.104549382670 Henry Cohn, 2026, needs more optimization.
29 137 0.105716868041 Henry Cohn, 2026, needs more optimization.
29 138 0.106968430095 Henry Cohn, 2026, needs more optimization.
29 139 0.108500224962 Henry Cohn, 2026, needs more optimization.
29 140 0.109135790271 Henry Cohn, 2026, needs more optimization.
29 141 0.109885109312 Henry Cohn, 2026, needs more optimization.
29 142 0.110534870947 Henry Cohn, 2026, needs more optimization.
29 143 0.111134489703 Henry Cohn, 2026, needs more optimization.
29 144 0.111673072478 Henry Cohn, 2026, needs more optimization.
29 145 0.112055131374 Henry Cohn, 2026, needs more optimization.
29 146 0.112968581704 Henry Cohn, 2026, needs more optimization.
29 147 0.113810891143 Henry Cohn, 2026, needs more optimization.
29 148 0.114777430870 Henry Cohn, 2026, needs more optimization.
29 149 0.115518653570 Henry Cohn, 2026, needs more optimization.
29 150 0.116432593899 Henry Cohn, 2026, needs more optimization.
29 151 0.116995516238 Henry Cohn, 2026, needs more optimization.
29 152 0.117614455697 Henry Cohn, 2026, needs more optimization.
29 153 0.118539039607 Henry Cohn, 2026, needs more optimization.
29 154 0.119416774004 Henry Cohn, 2026, needs more optimization.
29 155 0.120780228702 Henry Cohn, 2026, needs more optimization.
29 156 0.121735974276 Henry Cohn, 2026, needs more optimization.
29 157 0.123211023619 Henry Cohn, 2026, needs more optimization.
29 158 0.124005516993 Henry Cohn, 2026, needs more optimization.
29 159 0.125569109661 Henry Cohn, 2026, needs more optimization.
29 160 0.126593121474 Henry Cohn, 2026, needs more optimization.
29 161 0.128117470657 Henry Cohn, 2026, needs more optimization.
29 162 0.129076437832 Henry Cohn, 2026, needs more optimization.
29 163 0.129845186313 Henry Cohn, 2026, needs more optimization.
29 164 0.130300317579 Henry Cohn, 2026, needs more optimization.
29 165 0.130646648921 Henry Cohn, 2026, needs more optimization.
29 166 0.130946704129 Henry Cohn, 2026, needs more optimization.
29 167 0.131132311447 Henry Cohn, 2026, needs more optimization.
29 168 0.131485542126 Henry Cohn, 2026, needs more optimization.
29 169 0.131651150618 Henry Cohn, 2026, needs more optimization.
29 170 0.133396933855 Orthogonal union of 168 points in 28 dimensions and 2 points in 1 dimension.
29 171 0.133529412089 Orthogonal union of 169 points in 28 dimensions and 2 points in 1 dimension.
29 172 0.133649900231 Henry Cohn, 2026, needs more optimization.
29 173 0.134509957971 Henry Cohn, 2026, needs more optimization.
29 174 0.134671647999 Henry Cohn, 2026, needs more optimization.
29 175 0.138624361890 Henry Cohn, 2026, needs more optimization.
29 176 0.138855724948 Henry Cohn, 2026, needs more optimization.
29 177 0.139317417799 Henry Cohn, 2026, needs more optimization.
29 178 0.139713713883 Henry Cohn, 2026, needs more optimization.
29 179 0.139781235794 Henry Cohn, 2026, needs more optimization.
29 180 0.139950164074 Henry Cohn, 2026, needs more optimization.
29 181 0.140273647084 Henry Cohn, 2026, needs more optimization.
29 182 0.140419490459 Henry Cohn, 2026, needs more optimization.
29 183 0.140693847424 Henry Cohn, 2026, needs more optimization.
29 184 0.140823032442 Henry Cohn, 2026, needs more optimization.
29 185 0.140942351537 Henry Cohn, 2026, needs more optimization.
29 186 0.141043977325 Henry Cohn, 2026, needs more optimization.
29 187 0.141127321815 Henry Cohn, 2026, needs more optimization.
29 188 0.141224176510 Henry Cohn, 2026, needs more optimization.
29 189 0.141358528086 Henry Cohn, 2026, needs more optimization.
29 190 0.141388909954 Henry Cohn, 2026, needs more optimization.
29 191 0.141627034115 Henry Cohn, 2026, needs more optimization.
29 192 0.141764941810 Henry Cohn, 2026, needs more optimization.
29 193 0.141789194992 Henry Cohn, 2026, needs more optimization.
29 194 0.142103375568 Henry Cohn, 2026, needs more optimization.
29 195 0.142127593760 Henry Cohn, 2026, needs more optimization.
29 196 0.142172392479 Henry Cohn, 2026, needs more optimization.
29 197 0.142196306785 Henry Cohn, 2026, needs more optimization.
29 198 0.142330667403 Henry Cohn, 2026, needs more optimization.
29 199 0.142356944114 Henry Cohn, 2026, needs more optimization.
29 200 0.142384544842 Henry Cohn, 2026, needs more optimization.
29 201 0.142552268090 Henry Cohn, 2026, needs more optimization.
29 202 0.142579444257 Henry Cohn, 2026, needs more optimization.
29 203 0.142616789565 Henry Cohn, 2026, needs more optimization.
29 204 0.142660726955 Henry Cohn, 2026, needs more optimization.
29 205 0.142725522632 Henry Cohn, 2026, needs more optimization.
29 206 0.142828209593 Henry Cohn, 2026, needs more optimization.
29 207 0.142963009616 Henry Cohn, 2026, needs more optimization.
29 208 0.143117030567 Henry Cohn, 2026, needs more optimization.
29 209 0.143562328582 Henry Cohn, 2026, needs more optimization.
29 210 0.143857306343 Henry Cohn, 2026, needs more optimization.
29 211 0.144784310607 Henry Cohn, 2026, needs more optimization.
29 212 0.144996401879 Henry Cohn, 2026, needs more optimization.
29 213 0.145555877949 Henry Cohn, 2026, needs more optimization.
29 214 0.145969104797 Henry Cohn, 2026, needs more optimization.
29 215 0.147153016359 Henry Cohn, 2026, needs more optimization.
29 216 0.148088006173 Henry Cohn, 2026, needs more optimization.
29 217 0.148662395515 Henry Cohn, 2026, needs more optimization.
29 218 0.148736578891 Henry Cohn, 2026, needs more optimization.
29 219 0.148936748716 Henry Cohn, 2026, needs more optimization.
29 220 0.149277800939 Henry Cohn, 2026, needs more optimization.
29 221 0.149359469023 Henry Cohn, 2026, needs more optimization.
29 222 0.150271805195 Henry Cohn, 2026, needs more optimization.
29 223 0.151376567278 Henry Cohn, 2026, needs more optimization.
29 224 0.157792007743 Henry Cohn, 2026, needs more optimization.
29 225 0.158520992303 Henry Cohn, 2026, needs more optimization.
29 226 0.158614196833 Henry Cohn, 2026, needs more optimization.
29 227 0.158636702904 Henry Cohn, 2026, needs more optimization.
29 228 0.158741397775 Henry Cohn, 2026, needs more optimization.
29 229 0.158798185069 Henry Cohn, 2026, needs more optimization.
29 230 0.158979668295 Henry Cohn, 2026, needs more optimization.
29 231 0.159263289806 Henry Cohn, 2026, needs more optimization.
29 232 0.159388738588 Henry Cohn, 2026, needs more optimization.
29 233 0.159755416603 Henry Cohn, 2026, needs more optimization.
29 235 0.159936513481 Henry Cohn, 2026, needs more optimization.
29 236 0.160079733993 Henry Cohn, 2026, needs more optimization.
29 237 0.160221329145 Henry Cohn, 2026, needs more optimization.
29 240 0.160475104220 Henry Cohn, 2026, needs more optimization.
29 241 0.160618460240 Henry Cohn, 2026, needs more optimization.
29 244 0.160815568094 Henry Cohn, 2026, needs more optimization.
29 245 0.160946930924 Henry Cohn, 2026, needs more optimization.
29 247 0.161109976308 Henry Cohn, 2026, needs more optimization.
29 250 0.161395387145 Henry Cohn, 2026, needs more optimization.
29 251 0.162102529586 Henry Cohn, 2026, needs more optimization.
29 252 0.162513266043 Henry Cohn, 2026, needs more optimization.
29 253 0.162611411800 Henry Cohn, 2026, needs more optimization.
29 254 0.162727880600 Henry Cohn, 2026, needs more optimization.
29 256 0.162853060469 Henry Cohn, 2026, needs more optimization.
29 257 0.163075299559 Henry Cohn, 2026, needs more optimization.
29 258 0.163090450261 Henry Cohn, 2026, needs more optimization.
29 259 0.163097347857 Henry Cohn, 2026, needs more optimization.
29 260 0.163107531292 Henry Cohn, 2026, needs more optimization.
29 262 0.163243181453 Henry Cohn, 2026, needs more optimization.
29 263 0.163360276104 Henry Cohn, 2026, needs more optimization.
29 265 0.163508341785 Henry Cohn, 2026, needs more optimization.
29 268 0.163571298625 Henry Cohn, 2026, needs more optimization.
29 269 0.163684033131 Henry Cohn, 2026, needs more optimization.
29 270 0.164048277666 Henry Cohn, 2026, needs more optimization.
29 271 0.164150360669 Henry Cohn, 2026, needs more optimization.
29 272 0.164322412957 Henry Cohn, 2026, needs more optimization.
29 273 0.164443779536 Henry Cohn, 2026, needs more optimization.
29 274 0.164680727534 Henry Cohn, 2026, needs more optimization.
29 275 0.164920743984 Henry Cohn, 2026, needs more optimization.
29 276 0.165217774917 Henry Cohn, 2026, needs more optimization.
29 277 0.165366512551 Henry Cohn, 2026, needs more optimization.
29 278 0.165708641240 Henry Cohn, 2026, needs more optimization.
29 279 0.165973399728 Henry Cohn, 2026, needs more optimization.
29 280 0.166426723110 Henry Cohn, 2026, needs more optimization.
29 281 0.166434973048 Henry Cohn, 2026, needs more optimization.
29 282 0.166443297326 Henry Cohn, 2026, needs more optimization.
29 283 0.166451362284 Henry Cohn, 2026, needs more optimization.
29 284 0.166460123388 Henry Cohn, 2026, needs more optimization.
29 285 0.166470647712 Henry Cohn, 2026, needs more optimization.
29 286 0.166484653796 Henry Cohn, 2026, needs more optimization.
29 287 0.166610722787 Henry Cohn, 2026, needs more optimization.
29 288 0.166612878295 Henry Cohn, 2026, needs more optimization.
29 289 0.166614956907 Henry Cohn, 2026, needs more optimization.
29 290 0.166616986969 Henry Cohn, 2026, needs more optimization.
29 291 0.166619570891 Henry Cohn, 2026, needs more optimization.
29 292 0.166621958488 Henry Cohn, 2026, needs more optimization.
29 293 0.166624289278 Henry Cohn, 2026, needs more optimization.
29 294 0.166626957914 Henry Cohn, 2026, needs more optimization.
29 295 0.166630009342 Henry Cohn, 2026, needs more optimization.
29 296 0.166633355804 Henry Cohn, 2026, needs more optimization.
29 297 0.166637875888 Henry Cohn, 2026, needs more optimization.
29 298 0.166641962421 Henry Cohn, 2026, needs more optimization.
29 299 0.166645655945 Henry Cohn, 2026, needs more optimization.
29 300 0.166649699367 Henry Cohn, 2026, needs more optimization.
29 301 0.166681308189 Henry Cohn, 2026, needs more optimization.
29 304 0.176498297560 Henry Cohn, 2026, needs more optimization.
29 305 0.176505613813 Henry Cohn, 2025, needs more optimization.
29 306 0.176545037841 Henry Cohn, 2026, needs more optimization.
29 307 0.176625904401 Henry Cohn, 2026, needs more optimization.
29 308 0.177279328661 Henry Cohn, 2026, needs more optimization.
29 309 0.178795972454 Henry Cohn, 2025, needs more optimization.
29 310 0.179391364267 Henry Cohn, 2025, needs more optimization.
29 312 0.191491123327 Henry Cohn, 2026, needs more optimization.
29 313 0.191495617140 Henry Cohn, 2026, needs more optimization.
29 314 0.191495621365 Henry Cohn, 2025, needs more optimization.
29 315 0.191498520120 Henry Cohn, 2026, needs more optimization.
29 316 0.191498528849 Henry Cohn, 2026, needs more optimization.
29 318 0.191498850673 Henry Cohn, 2026, needs more optimization.
29 319 0.191498851903 Henry Cohn, 2025, needs more optimization.
29 320 0.191504815568 Henry Cohn, 2025, needs more optimization.
29 321 0.191519474423 Henry Cohn, 2025, needs more optimization.
29 322 0.191519475722 Henry Cohn, 2025, needs more optimization.
29 324 0.191525587848 Henry Cohn, 2026, needs more optimization.
29 325 0.191525588084 Henry Cohn, 2025, needs more optimization.
29 327 0.191536324151 Henry Cohn, 2025, needs more optimization.
29 328 0.191554335068 Henry Cohn, 2026, needs more optimization.
29 330 0.191557376322 Henry Cohn, 2026, needs more optimization.
29 331 0.191581140007 Henry Cohn, 2025, needs more optimization.
29 344 0.191627719659 Henry Cohn, 2026, needs more optimization.
29 360 0.193991725221 Henry Cohn, 2026, needs more optimization.
29 368 0.195805445751 Henry Cohn, 2026, needs more optimization.
29 376 0.196771724184 Henry Cohn, 2026, needs more optimization.
29 379 0.199999985172 Henry Cohn, 2026, needs more optimization.
29 570 0.2 Orthogonal union of 552 points in 23 dimensions and 18 points in 6 dimensions.
5⁢x−1
29 572 0.200055249226 Henry Cohn, 2026, needs more optimization.
29 575 0.200056882243 Henry Cohn, 2026, needs more optimization.
29 577 0.200056900350 Henry Cohn, 2026, needs more optimization.
29 580 0.200061881180 Henry Cohn, 2025, needs more optimization.
29 583 0.200084219050 Henry Cohn, 2026, needs more optimization.
29 584 0.200099371985 Henry Cohn, 2026, needs more optimization.
29 585 0.235221457188 Henry Cohn, 2026, needs more optimization.
29 586 0.235624165467 Henry Cohn, 2026, needs more optimization.
29 587 0.235648905409 Henry Cohn, 2026, needs more optimization.
29 588 0.235654509680 Henry Cohn, 2026, needs more optimization.
29 589 0.235745981170 Henry Cohn, 2026, needs more optimization.
29 590 0.235925600017 Henry Cohn, 2026, needs more optimization.
