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 preprint.
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 preprint.
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 preprint.
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 0.952386964146 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.
3 142 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 0.953228658095 Henry Cohn, 2024.
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 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).
3 147 0.954232032048 Henry Cohn, 2024.
3 148 0.954536844663 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).
3 149 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 0.955934494320 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.
3 154 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 0.959759379334 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).
3 169 0.960021874369 Henry Cohn, 2024.
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 0.960456779730 Henry Cohn, 2024.
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 0.960986468709 Henry Cohn, 2024.
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 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).
3 177 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 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).
3 184 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 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).
3 190 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 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).
3 197 0.965672149432 Henry Cohn, 2024.
3 198 0.965829315374 Henry Cohn, 2024.
3 199 0.965916172795 Henry Cohn, 2024.
3 200 0.965942282148 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.
3 201 0.966306900791 Henry Cohn, 2024.
3 202 0.966421093222 Henry Cohn, 2024.
3 203 0.966622724376 Henry Cohn, 2024.
3 204 0.966712897537 Henry Cohn, 2024.
3 205 0.966826988724 Henry Cohn, 2024.
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 0.968277562077 Henry Cohn, 2024.
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 0.968883813017 Henry Cohn, 2024.
3 219 0.969051824494 Henry Cohn, 2024.
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 0.970130470358 Henry Cohn, 2024.
3 228 0.970249147842 Henry Cohn, 2024.
3 229 0.970371960081 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 0.970852351181 Henry Cohn, 2024.
3 234 0.970907365376 Henry Cohn, 2024.
3 235 0.971108986707 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 0.971893680990 Henry Cohn, 2024.
3 243 0.971985441053 Henry Cohn, 2024.
3 244 0.972112317307 Henry Cohn, 2024.
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 0.972810481678 Henry Cohn, 2024.
3 251 0.972879991602 Henry Cohn, 2024.
3 252 0.973005270899 Henry Cohn, 2024.
3 253 0.973112111220 Henry Cohn, 2024.
3 254 0.973167964183 Henry Cohn, 2024.
3 255 0.973336938776 Henry Cohn, 2024.
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 0.973920872604 Henry Cohn, 2024.
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 0.974465987486 Henry Cohn, 2024.
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.
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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.
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3 298 0.977140172393 Henry Cohn, 2024.
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.
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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 0.981969354778 R. H. Hardin, N. J. A. Sloane, and W. D. Smith, Tables of spherical codes with icosahedral symmetry, 1994–2000.
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 0.985721554115 Henry Cohn, 2024.
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 0.986562996172 R. H. Hardin, N. J. A. Sloane, and W. D. Smith, Tables of spherical codes with icosahedral symmetry, 1994–2000.
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 0.988045168272 R. H. Hardin, N. J. A. Sloane, and W. D. Smith, Tables of spherical codes with icosahedral symmetry, 1994–2000.
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.
3 620 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.
3 692 0.990060116362 R. H. Hardin, N. J. A. Sloane, and W. D. Smith, Tables of spherical codes with icosahedral symmetry, 1994–2000.
3 702 0.990207682442 R. H. Hardin, N. J. A. Sloane, and W. D. Smith, Tables of spherical codes with icosahedral symmetry, 1994–2000.
3 703 0.990340880428 Henry Cohn, 2024, needs more optimization.
3 704 0.990350573317 Henry Cohn, 2024, needs more optimization.
3 706 0.990376246150 Henry Cohn, 2024, needs more optimization.
3 707 0.990401112844 Henry Cohn, 2024, needs more optimization.
3 708 0.990414278256 Henry Cohn, 2024, needs more optimization.
3 710 0.990426810586 Henry Cohn, 2024, needs more optimization.
3 711 0.990450177778 Henry Cohn, 2024, needs more optimization.
3 712 0.990461738716 Henry Cohn, 2024, needs more optimization.
3 715 0.990479613717 Henry Cohn, 2024, needs more optimization.
3 720 0.990483363237 Henry Cohn, 2024.
3 721 0.990580797616 Henry Cohn, 2024, needs more optimization.
3 722 0.990610436585 Henry Cohn, 2024, needs more optimization.
3 723 0.990613217077 Henry Cohn, 2024, needs more optimization.
3 732 0.990623187196 R. H. Hardin, N. J. A. Sloane, and W. D. Smith, Tables of spherical codes with icosahedral symmetry, 1994–2000.
3 740 0.990730815439 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.
3 752 0.990872395915 Henry Cohn, 2024.
3 753 0.990991032801 Henry Cohn, 2024, needs more optimization.
3 754 0.991014149489 Henry Cohn, 2024, needs more optimization.
3 755 0.991017806028 Henry Cohn, 2024, needs more optimization.
3 757 0.991031455946 Henry Cohn, 2024, needs more optimization.
3 758 0.991038437820 Henry Cohn, 2024, needs more optimization.
3 759 0.991048129281 Henry Cohn, 2024, needs more optimization.
3 761 0.991063426688 Henry Cohn, 2024, needs more optimization.
3 770 0.991085755280 Henry Cohn, 2024.
3 780 0.991203514614 Henry Cohn, 2024.
3 782 0.991222201087 Henry Cohn, 2024.
3 783 0.991328528269 Henry Cohn, 2024, needs more optimization.
3 792 0.991331558735 Henry Cohn, 2024.
3 800 0.991421236921 Henry Cohn, 2024.
3 801 0.991531702230 Henry Cohn, 2024, needs more optimization.
3 802 0.991539847367 Henry Cohn, 2024, needs more optimization.
3 812 0.991551443868 Henry Cohn, 2024.
3 813 0.991634158400 Henry Cohn, 2024, needs more optimization.
3 815 0.991651531575 Henry Cohn, 2024, needs more optimization.
3 816 0.991674170087 Henry Cohn, 2024, needs more optimization.
3 817 0.991693736070 Henry Cohn, 2024, needs more optimization.
3 818 0.991700527667 Henry Cohn, 2024, needs more optimization.
3 819 0.991714320469 Henry Cohn, 2024, needs more optimization.
3 830 0.991724915725 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.
3 852 0.991904249523 R. H. Hardin, N. J. A. Sloane, and W. D. Smith, Tables of spherical codes with icosahedral symmetry, 1994–2000.
3 860 0.992000324488 R. H. Hardin, N. J. A. Sloane, and W. D. Smith, Tables of spherical codes with icosahedral symmetry, 1994–2000.
3 872 0.992098850920 R. H. Hardin, N. J. A. Sloane, and W. D. Smith, Tables of spherical codes with icosahedral symmetry, 1994–2000.
3 873 0.992201290404 Henry Cohn, 2024, needs more optimization.
3 882 0.992208997020 Henry Cohn, 2024.
3 883 0.992314839844 Henry Cohn, 2024, needs more optimization.