29 591 0.236072283800 Henry Cohn, 2026, needs more optimization.
29 592 0.236109405881 Henry Cohn, 2026, needs more optimization.
29 593 0.236190721234 Henry Cohn, 2026, needs more optimization.
29 594 0.236190721353 Henry Cohn, 2026, needs more optimization.
29 595 0.236228408721 Henry Cohn, 2026, needs more optimization.
29 596 0.236233830934 Henry Cohn, 2026, needs more optimization.
29 597 0.236299967472 Henry Cohn, 2026, needs more optimization.
29 598 0.236348373451 Henry Cohn, 2026, needs more optimization.
29 599 0.236476403828 Henry Cohn, 2026, needs more optimization.
29 600 0.236655990754 Henry Cohn, 2026, needs more optimization.
29 602 0.236707974235 Henry Cohn, 2026, needs more optimization.
29 603 0.236746113239 Henry Cohn, 2026, needs more optimization.
29 604 0.236755244569 Henry Cohn, 2026, needs more optimization.
29 605 0.236792082737 Henry Cohn, 2026, needs more optimization.
29 606 0.236889761101 Henry Cohn, 2026, needs more optimization.
29 607 0.237573215381 Henry Cohn, 2026, needs more optimization.
29 608 0.237579102548 Henry Cohn, 2026, needs more optimization.
29 609 0.237806711978 Henry Cohn, 2026, needs more optimization.
29 612 0.237999515348 Henry Cohn, 2026, needs more optimization.
29 620 0.238053596052 Henry Cohn, 2026, needs more optimization.
29 628 0.238114041981 Henry Cohn, 2026, needs more optimization.
29 632 0.238266310179 Henry Cohn, 2026, needs more optimization.
29 636 0.238294864888 Henry Cohn, 2026, needs more optimization.
29 640 0.239119677104 Henry Cohn, 2026, needs more optimization.
29 644 0.242764941664 Henry Cohn, 2026, needs more optimization.
29 652 0.244065241831 Henry Cohn, 2026, needs more optimization.
29 660 0.245112529344 Henry Cohn, 2026, needs more optimization.
29 668 0.245962641511 Henry Cohn, 2026, needs more optimization.
29 676 0.246706257197 Henry Cohn, 2026, needs more optimization.
29 684 0.247357276864 Henry Cohn, 2026, needs more optimization.
29 692 0.247880663422 Henry Cohn, 2026, needs more optimization.
29 700 0.248321560167 Henry Cohn, 2026, needs more optimization.
29 708 0.248723777585 Henry Cohn, 2026, needs more optimization.
29 716 0.249034989391 Henry Cohn, 2026, needs more optimization.
29 724 0.249304310113 Henry Cohn, 2026, needs more optimization.
29 732 0.249523160642 Henry Cohn, 2026, needs more optimization.
29 740 0.249688314265 Henry Cohn, 2026, needs more optimization.
29 748 0.249810059668 Henry Cohn, 2026, needs more optimization.
29 756 0.249895790139 Henry Cohn, 2026, needs more optimization.
29 760 0.249945457832 Henry Cohn, 2026, needs more optimization.
29 764 0.249948561778 Henry Cohn, 2026, needs more optimization.
29 768 0.249983994111 Henry Cohn, 2026, needs more optimization.
29 769 0.249999521611 Henry Cohn, 2026, needs more optimization.
29 947 0.25 Orthogonal union of 945 points in 28 dimensions and 2 points in 1 dimension.
4⁢x−1
29 1024 0.272727272728 Code with 1024 points in 22 dimensions.
11⁢x−3
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 0.031275273372 Henry Cohn, 2024.
30 63 0.039847183148 Ilmari Vahteristo, 2026.
30 64 0.042119395903 Henry Cohn, 2026, needs more optimization.
30 65 0.043892244528 Henry Cohn, 2024, needs more optimization.
30 66 0.044324649525 Henry Cohn, 2024, needs more optimization.
30 67 0.044477390970 Henry Cohn, 2026, needs more optimization.
30 69 0.044564148567 Ilmari Vahteristo, 2026.
30 70 0.044757478679 Henry Cohn, 2026, needs more optimization.
30 71 0.049847936443 Ilmari Vahteristo, 2026.
30 72 0.051438573624 Ilmari Vahteristo, 2026.
30 73 0.052492486450 Ilmari Vahteristo, 2026.
30 74 0.054445772855 Henry Cohn, 2026, needs more optimization.
30 75 0.056244486017 Ilmari Vahteristo, 2026.
30 76 0.057653765926 Ilmari Vahteristo, 2026.
30 77 0.059053763774 Ilmari Vahteristo, 2026.
30 78 0.060518692699 Henry Cohn, 2026, needs more optimization.
30 79 0.062144623806 Henry Cohn, 2026, needs more optimization.
30 80 0.062631942900 Henry Cohn, 2026, needs more optimization.
30 81 0.062875876892 Henry Cohn, 2026, needs more optimization.
30 82 0.064293775609 Henry Cohn, 2026, needs more optimization.
30 83 0.065169467412 Henry Cohn, 2026, needs more optimization.
30 84 0.066573122595 Henry Cohn, 2026, needs more optimization.
30 85 0.068034028230 Henry Cohn, 2026, needs more optimization.
30 86 0.069497177062 Henry Cohn, 2026, needs more optimization.
30 87 0.072164299648 Henry Cohn, 2026, needs more optimization.
30 88 0.073420490529 Henry Cohn, 2026, needs more optimization.
30 89 0.074323577155 Henry Cohn, 2026, needs more optimization.
30 90 0.074436471105 Henry Cohn, 2026, needs more optimization.
30 91 0.075459822219 Henry Cohn, 2026, needs more optimization.
30 92 0.076343786739 Henry Cohn, 2026, needs more optimization.
30 93 0.076933864773 Henry Cohn, 2026, needs more optimization.
30 94 0.076951866149 Henry Cohn, 2026, needs more optimization.
30 95 0.077101887924 Henry Cohn, 2026, needs more optimization.
30 96 0.077126502047 Henry Cohn, 2026, needs more optimization.
30 97 0.077240325474 Henry Cohn, 2026, needs more optimization.
30 98 0.077337843516 Henry Cohn, 2026, needs more optimization.
30 99 0.077544877462 Henry Cohn, 2026, needs more optimization.
30 100 0.077780924032 Henry Cohn, 2026, needs more optimization.
30 101 0.078200318016 Henry Cohn, 2026, needs more optimization.
30 102 0.078575345573 Henry Cohn, 2026, needs more optimization.
30 103 0.078838823190 Henry Cohn, 2026, needs more optimization.
30 104 0.079356715932 Henry Cohn, 2026, needs more optimization.
30 105 0.080063162277 Henry Cohn, 2026, needs more optimization.
30 107 0.080696465980 Henry Cohn, 2026, needs more optimization.
30 108 0.080958022536 Henry Cohn, 2026, needs more optimization.
30 109 0.081528281018 Henry Cohn, 2026, needs more optimization.
30 110 0.082229217025 Henry Cohn, 2026, needs more optimization.
30 111 0.082539510507 Henry Cohn, 2026, needs more optimization.
30 112 0.084724926264 Henry Cohn, 2026, needs more optimization.
30 113 0.085945170902 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
30 116 0.088659560996 Henry Cohn, 2026, needs more optimization.
30 117 0.088845573094 Henry Cohn, 2026, needs more optimization.
30 118 0.089181237724 Henry Cohn, 2026, needs more optimization.
30 119 0.089833708432 Henry Cohn, 2026, needs more optimization.
30 120 0.090074915033 Henry Cohn, 2026, needs more optimization.
30 121 0.090268240546 Henry Cohn, 2026, needs more optimization.
30 122 0.090659008247 Henry Cohn, 2026, needs more optimization.
30 123 0.090750600893 Henry Cohn, 2026, needs more optimization.
30 124 0.091006887122 Henry Cohn, 2026, needs more optimization.
30 125 0.091260409072 Henry Cohn, 2026, needs more optimization.
30 126 0.091690785810 Henry Cohn, 2026, needs more optimization.
30 127 0.092796803458 Henry Cohn, 2026, needs more optimization.
30 128 0.094172573301 Henry Cohn, 2026, needs more optimization.
30 129 0.095358128978 Henry Cohn, 2026, needs more optimization.
30 130 0.097466955849 Henry Cohn, 2026, needs more optimization.
30 131 0.098524080828 Henry Cohn, 2026, needs more optimization.
30 132 0.099574278309 Henry Cohn, 2026, needs more optimization.
30 133 0.101697914587 Henry Cohn, 2026, needs more optimization.
30 134 0.102113141272 Henry Cohn, 2026, needs more optimization.
30 136 0.102785023577 Henry Cohn, 2026, needs more optimization.
30 137 0.102822666529 Henry Cohn, 2026, needs more optimization.
30 138 0.102850207618 Henry Cohn, 2026, needs more optimization.
30 139 0.103275654423 Henry Cohn, 2026, needs more optimization.
30 140 0.103825669063 Henry Cohn, 2026, needs more optimization.
30 141 0.104129131817 Henry Cohn, 2026, needs more optimization.
30 142 0.104872894541 Henry Cohn, 2026, needs more optimization.
30 143 0.105814382083 Henry Cohn, 2026, needs more optimization.
30 144 0.106683456284 Henry Cohn, 2026, needs more optimization.
30 145 0.107298001098 Henry Cohn, 2026, needs more optimization.
30 146 0.108602991679 Henry Cohn, 2026, needs more optimization.
30 147 0.109013645687 Henry Cohn, 2026, needs more optimization.
30 148 0.110283346456 Henry Cohn, 2026, needs more optimization.
30 149 0.110779301779 Henry Cohn, 2026, needs more optimization.
30 150 0.111413422403 Henry Cohn, 2026, needs more optimization.
30 151 0.111672843321 Henry Cohn, 2026, needs more optimization.
30 152 0.111746929655 Henry Cohn, 2026, needs more optimization.
30 153 0.112492446055 Henry Cohn, 2026, needs more optimization.
30 154 0.113238724713 Henry Cohn, 2026, needs more optimization.
30 155 0.113799211167 Henry Cohn, 2026, needs more optimization.
30 156 0.114491385424 Henry Cohn, 2026, needs more optimization.
30 157 0.115471033162 Henry Cohn, 2026, needs more optimization.
30 158 0.116347457176 Henry Cohn, 2026, needs more optimization.
30 159 0.117296736698 Henry Cohn, 2026, needs more optimization.
30 160 0.118476348966 Henry Cohn, 2026, needs more optimization.
30 161 0.119301044540 Henry Cohn, 2026, needs more optimization.
30 162 0.120169474423 Henry Cohn, 2026, needs more optimization.
30 163 0.121505553131 Henry Cohn, 2026, needs more optimization.
30 164 0.122674256671 Henry Cohn, 2026, needs more optimization.
30 165 0.123366924432 Henry Cohn, 2026, needs more optimization.
30 166 0.124328485299 Henry Cohn, 2026, needs more optimization.
30 167 0.125421167309 Henry Cohn, 2026, needs more optimization.
30 168 0.126456251396 Henry Cohn, 2026, needs more optimization.
30 169 0.127634393593 Henry Cohn, 2026, needs more optimization.
30 170 0.131485542126 Orthogonal union of 168 points in 29 dimensions and 2 points in 1 dimension.
30 171 0.131651150618 Orthogonal union of 169 points in 29 dimensions and 2 points in 1 dimension.
30 172 0.131926154706 Henry Cohn, 2026, needs more optimization.
30 173 0.132085652401 Henry Cohn, 2026, needs more optimization.
30 174 0.132272132450 Henry Cohn, 2026, needs more optimization.
30 175 0.132820808585 Henry Cohn, 2026, needs more optimization.
30 176 0.133008555288 Henry Cohn, 2026, needs more optimization.
30 177 0.133214069448 Henry Cohn, 2026, needs more optimization.
30 178 0.133393486190 Henry Cohn, 2026, needs more optimization.
30 179 0.133594228866 Henry Cohn, 2026, needs more optimization.
30 180 0.133842215763 Henry Cohn, 2026, needs more optimization.
30 181 0.133861808320 Henry Cohn, 2026, needs more optimization.
30 182 0.133941886792 Henry Cohn, 2026, needs more optimization.
30 183 0.134093870150 Henry Cohn, 2026, needs more optimization.
30 184 0.134113160674 Henry Cohn, 2026, needs more optimization.
30 185 0.138579367884 Henry Cohn, 2026, needs more optimization.
30 186 0.138752639569 Henry Cohn, 2026, needs more optimization.
30 187 0.138925452489 Henry Cohn, 2026, needs more optimization.
30 188 0.139337929241 Henry Cohn, 2026, needs more optimization.
30 189 0.139480807544 Henry Cohn, 2026, needs more optimization.
30 190 0.139619149911 Henry Cohn, 2026, needs more optimization.
30 191 0.139688613976 Henry Cohn, 2026, needs more optimization.
30 192 0.140026792559 Henry Cohn, 2026, needs more optimization.
30 193 0.140088325240 Henry Cohn, 2026, needs more optimization.
30 194 0.140406577923 Henry Cohn, 2026, needs more optimization.
30 195 0.140717838456 Henry Cohn, 2026, needs more optimization.
30 196 0.140793558007 Henry Cohn, 2026, needs more optimization.
30 197 0.140911079337 Henry Cohn, 2026, needs more optimization.
30 198 0.141022490627 Henry Cohn, 2026, needs more optimization.
30 199 0.141105960764 Henry Cohn, 2026, needs more optimization.
30 200 0.141332336882 Henry Cohn, 2026, needs more optimization.
30 201 0.141336633550 Henry Cohn, 2026, needs more optimization.
30 203 0.141481329440 Henry Cohn, 2026, needs more optimization.
30 204 0.141908528192 Henry Cohn, 2026, needs more optimization.
30 205 0.141958693179 Henry Cohn, 2026, needs more optimization.
30 206 0.142002426663 Henry Cohn, 2026, needs more optimization.
30 207 0.142059963262 Henry Cohn, 2026, needs more optimization.
30 208 0.142150721180 Henry Cohn, 2026, needs more optimization.
30 209 0.142302777258 Henry Cohn, 2026, needs more optimization.
30 210 0.142327420888 Henry Cohn, 2026, needs more optimization.
30 211 0.142378947987 Henry Cohn, 2026, needs more optimization.
30 212 0.142409221042 Henry Cohn, 2026, needs more optimization.
30 213 0.142466444870 Henry Cohn, 2026, needs more optimization.
30 214 0.142502608637 Henry Cohn, 2026, needs more optimization.
30 215 0.142700814686 Henry Cohn, 2026, needs more optimization.
30 216 0.142957097006 Henry Cohn, 2026, needs more optimization.
30 217 0.143011823417 Henry Cohn, 2026, needs more optimization.
30 218 0.143382759193 Henry Cohn, 2026, needs more optimization.
30 219 0.143742379616 Henry Cohn, 2026, needs more optimization.
30 220 0.144047234703 Henry Cohn, 2026, needs more optimization.
30 221 0.144466655682 Henry Cohn, 2026, needs more optimization.
30 222 0.145008812108 Henry Cohn, 2026, needs more optimization.
30 223 0.145801859896 Henry Cohn, 2026, needs more optimization.
30 224 0.146280431376 Henry Cohn, 2026, needs more optimization.
30 225 0.146844335619 Henry Cohn, 2026, needs more optimization.
30 226 0.146996774319 Henry Cohn, 2026, needs more optimization.
30 227 0.147574167934 Henry Cohn, 2026, needs more optimization.
30 228 0.148149208028 Henry Cohn, 2026, needs more optimization.
30 229 0.148413013290 Henry Cohn, 2026, needs more optimization.
30 230 0.148895859133 Henry Cohn, 2026, needs more optimization.
30 231 0.149162320975 Henry Cohn, 2026, needs more optimization.
30 232 0.149739099217 Henry Cohn, 2026, needs more optimization.
30 233 0.150421501271 Henry Cohn, 2026, needs more optimization.
30 234 0.150991742870 Henry Cohn, 2026, needs more optimization.
30 235 0.151407500809 Henry Cohn, 2026, needs more optimization.
30 236 0.152330292922 Henry Cohn, 2026, needs more optimization.
30 237 0.152993298295 Henry Cohn, 2026, needs more optimization.
30 238 0.153602187886 Henry Cohn, 2026, needs more optimization.
30 239 0.154785297300 Henry Cohn, 2026, needs more optimization.
30 240 0.155500278615 Henry Cohn, 2026, needs more optimization.
30 241 0.157118195123 Henry Cohn, 2026, needs more optimization.
30 242 0.157205488001 Henry Cohn, 2026, needs more optimization.
30 243 0.158063875706 Henry Cohn, 2026, needs more optimization.
30 244 0.158080682755 Henry Cohn, 2026, needs more optimization.
30 245 0.158470425414 Henry Cohn, 2026, needs more optimization.
30 246 0.159388865247 Henry Cohn, 2026, needs more optimization.
30 247 0.159414016083 Henry Cohn, 2026, needs more optimization.
30 248 0.159553983219 Henry Cohn, 2026, needs more optimization.
30 249 0.159588021349 Henry Cohn, 2026, needs more optimization.
30 250 0.160377813467 Henry Cohn, 2026, needs more optimization.
30 251 0.160405924336 Henry Cohn, 2026, needs more optimization.
30 252 0.160444386999 Henry Cohn, 2026, needs more optimization.
30 253 0.160502781721 Henry Cohn, 2026, needs more optimization.
30 254 0.160540059681 Henry Cohn, 2026, needs more optimization.
30 255 0.160572193922 Henry Cohn, 2026, needs more optimization.
30 256 0.160639810212 Henry Cohn, 2026, needs more optimization.
30 257 0.160692153013 Henry Cohn, 2026, needs more optimization.
30 258 0.160723005421 Henry Cohn, 2026, needs more optimization.
30 259 0.160756819419 Henry Cohn, 2026, needs more optimization.
30 260 0.160797767070 Henry Cohn, 2026, needs more optimization.
30 261 0.160848086319 Henry Cohn, 2026, needs more optimization.
30 262 0.160893850546 Henry Cohn, 2026, needs more optimization.
30 263 0.160937554747 Henry Cohn, 2026, needs more optimization.
30 264 0.161001270501 Henry Cohn, 2026, needs more optimization.
30 265 0.161040273593 Henry Cohn, 2026, needs more optimization.
30 266 0.161189369449 Henry Cohn, 2026, needs more optimization.
30 267 0.161584735708 Henry Cohn, 2026, needs more optimization.
30 269 0.161824282027 Henry Cohn, 2026, needs more optimization.
30 270 0.161876533651 Henry Cohn, 2026, needs more optimization.
30 275 0.161883303905 Henry Cohn, 2026, needs more optimization.
30 276 0.162020852481 Henry Cohn, 2026, needs more optimization.
30 277 0.162054776249 Henry Cohn, 2026, needs more optimization.
30 278 0.162167416964 Henry Cohn, 2026, needs more optimization.
30 279 0.162250570612 Henry Cohn, 2026, needs more optimization.
30 280 0.162614818922 Henry Cohn, 2026, needs more optimization.
30 281 0.162857310340 Henry Cohn, 2026, needs more optimization.
30 282 0.163576214200 Henry Cohn, 2026, needs more optimization.
30 283 0.164228728988 Henry Cohn, 2026, needs more optimization.
30 284 0.164475805018 Henry Cohn, 2026, needs more optimization.
30 285 0.165453112756 Henry Cohn, 2026, needs more optimization.
30 286 0.165504846353 Henry Cohn, 2026, needs more optimization.
30 287 0.165532577858 Henry Cohn, 2026, needs more optimization.
30 288 0.165600722484 Henry Cohn, 2026, needs more optimization.
30 290 0.165842479520 Henry Cohn, 2026, needs more optimization.
30 291 0.166088480470 Henry Cohn, 2026, needs more optimization.
30 292 0.166116146189 Henry Cohn, 2026, needs more optimization.
30 293 0.166144700871 Henry Cohn, 2026, needs more optimization.
30 294 0.166173272541 Henry Cohn, 2026, needs more optimization.
30 295 0.166204936677 Henry Cohn, 2026, needs more optimization.
30 296 0.166232023417 Henry Cohn, 2026, needs more optimization.
30 297 0.166260964819 Henry Cohn, 2026, needs more optimization.
30 298 0.166291501003 Henry Cohn, 2026, needs more optimization.
30 299 0.166323816581 Henry Cohn, 2026, needs more optimization.
30 300 0.166358525068 Henry Cohn, 2026, needs more optimization.
30 301 0.166485910986 Henry Cohn, 2026, needs more optimization.
30 302 0.166485911052 Henry Cohn, 2026, needs more optimization.
30 303 0.166681308189 Orthogonal union of 301 points in 29 dimensions and 2 points in 1 dimension.
30 304 0.176000456719 Henry Cohn, 2026, needs more optimization.
30 305 0.176030393809 Henry Cohn, 2026, needs more optimization.
30 306 0.176031946478 Henry Cohn, 2026, needs more optimization.
30 307 0.176046588051 Henry Cohn, 2025, needs more optimization.
30 308 0.176116804921 Henry Cohn, 2026, needs more optimization.
30 309 0.176268389777 Henry Cohn, 2026, needs more optimization.
30 310 0.176277663143 Henry Cohn, 2026, needs more optimization.
30 311 0.176287752274 Henry Cohn, 2025, needs more optimization.
30 312 0.176297427668 Henry Cohn, 2026, needs more optimization.
30 313 0.176309067334 Henry Cohn, 2025, needs more optimization.
30 314 0.176351126005 Henry Cohn, 2026, needs more optimization.
30 315 0.185614819721 Henry Cohn, 2026, needs more optimization.
30 316 0.186279290289 Henry Cohn, 2026, needs more optimization.
30 317 0.186370340436 Henry Cohn, 2025, needs more optimization.
30 318 0.186437561962 Henry Cohn, 2025, needs more optimization.
30 320 0.186842500013 Henry Cohn, 2026, needs more optimization.
30 321 0.186975764954 Henry Cohn, 2025, needs more optimization.
30 322 0.187613329381 Henry Cohn, 2025, needs more optimization.
30 323 0.187643458067 Henry Cohn, 2025, needs more optimization.
30 324 0.187825729198 Henry Cohn, 2025, needs more optimization.
30 325 0.188175990458 Henry Cohn, 2025, needs more optimization.
30 326 0.188255503724 Henry Cohn, 2026, needs more optimization.
30 327 0.188630642966 Henry Cohn, 2025, needs more optimization.
30 328 0.188995191611 Henry Cohn, 2026, needs more optimization.
30 330 0.189024561117 Henry Cohn, 2025, needs more optimization.
30 331 0.189792490156 Henry Cohn, 2025, needs more optimization.
30 333 0.189802882753 Henry Cohn, 2025, needs more optimization.
30 335 0.189823445556 Henry Cohn, 2025, needs more optimization.
30 336 0.189849011203 Henry Cohn, 2026, needs more optimization.
30 337 0.189939059321 Henry Cohn, 2026, needs more optimization.
30 338 0.190213722271 Henry Cohn, 2025, needs more optimization.
30 339 0.190543421562 Henry Cohn, 2026, needs more optimization.
30 340 0.190816392674 Henry Cohn, 2026, needs more optimization.
30 341 0.190830069057 Henry Cohn, 2026, needs more optimization.
30 344 0.190849076545 Henry Cohn, 2026, needs more optimization.
30 345 0.190906814513 Henry Cohn, 2025, needs more optimization.
30 346 0.190927954778 Henry Cohn, 2025, needs more optimization.
30 347 0.190989882585 Henry Cohn, 2026, needs more optimization.
30 360 0.191182556614 Henry Cohn, 2026, needs more optimization.
30 368 0.192526755988 Henry Cohn, 2026, needs more optimization.
30 376 0.193330704685 Henry Cohn, 2026, needs more optimization.
30 384 0.194582190266 Henry Cohn, 2026, needs more optimization.
30 392 0.196560028633 Henry Cohn, 2026, needs more optimization.
30 394 0.199999985028 Henry Cohn, 2026, needs more optimization.
30 576 0.2 Orthogonal union of 552 points in 23 dimensions and 24 points in 7 dimensions.
5⁢x−1
30 577 0.200040738021 Henry Cohn, 2025, needs more optimization.
30 584 0.200044686574 Henry Cohn, 2026, needs more optimization.
30 585 0.200045798599 Henry Cohn, 2025, needs more optimization.
30 586 0.200050687732 Henry Cohn, 2025, needs more optimization.
30 588 0.200053323442 Henry Cohn, 2026, needs more optimization.
30 590 0.200056685754 Henry Cohn, 2025, needs more optimization.
30 592 0.200062139434 Henry Cohn, 2026, needs more optimization.
30 593 0.233997314950 Henry Cohn, 2026, needs more optimization.
30 594 0.234094005201 Henry Cohn, 2026, needs more optimization.
30 595 0.234180864277 Henry Cohn, 2026, needs more optimization.
30 596 0.234300790850 Henry Cohn, 2026, needs more optimization.
30 597 0.234356299751 Henry Cohn, 2026, needs more optimization.
30 598 0.234512556904 Henry Cohn, 2026, needs more optimization.
30 599 0.234653514858 Henry Cohn, 2026, needs more optimization.
30 600 0.234739250135 Henry Cohn, 2026, needs more optimization.
30 601 0.234873647733 Henry Cohn, 2026, needs more optimization.
30 602 0.234935594669 Henry Cohn, 2026, needs more optimization.
30 603 0.235075102783 Henry Cohn, 2026, needs more optimization.
30 604 0.235095384311 Henry Cohn, 2026, needs more optimization.
30 605 0.235187552255 Henry Cohn, 2026, needs more optimization.
30 606 0.235882290588 Henry Cohn, 2026, needs more optimization.
30 607 0.235938658277 Henry Cohn, 2026, needs more optimization.
30 608 0.236017797427 Henry Cohn, 2026, needs more optimization.
30 609 0.236182241133 Henry Cohn, 2026, needs more optimization.
30 610 0.236250907023 Henry Cohn, 2026, needs more optimization.
30 611 0.236399171153 Henry Cohn, 2026, needs more optimization.
30 612 0.236420141706 Henry Cohn, 2026, needs more optimization.
30 613 0.236893313278 Henry Cohn, 2026, needs more optimization.
30 614 0.237068701693 Henry Cohn, 2026, needs more optimization.
30 615 0.237192508678 Henry Cohn, 2026, needs more optimization.
30 616 0.237310122973 Henry Cohn, 2026, needs more optimization.
30 617 0.237457528731 Henry Cohn, 2026, needs more optimization.
30 618 0.237479243529 Henry Cohn, 2026, needs more optimization.
30 620 0.237573706626 Henry Cohn, 2026, needs more optimization.
30 628 0.237783750452 Henry Cohn, 2026, needs more optimization.
30 632 0.237950384877 Henry Cohn, 2026, needs more optimization.
30 636 0.237957907490 Henry Cohn, 2026, needs more optimization.
30 640 0.238099964973 Henry Cohn, 2026, needs more optimization.
30 642 0.239119677104 Orthogonal union of 640 points in 29 dimensions and 2 points in 1 dimension.
30 644 0.239137654418 Henry Cohn, 2026, needs more optimization.
30 648 0.242238173228 Henry Cohn, 2026, needs more optimization.
30 652 0.242586591608 Henry Cohn, 2026, needs more optimization.
30 660 0.243317522967 Henry Cohn, 2026, needs more optimization.
30 668 0.243921786992 Henry Cohn, 2026, needs more optimization.
30 676 0.244440936914 Henry Cohn, 2026, needs more optimization.
30 684 0.244896295139 Henry Cohn, 2026, needs more optimization.
30 692 0.245333539172 Henry Cohn, 2026, needs more optimization.
30 700 0.245790785376 Henry Cohn, 2026, needs more optimization.
30 708 0.246268062658 Henry Cohn, 2026, needs more optimization.
30 716 0.246805526175 Henry Cohn, 2026, needs more optimization.
30 724 0.247298397590 Henry Cohn, 2026, needs more optimization.
30 732 0.247788955550 Henry Cohn, 2026, needs more optimization.
30 740 0.248269630648 Henry Cohn, 2026, needs more optimization.
30 748 0.248715615408 Henry Cohn, 2026, needs more optimization.
30 756 0.249113211974 Henry Cohn, 2026, needs more optimization.
30 764 0.249415456680 Henry Cohn, 2026, needs more optimization.
30 772 0.249623189721 Henry Cohn, 2026, needs more optimization.
30 780 0.249770033552 Henry Cohn, 2026, needs more optimization.
30 788 0.249874545166 Henry Cohn, 2026, needs more optimization.
30 792 0.249946240144 Henry Cohn, 2026, needs more optimization.
30 796 0.249947613533 Henry Cohn, 2026, needs more optimization.
30 800 0.249971492472 Henry Cohn, 2026, needs more optimization.
30 804 0.249972526190 Henry Cohn, 2026, needs more optimization.
30 949 0.25 Orthogonal union of 945 points in 28 dimensions and 4 points in 2 dimensions.
4⁢x−1
30 1024 0.272727272728 Code with 1024 points in 22 dimensions.
11⁢x−3
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 0.030326003112 Henry Cohn, 2024.
31 65 0.038595357846 Ilmari Vahteristo, 2026.
31 66 0.040754454886 Henry Cohn, 2026, needs more optimization.
31 67 0.043516436781 Henry Cohn, 2026, needs more optimization.
31 68 0.043771299231 Henry Cohn, 2024, needs more optimization.
31 69 0.043848823673 Henry Cohn, 2026, needs more optimization.
31 70 0.043850566744 Henry Cohn, 2026, needs more optimization.
31 71 0.044034290893 Henry Cohn, 2026, needs more optimization.
31 72 0.044612092149 Henry Cohn, 2026, needs more optimization.
31 73 0.048705912808 Henry Cohn, 2026, needs more optimization.
31 74 0.050109588402 Henry Cohn, 2026, needs more optimization.
31 75 0.051193125528 Ilmari Vahteristo, 2026.
31 76 0.053172900077 Henry Cohn, 2026, needs more optimization.
31 77 0.054541789252 Ilmari Vahteristo, 2026.
31 78 0.055759550294 Henry Cohn, 2026, needs more optimization.
31 79 0.057285189631 Ilmari Vahteristo, 2026.
31 80 0.058638157280 Ilmari Vahteristo, 2026.
31 81 0.060011874851 Ilmari Vahteristo, 2026.
31 82 0.061389153148 Henry Cohn, 2026, needs more optimization.
31 83 0.061700535691 Henry Cohn, 2026, needs more optimization.
31 84 0.063032047515 Henry Cohn, 2026, needs more optimization.
31 85 0.063624918113 Henry Cohn, 2026, needs more optimization.
31 86 0.064512597527 Henry Cohn, 2026, needs more optimization.
31 87 0.065642283653 Henry Cohn, 2026, needs more optimization.
31 88 0.067430481351 Henry Cohn, 2026, needs more optimization.
31 89 0.069604359641 Henry Cohn, 2026, needs more optimization.
31 90 0.071144600965 Henry Cohn, 2026, needs more optimization.
31 91 0.072117378345 Henry Cohn, 2026, needs more optimization.
31 92 0.073178256017 Henry Cohn, 2026, needs more optimization.
31 93 0.074060121245 Henry Cohn, 2026, needs more optimization.
31 94 0.074958577008 Henry Cohn, 2026, needs more optimization.
31 95 0.075964500693 Henry Cohn, 2026, needs more optimization.
31 96 0.076058280320 Henry Cohn, 2026, needs more optimization.
31 97 0.076853138747 Henry Cohn, 2026, needs more optimization.
31 98 0.076906791975 Henry Cohn, 2026, needs more optimization.
31 99 0.076945164278 Henry Cohn, 2026, needs more optimization.
31 100 0.077022985099 Henry Cohn, 2026, needs more optimization.
31 101 0.077098621728 Henry Cohn, 2026, needs more optimization.
31 102 0.077188117945 Henry Cohn, 2026, needs more optimization.
31 103 0.077360871628 Henry Cohn, 2026, needs more optimization.
31 104 0.077553765058 Henry Cohn, 2026, needs more optimization.
31 105 0.078008134730 Henry Cohn, 2026, needs more optimization.
31 106 0.078512999050 Henry Cohn, 2026, needs more optimization.
31 107 0.079045086344 Henry Cohn, 2026, needs more optimization.
31 108 0.079723463736 Henry Cohn, 2026, needs more optimization.
31 109 0.080039993698 Henry Cohn, 2026, needs more optimization.
31 110 0.080666149535 Henry Cohn, 2026, needs more optimization.
31 111 0.080729764516 Henry Cohn, 2026, needs more optimization.
31 112 0.080861666709 Henry Cohn, 2026, needs more optimization.
31 113 0.081355677556 Henry Cohn, 2026, needs more optimization.
31 114 0.083208747894 Henry Cohn, 2026, needs more optimization.
31 115 0.083497938965 Henry Cohn, 2026, needs more optimization.
31 116 0.084763174647 Henry Cohn, 2026, needs more optimization.
31 117 0.085993254384 Henry Cohn, 2026, needs more optimization.
31 118 0.086422834167 Henry Cohn, 2026, needs more optimization.
31 119 0.087557486847 Henry Cohn, 2026, needs more optimization.
31 120 0.088392556465 Henry Cohn, 2026, needs more optimization.
31 121 0.088505416224 Henry Cohn, 2026, needs more optimization.
31 122 0.089065758541 Henry Cohn, 2026, needs more optimization.
31 123 0.089283044827 Henry Cohn, 2026, needs more optimization.
31 124 0.089630684763 Henry Cohn, 2026, needs more optimization.
31 125 0.089771009486 Henry Cohn, 2026, needs more optimization.
31 126 0.090206642127 Henry Cohn, 2026, needs more optimization.
31 127 0.090549116788 Henry Cohn, 2026, needs more optimization.
31 128 0.090811839784 Henry Cohn, 2026, needs more optimization.
31 129 0.090891008036 Henry Cohn, 2026, needs more optimization.
31 130 0.091389703671 Henry Cohn, 2026, needs more optimization.
31 131 0.092342376448 Henry Cohn, 2026, needs more optimization.
31 132 0.093211127454 Henry Cohn, 2026, needs more optimization.
31 133 0.094741672299 Henry Cohn, 2026, needs more optimization.
31 134 0.095548273101 Henry Cohn, 2026, needs more optimization.
31 135 0.098112550572 Henry Cohn, 2026, needs more optimization.
31 136 0.099218628538 Henry Cohn, 2026, needs more optimization.
31 137 0.100132860355 Henry Cohn, 2026, needs more optimization.
31 138 0.100905029871 Henry Cohn, 2026, needs more optimization.
31 139 0.101875348472 Henry Cohn, 2026, needs more optimization.
31 141 0.102700308895 Henry Cohn, 2026, needs more optimization.
31 142 0.102713186203 Henry Cohn, 2026, needs more optimization.
31 143 0.102773311434 Henry Cohn, 2026, needs more optimization.
31 145 0.102780651623 Henry Cohn, 2026, needs more optimization.
31 146 0.103125107626 Henry Cohn, 2026, needs more optimization.
31 147 0.104050450693 Henry Cohn, 2026, needs more optimization.
31 148 0.105152211348 Henry Cohn, 2026, needs more optimization.
31 149 0.105929907246 Henry Cohn, 2026, needs more optimization.
31 150 0.106560251336 Henry Cohn, 2026, needs more optimization.
31 151 0.107368769232 Henry Cohn, 2026, needs more optimization.
31 152 0.108274864476 Henry Cohn, 2026, needs more optimization.
31 153 0.108984171163 Henry Cohn, 2026, needs more optimization.
31 154 0.109853349256 Henry Cohn, 2026, needs more optimization.
31 155 0.110506086603 Henry Cohn, 2026, needs more optimization.
31 156 0.111183781633 Henry Cohn, 2026, needs more optimization.
31 157 0.111854756743 Henry Cohn, 2026, needs more optimization.
31 158 0.112490456406 Henry Cohn, 2026, needs more optimization.
31 159 0.113059427192 Henry Cohn, 2026, needs more optimization.
31 160 0.113955531859 Henry Cohn, 2026, needs more optimization.
31 161 0.114430051874 Henry Cohn, 2026, needs more optimization.
31 162 0.115468591299 Henry Cohn, 2026, needs more optimization.
31 163 0.116171415540 Henry Cohn, 2026, needs more optimization.
31 164 0.117116822779 Henry Cohn, 2026, needs more optimization.
31 165 0.117852607212 Henry Cohn, 2026, needs more optimization.
31 166 0.118880566867 Henry Cohn, 2026, needs more optimization.
31 167 0.119762201020 Henry Cohn, 2026, needs more optimization.
31 168 0.120295593934 Henry Cohn, 2026, needs more optimization.
31 169 0.121245827105 Henry Cohn, 2026, needs more optimization.
31 170 0.125797676033 Henry Cohn, 2026, needs more optimization.
31 171 0.126325672231 Henry Cohn, 2026, needs more optimization.
31 172 0.127159877693 Henry Cohn, 2026, needs more optimization.
31 173 0.127778024421 Henry Cohn, 2026, needs more optimization.
31 174 0.128416261485 Henry Cohn, 2026, needs more optimization.
31 175 0.128890594992 Henry Cohn, 2026, needs more optimization.
31 176 0.129423886327 Henry Cohn, 2026, needs more optimization.
31 177 0.130178174322 Henry Cohn, 2026, needs more optimization.
31 178 0.130728893548 Henry Cohn, 2026, needs more optimization.
31 179 0.131376977275 Henry Cohn, 2026, needs more optimization.
31 180 0.131535820438 Henry Cohn, 2026, needs more optimization.
31 181 0.131666085028 Henry Cohn, 2026, needs more optimization.
31 182 0.131884279711 Henry Cohn, 2026, needs more optimization.
31 183 0.132054101754 Henry Cohn, 2026, needs more optimization.
31 184 0.132174246783 Henry Cohn, 2026, needs more optimization.
31 185 0.132351420989 Henry Cohn, 2026, needs more optimization.
31 186 0.132374585121 Henry Cohn, 2026, needs more optimization.
31 187 0.135892633051 Henry Cohn, 2026, needs more optimization.
31 188 0.136154100510 Henry Cohn, 2026, needs more optimization.
31 189 0.136915789169 Henry Cohn, 2026, needs more optimization.
31 190 0.136998939222 Henry Cohn, 2026, needs more optimization.
31 191 0.137170904985 Henry Cohn, 2026, needs more optimization.
31 192 0.137332693356 Henry Cohn, 2026, needs more optimization.
31 193 0.137458420887 Henry Cohn, 2026, needs more optimization.
31 194 0.137932677452 Henry Cohn, 2026, needs more optimization.
31 195 0.138149771575 Henry Cohn, 2026, needs more optimization.
31 196 0.138246680864 Henry Cohn, 2026, needs more optimization.
31 197 0.138430174155 Henry Cohn, 2026, needs more optimization.
31 198 0.138599507427 Henry Cohn, 2026, needs more optimization.
31 199 0.138761419527 Henry Cohn, 2026, needs more optimization.
31 200 0.138928817202 Henry Cohn, 2026, needs more optimization.
31 201 0.139096422297 Henry Cohn, 2026, needs more optimization.
31 202 0.139598408872 Henry Cohn, 2026, needs more optimization.
31 203 0.139900493131 Henry Cohn, 2026, needs more optimization.
31 204 0.139991122762 Henry Cohn, 2026, needs more optimization.
31 205 0.140274197311 Henry Cohn, 2026, needs more optimization.
31 206 0.140320530479 Henry Cohn, 2026, needs more optimization.
31 207 0.140568532343 Henry Cohn, 2026, needs more optimization.
31 208 0.140643987385 Henry Cohn, 2026, needs more optimization.
31 209 0.140808022215 Henry Cohn, 2026, needs more optimization.
31 210 0.141122996105 Henry Cohn, 2026, needs more optimization.
31 211 0.141156539440 Henry Cohn, 2026, needs more optimization.
31 212 0.141442246503 Henry Cohn, 2026, needs more optimization.
31 213 0.141483493729 Henry Cohn, 2026, needs more optimization.
31 214 0.141560359165 Henry Cohn, 2026, needs more optimization.
31 215 0.141620365611 Henry Cohn, 2026, needs more optimization.
31 216 0.141678772349 Henry Cohn, 2026, needs more optimization.
31 217 0.141870247456 Henry Cohn, 2026, needs more optimization.
31 218 0.141943271833 Henry Cohn, 2026, needs more optimization.
31 219 0.142041587858 Henry Cohn, 2026, needs more optimization.
31 220 0.142079924070 Henry Cohn, 2026, needs more optimization.
31 221 0.142172465059 Henry Cohn, 2026, needs more optimization.
31 222 0.142219595795 Henry Cohn, 2026, needs more optimization.
31 223 0.142246002619 Henry Cohn, 2026, needs more optimization.
31 224 0.142582522778 Henry Cohn, 2026, needs more optimization.
31 225 0.142619823916 Henry Cohn, 2026, needs more optimization.
31 226 0.142915613598 Henry Cohn, 2026, needs more optimization.
31 227 0.143186198982 Henry Cohn, 2026, needs more optimization.
31 228 0.143459229682 Henry Cohn, 2026, needs more optimization.
31 229 0.143883563006 Henry Cohn, 2026, needs more optimization.
31 230 0.144481816454 Henry Cohn, 2026, needs more optimization.
31 231 0.145024585197 Henry Cohn, 2026, needs more optimization.
31 232 0.145457411025 Henry Cohn, 2026, needs more optimization.
31 233 0.145518998520 Henry Cohn, 2026, needs more optimization.
31 234 0.145741549562 Henry Cohn, 2026, needs more optimization.
31 235 0.146770143955 Henry Cohn, 2026, needs more optimization.
31 236 0.146903577985 Henry Cohn, 2026, needs more optimization.
31 237 0.147471709386 Henry Cohn, 2026, needs more optimization.
31 238 0.147906526072 Henry Cohn, 2026, needs more optimization.
31 239 0.148101331959 Henry Cohn, 2026, needs more optimization.
31 240 0.148334696328 Henry Cohn, 2026, needs more optimization.
31 241 0.149092877861 Henry Cohn, 2026, needs more optimization.
31 242 0.149622396772 Henry Cohn, 2026, needs more optimization.
31 243 0.150264060209 Henry Cohn, 2026, needs more optimization.
31 244 0.150420089463 Henry Cohn, 2026, needs more optimization.
31 245 0.150953103710 Henry Cohn, 2026, needs more optimization.
31 246 0.151589576334 Henry Cohn, 2026, needs more optimization.
31 247 0.152192326456 Henry Cohn, 2026, needs more optimization.
31 248 0.152567767623 Henry Cohn, 2026, needs more optimization.
31 249 0.153504426690 Henry Cohn, 2026, needs more optimization.
31 250 0.153840919150 Henry Cohn, 2026, needs more optimization.
31 251 0.154500352140 Henry Cohn, 2026, needs more optimization.
31 252 0.155287121897 Henry Cohn, 2026, needs more optimization.
31 253 0.155986010319 Henry Cohn, 2026, needs more optimization.
31 254 0.156811259300 Henry Cohn, 2026, needs more optimization.
31 255 0.157859032643 Henry Cohn, 2026, needs more optimization.
31 256 0.157893617471 Henry Cohn, 2026, needs more optimization.
31 257 0.158031001765 Henry Cohn, 2026, needs more optimization.
31 258 0.158516840684 Henry Cohn, 2026, needs more optimization.
31 259 0.159130652171 Henry Cohn, 2026, needs more optimization.
31 260 0.159185321778 Henry Cohn, 2026, needs more optimization.
31 261 0.159221104627 Henry Cohn, 2026, needs more optimization.
31 262 0.159391453077 Henry Cohn, 2026, needs more optimization.
31 263 0.159621335916 Henry Cohn, 2026, needs more optimization.
31 264 0.159650739370 Henry Cohn, 2026, needs more optimization.
31 265 0.160021313587 Henry Cohn, 2026, needs more optimization.
31 266 0.160053592860 Henry Cohn, 2026, needs more optimization.
31 267 0.160073154171 Henry Cohn, 2026, needs more optimization.
31 268 0.160222359434 Henry Cohn, 2026, needs more optimization.
31 269 0.160304290854 Henry Cohn, 2026, needs more optimization.
31 270 0.160465724849 Henry Cohn, 2026, needs more optimization.
31 271 0.160489524533 Henry Cohn, 2026, needs more optimization.
31 273 0.160744220262 Henry Cohn, 2026, needs more optimization.
31 275 0.160812108817 Henry Cohn, 2026, needs more optimization.
31 276 0.160912514185 Henry Cohn, 2026, needs more optimization.
31 277 0.161369698303 Henry Cohn, 2026, needs more optimization.
31 279 0.161617401726 Henry Cohn, 2026, needs more optimization.
31 280 0.161751654446 Henry Cohn, 2026, needs more optimization.
31 281 0.161776453708 Henry Cohn, 2026, needs more optimization.
31 282 0.161900062649 Henry Cohn, 2026, needs more optimization.
31 283 0.162253339043 Henry Cohn, 2026, needs more optimization.
31 284 0.162510336015 Henry Cohn, 2026, needs more optimization.
31 285 0.162689770843 Henry Cohn, 2026, needs more optimization.
31 287 0.162808782868 Henry Cohn, 2026, needs more optimization.
31 288 0.162959910319 Henry Cohn, 2026, needs more optimization.
31 289 0.163102051289 Henry Cohn, 2026, needs more optimization.
31 290 0.163285089227 Henry Cohn, 2026, needs more optimization.
31 291 0.163484849641 Henry Cohn, 2026, needs more optimization.
31 292 0.163689188427 Henry Cohn, 2026, needs more optimization.
31 293 0.164255614696 Henry Cohn, 2026, needs more optimization.
31 294 0.164282708990 Henry Cohn, 2026, needs more optimization.
31 295 0.164351486385 Henry Cohn, 2026, needs more optimization.
31 296 0.164380156732 Henry Cohn, 2026, needs more optimization.
31 298 0.164813264665 Henry Cohn, 2026, needs more optimization.
31 300 0.165039835614 Henry Cohn, 2026, needs more optimization.
31 301 0.165517859067 Henry Cohn, 2026, needs more optimization.
31 302 0.165531195303 Henry Cohn, 2026, needs more optimization.
31 304 0.165552292076 Henry Cohn, 2026, needs more optimization.
31 305 0.165585981557 Henry Cohn, 2026, needs more optimization.
31 306 0.165596606663 Henry Cohn, 2025, needs more optimization.
31 307 0.166666666662 Henry Cohn, 2025, needs more optimization.
31 309 0.174563450677 Henry Cohn, 2026, needs more optimization.
31 310 0.174573881109 Henry Cohn, 2025, needs more optimization.
31 311 0.174614374028 Henry Cohn, 2025, needs more optimization.
31 312 0.174619345986 Henry Cohn, 2026, needs more optimization.
31 313 0.175586810624 Henry Cohn, 2025, needs more optimization.
31 314 0.175643175584 Henry Cohn, 2026, needs more optimization.
31 315 0.175683376665 Henry Cohn, 2025, needs more optimization.
31 316 0.175744323543 Henry Cohn, 2025, needs more optimization.
31 317 0.175792168087 Henry Cohn, 2026, needs more optimization.
31 320 0.175814222432 Henry Cohn, 2026, needs more optimization.
31 321 0.175847644698 Henry Cohn, 2025, needs more optimization.
31 322 0.175900408725 Henry Cohn, 2025, needs more optimization.
31 323 0.176086193436 Henry Cohn, 2026, needs more optimization.
31 328 0.180661722317 Henry Cohn, 2026, needs more optimization.
31 336 0.183212551948 Henry Cohn, 2026, needs more optimization.
31 344 0.183603862947 Henry Cohn, 2026, needs more optimization.
31 360 0.185818398040 Henry Cohn, 2026, needs more optimization.
31 368 0.187537100422 Henry Cohn, 2026, needs more optimization.
31 376 0.188304886743 Henry Cohn, 2026, needs more optimization.
31 384 0.190040337084 Henry Cohn, 2026, needs more optimization.
31 386 0.194582190266 Orthogonal union of 384 points in 30 dimensions and 2 points in 1 dimension.
31 392 0.195292487253 Henry Cohn, 2026, needs more optimization.
31 394 0.196560028633 Orthogonal union of 392 points in 30 dimensions and 2 points in 1 dimension.
31 400 0.199988209755 Henry Cohn, 2026, needs more optimization.
31 408 0.199991473197 Henry Cohn, 2026, needs more optimization.
31 410 0.199999999977 Henry Cohn, 2026, needs more optimization.
31 581 0.2 Orthogonal union of 552 points in 23 dimensions and 29 points in 8 dimensions.
5⁢x−1
31 592 0.200038666970 Henry Cohn, 2026, needs more optimization.
31 596 0.200046007219 Henry Cohn, 2026, needs more optimization.
31 598 0.200057421527 Henry Cohn, 2025, needs more optimization.
31 599 0.200078681940 Henry Cohn, 2025, needs more optimization.
31 600 0.200177422653 Henry Cohn, 2026, needs more optimization.
31 601 0.228288343916 Henry Cohn, 2025, needs more optimization.
31 602 0.228318554413 Henry Cohn, 2025, needs more optimization.
31 604 0.228521110265 Henry Cohn, 2026, needs more optimization.
31 605 0.228594247973 Henry Cohn, 2025, needs more optimization.
31 606 0.228797549321 Henry Cohn, 2025, needs more optimization.
31 608 0.228807807756 Henry Cohn, 2026, needs more optimization.
31 609 0.228911380982 Henry Cohn, 2025, needs more optimization.
31 610 0.229347513462 Henry Cohn, 2025, needs more optimization.
31 611 0.229375267707 Henry Cohn, 2025, needs more optimization.
31 612 0.229408600685 Henry Cohn, 2026, needs more optimization.
31 613 0.229611317157 Henry Cohn, 2025, needs more optimization.
31 614 0.229627532985 Henry Cohn, 2025, needs more optimization.
31 615 0.229637706316 Henry Cohn, 2025, needs more optimization.
31 616 0.229765500078 Henry Cohn, 2026, needs more optimization.
31 617 0.230100153601 Henry Cohn, 2025, needs more optimization.
31 618 0.230165831539 Henry Cohn, 2025, needs more optimization.
31 619 0.230176280206 Henry Cohn, 2025, needs more optimization.
31 620 0.230177109186 Henry Cohn, 2026, needs more optimization.
31 621 0.230213927702 Henry Cohn, 2025, needs more optimization.
31 622 0.230237270975 Henry Cohn, 2025, needs more optimization.
31 623 0.230310598199 Henry Cohn, 2025, needs more optimization.
31 624 0.230379363849 Henry Cohn, 2026, needs more optimization.
31 625 0.230419067002 Henry Cohn, 2025, needs more optimization.
31 626 0.230439769568 Henry Cohn, 2025, needs more optimization.
31 627 0.231094852576 Henry Cohn, 2025, needs more optimization.
31 628 0.231147817128 Henry Cohn, 2026, needs more optimization.
31 629 0.231170931136 Henry Cohn, 2025, needs more optimization.
31 630 0.231210954166 Henry Cohn, 2025, needs more optimization.
31 631 0.231259889127 Henry Cohn, 2025, needs more optimization.
31 632 0.231270213175 Henry Cohn, 2026, needs more optimization.
31 633 0.231302105729 Henry Cohn, 2025, needs more optimization.
31 634 0.231312934261 Henry Cohn, 2025, needs more optimization.
31 635 0.231355294469 Henry Cohn, 2025, needs more optimization.
31 636 0.231359517734 Henry Cohn, 2026, needs more optimization.
31 637 0.231392613489 Henry Cohn, 2025, needs more optimization.
31 638 0.231764210234 Henry Cohn, 2026, needs more optimization.
31 639 0.231777922428 Henry Cohn, 2026, needs more optimization.
31 640 0.231779603130 Henry Cohn, 2026, needs more optimization.
31 641 0.231798724736 Henry Cohn, 2025, needs more optimization.
31 642 0.231822795370 Henry Cohn, 2025, needs more optimization.
31 643 0.231868141337 Henry Cohn, 2025, needs more optimization.
31 644 0.231889970832 Henry Cohn, 2026, needs more optimization.
31 645 0.231933887254 Henry Cohn, 2025, needs more optimization.
31 646 0.231975442250 Henry Cohn, 2025, needs more optimization.
31 647 0.232596876139 Henry Cohn, 2025, needs more optimization.
31 648 0.232609206426 Henry Cohn, 2026, needs more optimization.
31 649 0.232626690337 Henry Cohn, 2025, needs more optimization.
31 650 0.232920515026 Henry Cohn, 2026, needs more optimization.
31 652 0.232965589233 Henry Cohn, 2026, needs more optimization.
31 653 0.232993455442 Henry Cohn, 2025, needs more optimization.
31 654 0.233006135516 Henry Cohn, 2025, needs more optimization.
31 655 0.233010397609 Henry Cohn, 2025, needs more optimization.
31 656 0.233064513885 Henry Cohn, 2026, needs more optimization.
31 657 0.233084750151 Henry Cohn, 2025, needs more optimization.
31 658 0.233159875790 Henry Cohn, 2025, needs more optimization.
31 659 0.233246714387 Henry Cohn, 2025, needs more optimization.
31 660 0.233280732911 Henry Cohn, 2026, needs more optimization.
31 662 0.233306780230 Henry Cohn, 2025, needs more optimization.
31 663 0.233377399103 Henry Cohn, 2025, needs more optimization.
31 664 0.233396415455 Henry Cohn, 2026, needs more optimization.
31 665 0.233439114500 Henry Cohn, 2025, needs more optimization.
31 666 0.233459192577 Henry Cohn, 2025, needs more optimization.
31 667 0.233485716668 Henry Cohn, 2025, needs more optimization.
31 668 0.233495305468 Henry Cohn, 2026, needs more optimization.
31 669 0.233531137768 Henry Cohn, 2025, needs more optimization.
31 670 0.234106079119 Henry Cohn, 2025, needs more optimization.
31 672 0.234148576014 Henry Cohn, 2026, needs more optimization.
31 673 0.234264037303 Henry Cohn, 2025, needs more optimization.
31 674 0.234286780563 Henry Cohn, 2025, needs more optimization.
31 675 0.234316213878 Henry Cohn, 2025, needs more optimization.
31 676 0.234354210179 Henry Cohn, 2026, needs more optimization.
31 677 0.234754103881 Henry Cohn, 2025, needs more optimization.
31 678 0.234776072945 Henry Cohn, 2025, needs more optimization.
31 679 0.234784015578 Henry Cohn, 2025, needs more optimization.
31 680 0.234808509908 Henry Cohn, 2026, needs more optimization.
31 681 0.234853838763 Henry Cohn, 2025, needs more optimization.
31 682 0.235210375825 Henry Cohn, 2025, needs more optimization.
31 684 0.235219164902 Henry Cohn, 2026, needs more optimization.
31 685 0.235307691937 Henry Cohn, 2025, needs more optimization.
31 686 0.235381851010 Henry Cohn, 2025, needs more optimization.
31 687 0.235389063723 Henry Cohn, 2025, needs more optimization.
31 688 0.235470730772 Henry Cohn, 2026, needs more optimization.
31 689 0.235595152506 Henry Cohn, 2025, needs more optimization.
31 690 0.235656537804 Henry Cohn, 2025, needs more optimization.
31 691 0.235707236567 Henry Cohn, 2025, needs more optimization.
31 692 0.235994166840 Henry Cohn, 2026, needs more optimization.
31 693 0.236025681955 Henry Cohn, 2025, needs more optimization.
31 694 0.236044634998 Henry Cohn, 2025, needs more optimization.
31 696 0.236057179564 Henry Cohn, 2026, needs more optimization.
31 697 0.236090388931 Henry Cohn, 2025, needs more optimization.
31 698 0.236131741175 Henry Cohn, 2025, needs more optimization.
31 699 0.236337835127 Henry Cohn, 2025, needs more optimization.
31 700 0.236372883806 Henry Cohn, 2026, needs more optimization.
31 701 0.236620154373 Henry Cohn, 2025, needs more optimization.
31 702 0.236646481310 Henry Cohn, 2025, needs more optimization.
31 704 0.236666774311 Henry Cohn, 2026, needs more optimization.
31 705 0.236797875878 Henry Cohn, 2025, needs more optimization.
31 706 0.236805004134 Henry Cohn, 2025, needs more optimization.
31 707 0.236812809389 Henry Cohn, 2025, needs more optimization.
31 708 0.236966553041 Henry Cohn, 2026, needs more optimization.
31 709 0.237028687220 Henry Cohn, 2025, needs more optimization.
31 710 0.237185244023 Henry Cohn, 2025, needs more optimization.
31 711 0.237416168837 Henry Cohn, 2025, needs more optimization.
31 712 0.237459750641 Henry Cohn, 2026, needs more optimization.
31 713 0.237544942961 Henry Cohn, 2025, needs more optimization.
31 714 0.237579574030 Henry Cohn, 2025, needs more optimization.
31 716 0.237804186749 Henry Cohn, 2026, needs more optimization.
31 717 0.237933018131 Henry Cohn, 2025, 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 0.029441641365 Henry Cohn, 2026, needs more optimization.
32 67 0.037512550596 Ilmari Vahteristo, 2026.
32 68 0.039751994329 Henry Cohn, 2026, needs more optimization.
32 69 0.042646611592 Henry Cohn, 2026, needs more optimization.
32 70 0.042909209261 Henry Cohn, 2026, needs more optimization.
32 71 0.043172590160 Henry Cohn, 2026, needs more optimization.
32 72 0.043401883785 Henry Cohn, 2026, needs more optimization.
32 73 0.043663687435 Henry Cohn, 2026, needs more optimization.
32 74 0.044491944474 Henry Cohn, 2026, needs more optimization.
32 75 0.047693641178 Ilmari Vahteristo, 2026.
32 76 0.049042197562 Henry Cohn, 2026, needs more optimization.
32 77 0.049931040927 Henry Cohn, 2026, needs more optimization.
32 78 0.051771887273 Henry Cohn, 2026, needs more optimization.
32 79 0.053168362134 Ilmari Vahteristo, 2026.
32 80 0.054916555110 Henry Cohn, 2026, needs more optimization.
32 81 0.056185889794 Henry Cohn, 2026, needs more optimization.
32 82 0.057036889730 Henry Cohn, 2026, needs more optimization.
32 83 0.058509847619 Henry Cohn, 2026, needs more optimization.
32 84 0.059661225346 Henry Cohn, 2026, needs more optimization.
32 85 0.060934217212 Henry Cohn, 2026, needs more optimization.
32 86 0.062024425595 Henry Cohn, 2026, needs more optimization.
32 87 0.063248875772 Henry Cohn, 2026, needs more optimization.
32 88 0.064377432074 Henry Cohn, 2026, needs more optimization.
32 89 0.065597544116 Henry Cohn, 2026, needs more optimization.
32 90 0.066440495115 Henry Cohn, 2026, needs more optimization.
32 91 0.067797956971 Henry Cohn, 2026, needs more optimization.
32 92 0.068770145779 Henry Cohn, 2026, needs more optimization.
32 93 0.069846895335 Henry Cohn, 2026, needs more optimization.
32 94 0.070670567572 Henry Cohn, 2026, needs more optimization.
32 95 0.071740168964 Henry Cohn, 2026, needs more optimization.
32 96 0.072895401416 Henry Cohn, 2026, needs more optimization.
32 97 0.073936939100 Henry Cohn, 2026, needs more optimization.
32 98 0.074775155543 Henry Cohn, 2026, needs more optimization.
32 99 0.075682114751 Henry Cohn, 2026, needs more optimization.
32 100 0.076381902978 Henry Cohn, 2026, needs more optimization.
32 101 0.076462512423 Henry Cohn, 2026, needs more optimization.
32 102 0.076479542972 Henry Cohn, 2026, needs more optimization.
32 103 0.076943629760 Henry Cohn, 2026, needs more optimization.
32 104 0.077051367376 Henry Cohn, 2026, needs more optimization.
32 105 0.077126786464 Henry Cohn, 2026, needs more optimization.
32 106 0.077326948869 Henry Cohn, 2026, needs more optimization.
32 107 0.077452122449 Henry Cohn, 2026, needs more optimization.
32 108 0.077820360587 Henry Cohn, 2026, needs more optimization.
32 109 0.078141818210 Henry Cohn, 2026, needs more optimization.
32 110 0.078806604647 Henry Cohn, 2026, needs more optimization.
32 111 0.079524125987 Henry Cohn, 2026, needs more optimization.
32 112 0.079751173251 Henry Cohn, 2026, needs more optimization.
32 113 0.079972067875 Henry Cohn, 2026, needs more optimization.
32 114 0.080657092134 Henry Cohn, 2026, needs more optimization.
32 115 0.080718933096 Henry Cohn, 2026, needs more optimization.
32 116 0.081042780182 Henry Cohn, 2026, needs more optimization.
32 117 0.081431847841 Henry Cohn, 2026, needs more optimization.
32 118 0.081752083274 Henry Cohn, 2026, needs more optimization.
32 119 0.082522769708 Henry Cohn, 2026, needs more optimization.
32 120 0.083555415086 Henry Cohn, 2026, needs more optimization.
32 121 0.084695639220 Henry Cohn, 2026, needs more optimization.
32 122 0.085741800289 Henry Cohn, 2026, needs more optimization.
32 123 0.086792324946 Henry Cohn, 2026, needs more optimization.
32 124 0.087209375728 Henry Cohn, 2026, needs more optimization.
32 127 0.088917943670 Henry Cohn, 2026, needs more optimization.
32 128 0.089212375672 Henry Cohn, 2026, needs more optimization.
32 129 0.089528677611 Henry Cohn, 2026, needs more optimization.
32 130 0.089939254769 Henry Cohn, 2026, needs more optimization.
32 131 0.090245683541 Henry Cohn, 2026, needs more optimization.
32 132 0.090460400487 Henry Cohn, 2026, needs more optimization.
32 133 0.090478049259 Henry Cohn, 2026, needs more optimization.
32 134 0.090585631813 Henry Cohn, 2026, needs more optimization.
32 135 0.092565244341 Henry Cohn, 2026, needs more optimization.
32 136 0.093714144392 Henry Cohn, 2026, needs more optimization.
32 137 0.094690375994 Henry Cohn, 2026, needs more optimization.
32 138 0.095711679862 Henry Cohn, 2026, needs more optimization.
32 139 0.096376486720 Henry Cohn, 2026, needs more optimization.
32 140 0.097364205812 Henry Cohn, 2026, needs more optimization.
32 141 0.098215151995 Henry Cohn, 2026, needs more optimization.
32 142 0.099271319297 Henry Cohn, 2026, needs more optimization.
32 143 0.100048244276 Henry Cohn, 2026, needs more optimization.
32 144 0.100998336865 Henry Cohn, 2026, needs more optimization.
32 145 0.102033718443 Henry Cohn, 2026, needs more optimization.
32 148 0.102463139198 Henry Cohn, 2026, needs more optimization.
32 149 0.102569501981 Henry Cohn, 2026, needs more optimization.
32 150 0.102698434698 Henry Cohn, 2026, needs more optimization.
32 151 0.102926921908 Henry Cohn, 2026, needs more optimization.
32 152 0.103232223823 Henry Cohn, 2026, needs more optimization.
32 153 0.103930302971 Henry Cohn, 2026, needs more optimization.
32 154 0.104751924739 Henry Cohn, 2026, needs more optimization.
32 155 0.105628603322 Henry Cohn, 2026, needs more optimization.
32 156 0.106218082149 Henry Cohn, 2026, needs more optimization.
32 157 0.106676578341 Henry Cohn, 2026, needs more optimization.
32 158 0.107365950172 Henry Cohn, 2026, needs more optimization.
32 159 0.108267391172 Henry Cohn, 2026, needs more optimization.
32 160 0.109260832571 Henry Cohn, 2026, needs more optimization.
32 161 0.109925908448 Henry Cohn, 2026, needs more optimization.
32 162 0.110627528839 Henry Cohn, 2026, needs more optimization.
32 163 0.111315579176 Henry Cohn, 2026, needs more optimization.
32 164 0.111845479247 Henry Cohn, 2026, needs more optimization.
32 165 0.112423565623 Henry Cohn, 2026, needs more optimization.
32 166 0.113115166683 Henry Cohn, 2026, needs more optimization.
32 167 0.113963552746 Henry Cohn, 2026, needs more optimization.
32 168 0.114832863391 Henry Cohn, 2026, needs more optimization.
32 169 0.115628466874 Henry Cohn, 2026, needs more optimization.
32 170 0.120180475026 Henry Cohn, 2026, needs more optimization.
32 171 0.120965264811 Henry Cohn, 2026, needs more optimization.
32 172 0.121580497173 Henry Cohn, 2026, needs more optimization.
32 173 0.121891662393 Henry Cohn, 2026, needs more optimization.
32 174 0.122519984393 Henry Cohn, 2026, needs more optimization.
32 175 0.123394998628 Henry Cohn, 2026, needs more optimization.
32 176 0.123812060361 Henry Cohn, 2026, needs more optimization.
32 177 0.124439558143 Henry Cohn, 2026, needs more optimization.
32 178 0.124999147916 Henry Cohn, 2026, needs more optimization.
32 179 0.125554406564 Henry Cohn, 2026, needs more optimization.
32 180 0.126083695205 Henry Cohn, 2026, needs more optimization.
32 181 0.126610465287 Henry Cohn, 2026, needs more optimization.
32 182 0.127246987760 Henry Cohn, 2026, needs more optimization.
32 183 0.127890560143 Henry Cohn, 2026, needs more optimization.
32 184 0.128600612325 Henry Cohn, 2026, needs more optimization.
32 185 0.128826144893 Henry Cohn, 2026, needs more optimization.
32 186 0.129503857590 Henry Cohn, 2026, needs more optimization.
32 187 0.130116887274 Henry Cohn, 2026, needs more optimization.
32 188 0.130535247288 Henry Cohn, 2026, needs more optimization.
32 189 0.131146452277 Henry Cohn, 2026, needs more optimization.
32 190 0.131725234363 Henry Cohn, 2026, needs more optimization.
32 191 0.132238133468 Henry Cohn, 2026, needs more optimization.
32 192 0.132586792580 Henry Cohn, 2026, needs more optimization.
32 193 0.133432965888 Henry Cohn, 2026, needs more optimization.
32 194 0.134014720786 Henry Cohn, 2026, needs more optimization.
32 195 0.134354854985 Henry Cohn, 2026, needs more optimization.
32 196 0.134725080932 Henry Cohn, 2026, needs more optimization.
32 197 0.134876936811 Henry Cohn, 2026, needs more optimization.
32 198 0.135259122525 Henry Cohn, 2026, needs more optimization.
32 199 0.135483206506 Henry Cohn, 2026, needs more optimization.
32 200 0.135749855507 Henry Cohn, 2026, needs more optimization.
32 201 0.136130859580 Henry Cohn, 2026, needs more optimization.
32 202 0.136231072528 Henry Cohn, 2026, needs more optimization.
32 203 0.136929709920 Henry Cohn, 2026, needs more optimization.
32 204 0.137755253651 Henry Cohn, 2026, needs more optimization.
32 205 0.137880714716 Henry Cohn, 2026, needs more optimization.
32 206 0.137959245933 Henry Cohn, 2026, needs more optimization.
32 207 0.138186868101 Henry Cohn, 2026, needs more optimization.
32 208 0.138289388018 Henry Cohn, 2026, needs more optimization.
32 209 0.138631040915 Henry Cohn, 2026, needs more optimization.
32 210 0.138934658195 Henry Cohn, 2026, needs more optimization.
32 211 0.139219987712 Henry Cohn, 2026, needs more optimization.
32 212 0.139273919268 Henry Cohn, 2026, needs more optimization.
32 213 0.139479357939 Henry Cohn, 2026, needs more optimization.
32 214 0.139648047299 Henry Cohn, 2026, needs more optimization.
32 215 0.139841496011 Henry Cohn, 2026, needs more optimization.
32 216 0.139882190916 Henry Cohn, 2026, needs more optimization.
32 217 0.139976430746 Henry Cohn, 2026, needs more optimization.
32 218 0.140250310238 Henry Cohn, 2026, needs more optimization.
32 219 0.140296615658 Henry Cohn, 2026, needs more optimization.
32 220 0.140351481746 Henry Cohn, 2026, needs more optimization.
32 221 0.140484401003 Henry Cohn, 2026, needs more optimization.
32 222 0.140853512036 Henry Cohn, 2026, needs more optimization.
32 223 0.140906190294 Henry Cohn, 2026, needs more optimization.
32 224 0.141126608431 Henry Cohn, 2026, needs more optimization.
32 225 0.141170435817 Henry Cohn, 2026, needs more optimization.
32 226 0.141218279206 Henry Cohn, 2026, needs more optimization.
32 227 0.141405363108 Henry Cohn, 2026, needs more optimization.
32 228 0.141467563656 Henry Cohn, 2026, needs more optimization.
32 229 0.141729421940 Henry Cohn, 2026, needs more optimization.
32 230 0.141778208443 Henry Cohn, 2026, needs more optimization.
32 231 0.141985935780 Henry Cohn, 2026, needs more optimization.
32 232 0.142031468860 Henry Cohn, 2026, needs more optimization.
32 233 0.142234908303 Henry Cohn, 2026, needs more optimization.
32 234 0.142298201777 Henry Cohn, 2026, needs more optimization.
32 235 0.142706910170 Henry Cohn, 2026, needs more optimization.
32 236 0.142799479270 Henry Cohn, 2026, needs more optimization.
32 237 0.143254975904 Henry Cohn, 2026, needs more optimization.
32 238 0.143288451497 Henry Cohn, 2026, needs more optimization.
32 239 0.143546280929 Henry Cohn, 2026, needs more optimization.
32 240 0.143682750184 Henry Cohn, 2026, needs more optimization.
32 241 0.144412996352 Henry Cohn, 2026, needs more optimization.
32 242 0.144495231547 Henry Cohn, 2026, needs more optimization.
32 243 0.145011846257 Henry Cohn, 2026, needs more optimization.
32 244 0.145317719576 Henry Cohn, 2026, needs more optimization.
32 245 0.145968752156 Henry Cohn, 2026, needs more optimization.
32 246 0.146394476252 Henry Cohn, 2026, needs more optimization.
32 247 0.146948804243 Henry Cohn, 2026, needs more optimization.
32 248 0.147194177848 Henry Cohn, 2026, needs more optimization.
32 249 0.147618508555 Henry Cohn, 2026, needs more optimization.
32 250 0.147874240625 Henry Cohn, 2026, needs more optimization.
32 251 0.148125015404 Henry Cohn, 2026, needs more optimization.
32 252 0.148668257398 Henry Cohn, 2026, needs more optimization.
32 253 0.149115961279 Henry Cohn, 2026, needs more optimization.
32 254 0.153931948493 Henry Cohn, 2026, needs more optimization.
32 255 0.154570611809 Henry Cohn, 2026, needs more optimization.
32 256 0.154848347265 Henry Cohn, 2026, needs more optimization.
32 257 0.155398175254 Henry Cohn, 2026, needs more optimization.
32 258 0.155793527495 Henry Cohn, 2026, needs more optimization.
32 259 0.155895929509 Henry Cohn, 2026, needs more optimization.
32 260 0.155925072075 Henry Cohn, 2026, needs more optimization.
32 261 0.156040265128 Henry Cohn, 2026, needs more optimization.
32 262 0.156149528233 Henry Cohn, 2026, needs more optimization.
32 263 0.156844347509 Henry Cohn, 2026, needs more optimization.
32 264 0.157037828748 Henry Cohn, 2026, needs more optimization.
32 265 0.157061777600 Henry Cohn, 2026, needs more optimization.
32 266 0.157201019839 Henry Cohn, 2026, needs more optimization.
32 267 0.157304500500 Henry Cohn, 2026, needs more optimization.
32 268 0.157423951931 Henry Cohn, 2026, needs more optimization.
32 269 0.157520327944 Henry Cohn, 2026, needs more optimization.
32 270 0.157723977759 Henry Cohn, 2026, needs more optimization.
32 271 0.158034103874 Henry Cohn, 2026, needs more optimization.
32 272 0.158143268792 Henry Cohn, 2026, needs more optimization.
32 273 0.158201032346 Henry Cohn, 2026, needs more optimization.
32 274 0.158343474308 Henry Cohn, 2026, needs more optimization.
32 275 0.158393711085 Henry Cohn, 2026, needs more optimization.
32 276 0.158444939660 Henry Cohn, 2026, needs more optimization.
32 277 0.158615633031 Henry Cohn, 2026, needs more optimization.
32 278 0.158747796273 Henry Cohn, 2026, needs more optimization.
32 279 0.159067937460 Henry Cohn, 2026, needs more optimization.
32 280 0.159138993041 Henry Cohn, 2026, needs more optimization.
32 281 0.159192599456 Henry Cohn, 2026, needs more optimization.
32 282 0.159435258038 Henry Cohn, 2026, needs more optimization.
32 283 0.159541905009 Henry Cohn, 2026, needs more optimization.
32 284 0.159840048372 Henry Cohn, 2026, needs more optimization.
32 285 0.159991985756 Henry Cohn, 2026, needs more optimization.
32 286 0.160104753370 Henry Cohn, 2026, needs more optimization.
32 287 0.160121138283 Henry Cohn, 2026, needs more optimization.
32 288 0.160320565411 Henry Cohn, 2026, needs more optimization.
32 289 0.160593115489 Henry Cohn, 2026, needs more optimization.
32 290 0.160950239548 Henry Cohn, 2026, needs more optimization.
32 291 0.160974336016 Henry Cohn, 2026, needs more optimization.
32 292 0.161155814452 Henry Cohn, 2026, needs more optimization.
32 293 0.161322140717 Henry Cohn, 2026, needs more optimization.
32 294 0.161388184705 Henry Cohn, 2026, needs more optimization.
32 295 0.161542000228 Henry Cohn, 2026, needs more optimization.
32 296 0.161699497204 Henry Cohn, 2026, needs more optimization.
32 297 0.162107072982 Henry Cohn, 2026, needs more optimization.
32 298 0.162273105492 Henry Cohn, 2026, needs more optimization.
32 299 0.162356027665 Henry Cohn, 2026, needs more optimization.
32 300 0.162519044522 Henry Cohn, 2026, needs more optimization.
32 301 0.163163113811 Henry Cohn, 2025, needs more optimization.
32 302 0.163517519625 Henry Cohn, 2025, needs more optimization.
32 303 0.163608940714 Henry Cohn, 2025, needs more optimization.
32 304 0.164101020235 Henry Cohn, 2026, needs more optimization.
32 305 0.164217939271 Henry Cohn, 2026, needs more optimization.
32 306 0.164234344669 Henry Cohn, 2026, needs more optimization.
32 307 0.164251856881 Henry Cohn, 2025, needs more optimization.
32 308 0.164292780495 Henry Cohn, 2025, needs more optimization.
32 309 0.164516330830 Henry Cohn, 2025, needs more optimization.
32 310 0.164533585225 Henry Cohn, 2025, needs more optimization.
32 311 0.164665715925 Henry Cohn, 2025, needs more optimization.
32 312 0.164736038826 Henry Cohn, 2026, needs more optimization.
32 313 0.164800531621 Henry Cohn, 2026, needs more optimization.
32 314 0.164800531709 Henry Cohn, 2025, needs more optimization.
32 315 0.164812333655 Henry Cohn, 2025, needs more optimization.
32 316 0.166688829321 Henry Cohn, 2025, needs more optimization.
32 320 0.166820612586 Henry Cohn, 2026, needs more optimization.
32 328 0.167922237102 Henry Cohn, 2026, needs more optimization.
32 336 0.169882736253 Henry Cohn, 2026, needs more optimization.
32 344 0.170713548028 Henry Cohn, 2026, needs more optimization.
32 352 0.172985497766 Henry Cohn, 2026, needs more optimization.
32 353 0.176428950350 Henry Cohn, 2026, needs more optimization.
32 354 0.176428973679 Henry Cohn, 2026, needs more optimization.
32 355 0.176451788501 Henry Cohn, 2026, needs more optimization.
32 356 0.177198954461 Henry Cohn, 2026, needs more optimization.
32 357 0.177208538829 Henry Cohn, 2026, needs more optimization.
32 358 0.177232516751 Henry Cohn, 2025, needs more optimization.
32 360 0.177294100324 Henry Cohn, 2026, needs more optimization.
32 362 0.177336700360 Henry Cohn, 2025, needs more optimization.
32 363 0.177355864571 Henry Cohn, 2025, needs more optimization.
32 365 0.177403896667 Henry Cohn, 2025, needs more optimization.
32 366 0.177457583407 Henry Cohn, 2025, needs more optimization.
32 367 0.177668635338 Henry Cohn, 2026, needs more optimization.
32 368 0.177952192805 Henry Cohn, 2026, needs more optimization.
32 369 0.177979746530 Henry Cohn, 2025, needs more optimization.
32 370 0.178032418622 Henry Cohn, 2025, needs more optimization.
32 371 0.178073828986 Henry Cohn, 2025, needs more optimization.
32 372 0.178095270406 Henry Cohn, 2025, needs more optimization.
32 373 0.178265672389 Henry Cohn, 2025, needs more optimization.
32 374 0.178292131328 Henry Cohn, 2025, needs more optimization.
32 375 0.178311620647 Henry Cohn, 2025, needs more optimization.
32 376 0.178315324403 Henry Cohn, 2026, needs more optimization.
32 377 0.178358605451 Henry Cohn, 2025, needs more optimization.
32 378 0.178362988122 Henry Cohn, 2025, needs more optimization.
32 379 0.178383961332 Henry Cohn, 2025, needs more optimization.
32 380 0.179041717229 Henry Cohn, 2025, needs more optimization.
32 381 0.179045766806 Henry Cohn, 2025, needs more optimization.
32 382 0.179092249430 Henry Cohn, 2025, needs more optimization.
32 383 0.179152446284 Henry Cohn, 2025, needs more optimization.
32 384 0.179335801156 Henry Cohn, 2026, needs more optimization.
32 385 0.179356786400 Henry Cohn, 2025, needs more optimization.
32 387 0.179718957095 Henry Cohn, 2025, needs more optimization.
32 388 0.179725817434 Henry Cohn, 2025, needs more optimization.
32 389 0.179852843579 Henry Cohn, 2025, needs more optimization.
32 390 0.179984710270 Henry Cohn, 2025, needs more optimization.
32 392 0.180688469816 Henry Cohn, 2026, needs more optimization.
32 393 0.180975856164 Henry Cohn, 2025, needs more optimization.
32 394 0.181069607451 Henry Cohn, 2025, needs more optimization.
32 395 0.181155096192 Henry Cohn, 2025, needs more optimization.
32 396 0.181240269570 Henry Cohn, 2025, needs more optimization.
32 397 0.181317830477 Henry Cohn, 2025, needs more optimization.
32 398 0.181527503920 Henry Cohn, 2025, needs more optimization.
32 399 0.181848571961 Henry Cohn, 2025, needs more optimization.
32 400 0.181945095808 Henry Cohn, 2026, needs more optimization.
32 401 0.181978777586 Henry Cohn, 2025, needs more optimization.
32 402 0.182219047973 Henry Cohn, 2025, needs more optimization.
32 403 0.182570899265 Henry Cohn, 2025, needs more optimization.
32 404 0.182677019279 Henry Cohn, 2025, needs more optimization.
32 405 0.182835710464 Henry Cohn, 2025, needs more optimization.
32 406 0.182853608628 Henry Cohn, 2025, needs more optimization.
32 407 0.182885908892 Henry Cohn, 2025, needs more optimization.
32 408 0.182925577504 Henry Cohn, 2026, needs more optimization.
32 409 0.183280877984 Henry Cohn, 2025, needs more optimization.
32 410 0.185029828930 Henry Cohn, 2025, needs more optimization.
32 412 0.185043786777 Henry Cohn, 2025, needs more optimization.
32 413 0.185059418161 Henry Cohn, 2025, needs more optimization.
32 414 0.185234156539 Henry Cohn, 2025, needs more optimization.
32 415 0.185270695609 Henry Cohn, 2025, needs more optimization.
32 416 0.185691300174 Henry Cohn, 2026, needs more optimization.
32 417 0.185767568064 Henry Cohn, 2025, needs more optimization.
32 418 0.185793807196 Henry Cohn, 2025, needs more optimization.
32 419 0.185849386954 Henry Cohn, 2025, needs more optimization.
32 420 0.186585101400 Henry Cohn, 2025, needs more optimization.
32 421 0.187264751378 Henry Cohn, 2025, needs more optimization.
32 422 0.187372569965 Henry Cohn, 2025, needs more optimization.
32 423 0.187500608309 Henry Cohn, 2025, needs more optimization.
32 424 0.187677162520 Henry Cohn, 2026, needs more optimization.
32 425 0.187748169214 Henry Cohn, 2025, needs more optimization.
32 426 0.187867093904 Henry Cohn, 2025, needs more optimization.
32 427 0.189248292876 Henry Cohn, 2025, needs more optimization.
32 428 0.189413600468 Henry Cohn, 2025, needs more optimization.
32 429 0.189496872293 Henry Cohn, 2025, needs more optimization.
32 430 0.189519385985 Henry Cohn, 2025, needs more optimization.
32 431 0.189613919573 Henry Cohn, 2025, needs more optimization.
32 432 0.190096051699 Henry Cohn, 2026, needs more optimization.
32 433 0.190140646596 Henry Cohn, 2025, needs more optimization.
32 434 0.190259774616 Henry Cohn, 2025, needs more optimization.
32 435 0.190275021051 Henry Cohn, 2025, needs more optimization.
32 436 0.190293352658 Henry Cohn, 2025, needs more optimization.
32 437 0.190412575829 Henry Cohn, 2025, needs more optimization.
32 438 0.190500167997 Henry Cohn, 2025, needs more optimization.
32 439 0.190594556573 Henry Cohn, 2025, needs more optimization.
32 440 0.190598729392 Henry Cohn, 2026, needs more optimization.
32 442 0.190695092184 Henry Cohn, 2025, needs more optimization.
32 443 0.190970654280 Henry Cohn, 2025, needs more optimization.
32 444 0.191778516690 Henry Cohn, 2025, needs more optimization.
32 445 0.192031953805 Henry Cohn, 2025, needs more optimization.
32 446 0.192165907569 Henry Cohn, 2025, needs more optimization.
32 447 0.192198301060 Henry Cohn, 2025, needs more optimization.
32 448 0.192575448488 Henry Cohn, 2026, needs more optimization.
32 449 0.192604978591 Henry Cohn, 2025, needs more optimization.
32 450 0.193705426727 Henry Cohn, 2025, needs more optimization.
32 451 0.193708611047 Henry Cohn, 2025, needs more optimization.
32 452 0.193771321059 Henry Cohn, 2025, needs more optimization.
32 453 0.193774937757 Henry Cohn, 2025, needs more optimization.
32 454 0.193785864652 Henry Cohn, 2025, needs more optimization.
32 455 0.193793357389 Henry Cohn, 2025, needs more optimization.
32 456 0.193820455278 Henry Cohn, 2026, needs more optimization.
32 457 0.193850961075 Henry Cohn, 2025, needs more optimization.
32 458 0.193882680642 Henry Cohn, 2025, needs more optimization.
32 459 0.193983485564 Henry Cohn, 2025, needs more optimization.
32 460 0.194047048217 Henry Cohn, 2025, needs more optimization.
32 461 0.194081363290 Henry Cohn, 2025, needs more optimization.
32 462 0.194297974813 Henry Cohn, 2025, needs more optimization.
32 463 0.194514027621 Henry Cohn, 2025, needs more optimization.
32 464 0.194671637019 Henry Cohn, 2026, needs more optimization.
32 465 0.194746076501 Henry Cohn, 2025, needs more optimization.
32 467 0.194936725834 Henry Cohn, 2025, needs more optimization.
32 468 0.194992476201 Henry Cohn, 2025, needs more optimization.
32 470 0.195041324171 Henry Cohn, 2025, needs more optimization.
32 471 0.195309985495 Henry Cohn, 2025, needs more optimization.
32 472 0.195329328789 Henry Cohn, 2026, needs more optimization.
32 473 0.195843486350 Henry Cohn, 2025, needs more optimization.
32 476 0.196783837506 Henry Cohn, 2026, needs more optimization.
32 477 0.196868046017 Henry Cohn, 2026, needs more optimization.
32 478 0.196868046050 Henry Cohn, 2025, needs more optimization.
32 480 0.196953029432 Henry Cohn, 2026, needs more optimization.
32 481 0.197048441972 Henry Cohn, 2025, needs more optimization.
32 483 0.197099123339 Henry Cohn, 2025, needs more optimization.
32 484 0.197143227415 Henry Cohn, 2026, needs more optimization.
32 485 0.197177452990 Henry Cohn, 2025, needs more optimization.
32 486 0.197200952183 Henry Cohn, 2025, needs more optimization.
32 488 0.197225446503 Henry Cohn, 2026, needs more optimization.
32 489 0.197286255999 Henry Cohn, 2025, needs more optimization.
32 490 0.197301717432 Henry Cohn, 2025, needs more optimization.
32 491 0.197330090496 Henry Cohn, 2025, needs more optimization.
32 492 0.197343760260 Henry Cohn, 2026, needs more optimization.
32 493 0.197415862215 Henry Cohn, 2025, needs more optimization.
32 494 0.197440959877 Henry Cohn, 2025, needs more optimization.
32 496 0.198146563805 Henry Cohn, 2026, needs more optimization.
32 497 0.198223211211 Henry Cohn, 2026, needs more optimization.
32 498 0.198246760918 Henry Cohn, 2026, needs more optimization.
32 499 0.198539780573 Henry Cohn, 2026, needs more optimization.
32 500 0.198554124984 Henry Cohn, 2026, needs more optimization.
32 501 0.199319841545 Henry Cohn, 2026, needs more optimization.
32 502 0.199319841599 Henry Cohn, 2025, needs more optimization.
32 504 0.199336113389 Henry Cohn, 2026, needs more optimization.
32 508 0.199362959024 Henry Cohn, 2026, needs more optimization.
32 509 0.199378564517 Henry Cohn, 2025, needs more optimization.
32 510 0.199386954560 Henry Cohn, 2025, needs more optimization.
32 512 0.199390912557 Henry Cohn, 2026, needs more optimization.
32 513 0.199399649703 Henry Cohn, 2025, needs more optimization.
32 514 0.199407130962 Henry Cohn, 2025, needs more optimization.
32 515 0.199416557987 Henry Cohn, 2025, needs more optimization.
32 516 0.199426209172 Henry Cohn, 2026, needs more optimization.
32 517 0.199432797025 Henry Cohn, 2025, needs more optimization.
32 518 0.199450104889 Henry Cohn, 2025, needs more optimization.
32 519 0.199507086822 Henry Cohn, 2025, needs more optimization.
32 520 0.199518644335 Henry Cohn, 2026, needs more optimization.
32 524 0.199541335713 Henry Cohn, 2026, needs more optimization.
32 525 0.199554430682 Henry Cohn, 2025, needs more optimization.
32 528 0.199558754784 Henry Cohn, 2026, needs more optimization.
32 529 0.199572873539 Henry Cohn, 2025, needs more optimization.
32 532 0.199587261641 Henry Cohn, 2026, needs more optimization.
32 533 0.199621988169 Henry Cohn, 2025, needs more optimization.
32 534 0.199625963538 Henry Cohn, 2025, needs more optimization.
32 536 0.199681375382 Henry Cohn, 2026, needs more optimization.
32 540 0.199684128978 Henry Cohn, 2026, needs more optimization.
32 543 0.199715301377 Henry Cohn, 2026, needs more optimization.
32 544 0.199732624672 Henry Cohn, 2026, needs more optimization.
32 545 0.199732737568 Henry Cohn, 2026, needs more optimization.
32 548 0.199734949274 Henry Cohn, 2026, needs more optimization.
32 552 0.199745278477 Henry Cohn, 2026, needs more optimization.
32 553 0.199768966540 Henry Cohn, 2025, needs more optimization.
32 554 0.199773953538 Henry Cohn, 2025, needs more optimization.
32 556 0.199774357232 Henry Cohn, 2026, needs more optimization.
32 560 0.199782046435 Henry Cohn, 2026, needs more optimization.
32 564 0.199796886903 Henry Cohn, 2026, needs more optimization.
32 566 0.199821586337 Henry Cohn, 2025, needs more optimization.
32 568 0.199826147563 Henry Cohn, 2026, needs more optimization.
32 572 0.199838559293 Henry Cohn, 2026, needs more optimization.
32 573 0.199857441710 Henry Cohn, 2025, needs more optimization.
32 576 0.199874346564 Henry Cohn, 2026, needs more optimization.
32 577 0.199896658507 Henry Cohn, 2025, needs more optimization.
32 580 0.199897063468 Henry Cohn, 2026, needs more optimization.
32 582 0.199912209372 Henry Cohn, 2025, needs more optimization.
32 584 0.199916090948 Henry Cohn, 2026, needs more optimization.
32 588 0.199924608878 Henry Cohn, 2026, needs more optimization.
32 592 0.199939470789 Henry Cohn, 2026, needs more optimization.
32 593 0.199955171974 Henry Cohn, 2025, needs more optimization.
32 594 0.199965982072 Henry Cohn, 2025, needs more optimization.
32 595 0.199968056167 Henry Cohn, 2025, needs more optimization.
32 596 0.199971184268 Henry Cohn, 2026, needs more optimization.
32 597 0.199999455451 Henry Cohn, 2025, needs more optimization.
32 599 0.199999980426 Henry Cohn, 2025, needs more optimization.
32 600 0.200023969452 Henry Cohn, 2026, needs more optimization.
32 601 0.200078681940 Orthogonal union of 599 points in 31 dimensions and 2 points in 1 dimension.
32 602 0.200177422653 Orthogonal union of 600 points in 31 dimensions and 2 points in 1 dimension.
32 603 0.221586593276 Henry Cohn, 2025, needs more optimization.
32 604 0.221662993664 Henry Cohn, 2026, needs more optimization.
32 605 0.221717120780 Henry Cohn, 2025, needs more optimization.
32 606 0.221813917898 Henry Cohn, 2025, needs more optimization.
32 607 0.222022765006 Henry Cohn, 2025, needs more optimization.
32 608 0.222048835718 Henry Cohn, 2026, needs more optimization.
32 609 0.222537944124 Henry Cohn, 2025, needs more optimization.
32 610 0.222560038881 Henry Cohn, 2025, needs more optimization.
32 611 0.222604300344 Henry Cohn, 2025, needs more optimization.
32 612 0.222837384274 Henry Cohn, 2026, needs more optimization.
32 613 0.222902158393 Henry Cohn, 2025, needs more optimization.
32 614 0.223071161667 Henry Cohn, 2025, needs more optimization.
32 615 0.223421524187 Henry Cohn, 2025, needs more optimization.
32 616 0.223459110719 Henry Cohn, 2026, needs more optimization.
32 617 0.223580573442 Henry Cohn, 2025, needs more optimization.
32 618 0.223636523074 Henry Cohn, 2025, needs more optimization.
32 619 0.224074090101 Henry Cohn, 2025, needs more optimization.
32 620 0.224125087730 Henry Cohn, 2026, needs more optimization.
32 621 0.224198109869 Henry Cohn, 2025, needs more optimization.
32 622 0.224349141028 Henry Cohn, 2025, needs more optimization.
32 623 0.224594176934 Henry Cohn, 2025, needs more optimization.
32 624 0.224628079332 Henry Cohn, 2026, needs more optimization.
32 625 0.224688239800 Henry Cohn, 2025, needs more optimization.
32 626 0.224908630287 Henry Cohn, 2025, needs more optimization.
32 627 0.225052208509 Henry Cohn, 2025, needs more optimization.
32 628 0.225235692634 Henry Cohn, 2026, needs more optimization.
32 629 0.225281047296 Henry Cohn, 2025, needs more optimization.
32 631 0.225529335344 Henry Cohn, 2025, needs more optimization.
32 632 0.225945372898 Henry Cohn, 2026, needs more optimization.
32 633 0.225983394293 Henry Cohn, 2025, needs more optimization.
32 634 0.226044109732 Henry Cohn, 2025, needs more optimization.
32 635 0.226369244528 Henry Cohn, 2025, needs more optimization.
32 636 0.226423782384 Henry Cohn, 2026, needs more optimization.
32 637 0.226562122518 Henry Cohn, 2025, needs more optimization.
32 638 0.226608149926 Henry Cohn, 2025, needs more optimization.
32 639 0.226972193420 Henry Cohn, 2025, needs more optimization.
32 640 0.227007393943 Henry Cohn, 2026, needs more optimization.
32 641 0.227081509842 Henry Cohn, 2025, needs more optimization.
32 642 0.227192756570 Henry Cohn, 2025, needs more optimization.
32 643 0.227375016220 Henry Cohn, 2025, needs more optimization.
32 644 0.227800189903 Henry Cohn, 2026, needs more optimization.
32 645 0.227876477524 Henry Cohn, 2025, needs more optimization.
32 646 0.228180662642 Henry Cohn, 2025, needs more optimization.
32 647 0.228227639935 Henry Cohn, 2025, needs more optimization.
32 648 0.228245509908 Henry Cohn, 2026, needs more optimization.
32 649 0.228297025478 Henry Cohn, 2025, needs more optimization.
32 650 0.228664894603 Henry Cohn, 2025, needs more optimization.
32 651 0.228706321354 Henry Cohn, 2025, needs more optimization.
32 652 0.228750666882 Henry Cohn, 2026, needs more optimization.
32 653 0.229028391919 Henry Cohn, 2025, needs more optimization.
32 654 0.229054054679 Henry Cohn, 2025, needs more optimization.
32 655 0.229370166746 Henry Cohn, 2025, needs more optimization.
32 656 0.229410131495 Henry Cohn, 2026, needs more optimization.
32 657 0.229470677006 Henry Cohn, 2025, needs more optimization.
32 658 0.229577565310 Henry Cohn, 2025, needs more optimization.
32 659 0.229842838967 Henry Cohn, 2025, needs more optimization.
32 660 0.229882266651 Henry Cohn, 2026, needs more optimization.
32 661 0.229937196740 Henry Cohn, 2025, needs more optimization.
32 662 0.230366676017 Henry Cohn, 2025, needs more optimization.
32 663 0.230440116248 Henry Cohn, 2025, needs more optimization.
32 664 0.230444353470 Henry Cohn, 2026, needs more optimization.
32 665 0.230515995016 Henry Cohn, 2025, needs more optimization.
32 666 0.230819239542 Henry Cohn, 2025, needs more optimization.
32 667 0.230873276163 Henry Cohn, 2025, needs more optimization.
32 668 0.230950717621 Henry Cohn, 2026, needs more optimization.
32 669 0.231005292055 Henry Cohn, 2025, needs more optimization.
32 670 0.231105951016 Henry Cohn, 2025, needs more optimization.
32 671 0.231291444753 Henry Cohn, 2025, needs more optimization.
32 672 0.231336958831 Henry Cohn, 2026, needs more optimization.
32 673 0.231602710515 Henry Cohn, 2025, needs more optimization.
32 674 0.231646681715 Henry Cohn, 2025, needs more optimization.
32 675 0.231710945281 Henry Cohn, 2025, needs more optimization.
32 676 0.231766221298 Henry Cohn, 2026, needs more optimization.
32 677 0.231948154617 Henry Cohn, 2025, needs more optimization.
32 678 0.231965445671 Henry Cohn, 2025, needs more optimization.
32 679 0.232051536283 Henry Cohn, 2025, needs more optimization.
32 680 0.232210470967 Henry Cohn, 2026, needs more optimization.
32 681 0.232241559297 Henry Cohn, 2025, needs more optimization.
32 682 0.232259409247 Henry Cohn, 2025, needs more optimization.
32 683 0.232311648171 Henry Cohn, 2025, needs more optimization.
32 684 0.232314107194 Henry Cohn, 2026, needs more optimization.
32 685 0.232346036283 Henry Cohn, 2025, needs more optimization.
32 686 0.232412324006 Henry Cohn, 2025, needs more optimization.
32 687 0.232422487684 Henry Cohn, 2025, needs more optimization.
32 688 0.232514326953 Henry Cohn, 2026, needs more optimization.
32 689 0.232646292853 Henry Cohn, 2025, needs more optimization.
32 690 0.232761417790 Henry Cohn, 2025, needs more optimization.
32 691 0.232784628989 Henry Cohn, 2025, needs more optimization.
32 692 0.232802252433 Henry Cohn, 2026, needs more optimization.
32 693 0.232846649554 Henry Cohn, 2025, needs more optimization.
32 694 0.232857383509 Henry Cohn, 2025, needs more optimization.
32 695 0.232957261911 Henry Cohn, 2025, needs more optimization.
32 696 0.233073726902 Henry Cohn, 2026, needs more optimization.
32 697 0.233088728155 Henry Cohn, 2025, needs more optimization.
32 698 0.233123581735 Henry Cohn, 2025, needs more optimization.
32 699 0.233165875520 Henry Cohn, 2025, needs more optimization.
32 700 0.233211637080 Henry Cohn, 2026, needs more optimization.
32 701 0.233280683689 Henry Cohn, 2025, needs more optimization.
32 702 0.233551310576 Henry Cohn, 2025, needs more optimization.
32 703 0.233574236086 Henry Cohn, 2025, needs more optimization.
32 704 0.233651474269 Henry Cohn, 2026, needs more optimization.
32 705 0.233686743834 Henry Cohn, 2025, needs more optimization.
32 706 0.233811611908 Henry Cohn, 2025, needs more optimization.
32 707 0.234273368337 Henry Cohn, 2025, needs more optimization.
32 708 0.234280236821 Henry Cohn, 2026, needs more optimization.
32 709 0.234358786111 Henry Cohn, 2025, needs more optimization.
32 710 0.234387985190 Henry Cohn, 2025, needs more optimization.
32 711 0.234403334418 Henry Cohn, 2025, needs more optimization.
32 712 0.234408094694 Henry Cohn, 2026, needs more optimization.
32 713 0.234451908934 Henry Cohn, 2025, needs more optimization.
32 714 0.234477850791 Henry Cohn, 2025, needs more optimization.
32 715 0.234508571554 Henry Cohn, 2025, needs more optimization.
32 716 0.234819711583 Henry Cohn, 2026, needs more optimization.
32 717 0.234865960112 Henry Cohn, 2025, needs more optimization.
32 718 0.235006789578 Henry Cohn, 2025, needs more optimization.
32 720 0.235108958563 Henry Cohn, 2026, needs more optimization.
32 722 0.235145318288 Henry Cohn, 2025, needs more optimization.
32 723 0.235160667649 Henry Cohn, 2025, needs more optimization.
32 724 0.235174527831 Henry Cohn, 2026, needs more optimization.
32 725 0.235261358131 Henry Cohn, 2025, needs more optimization.
32 726 0.235311219772 Henry Cohn, 2025, needs more optimization.
32 727 0.235330602148 Henry Cohn, 2025, needs more optimization.
32 728 0.235381651940 Henry Cohn, 2026, needs more optimization.
32 729 0.235411848687 Henry Cohn, 2025, needs more optimization.
32 730 0.235460693544 Henry Cohn, 2025, needs more optimization.
32 732 0.235464780241 Henry Cohn, 2026, needs more optimization.
32 733 0.235501564441 Henry Cohn, 2025, needs more optimization.
32 734 0.235522622240 Henry Cohn, 2025, needs more optimization.
32 735 0.235592448594 Henry Cohn, 2025, needs more optimization.
32 736 0.235653711267 Henry Cohn, 2026, needs more optimization.
32 737 0.236038834283 Henry Cohn, 2025, needs more optimization.
32 738 0.236062923210 Henry Cohn, 2025, needs more optimization.
32 739 0.236099705270 Henry Cohn, 2025, needs more optimization.
32 740 0.236276041096 Henry Cohn, 2026, needs more optimization.
32 741 0.237330609807 Henry Cohn, 2026, needs more optimization.
32 744 0.237344444185 Henry Cohn, 2026, needs more optimization.
32 745 0.237406770450 Henry Cohn, 2026, needs more optimization.
32 746 0.237418200653 Henry Cohn, 2026, needs more optimization.
32 747 0.237429998081 Henry Cohn, 2026, needs more optimization.
32 748 0.237434862207 Henry Cohn, 2026, needs more optimization.
32 749 0.237467505111 Henry Cohn, 2026, needs more optimization.
32 750 0.237500583996 Henry Cohn, 2026, needs more optimization.
32 751 0.237503643651 Henry Cohn, 2026, needs more optimization.
32 752 0.237539062019 Henry Cohn, 2026, needs more optimization.
32 753 0.237562634557 Henry Cohn, 2026, needs more optimization.
32 754 0.237583581990 Henry Cohn, 2026, needs more optimization.
32 756 0.237596636892 Henry Cohn, 2026, needs more optimization.
32 757 0.237607606558 Henry Cohn, 2026, needs more optimization.
32 760 0.237622301590 Henry Cohn, 2026, needs more optimization.
32 761 0.237646526637 Henry Cohn, 2025, needs more optimization.
32 762 0.237680659744 Henry Cohn, 2025, needs more optimization.
32 764 0.237910698138 Henry Cohn, 2026, needs more optimization.
32 765 0.237943461008 Henry Cohn, 2026, needs more optimization.
32 767 0.237963174223 Henry Cohn, 2026, needs more optimization.
32 768 0.237975403324 Henry Cohn, 2026, needs more optimization.
32 769 0.237996834278 Henry Cohn, 2026, needs more optimization.
32 772 0.238017976129 Henry Cohn, 2026, needs more optimization.
32 776 0.238030082474 Henry Cohn, 2026, needs more optimization.
32 780 0.238048209618 Henry Cohn, 2026, needs more optimization.
32 781 0.238068834038 Henry Cohn, 2025, needs more optimization.
32 782 0.238072141725 Henry Cohn, 2025, needs more optimization.
32 783 0.238082865036 Henry Cohn, 2025, 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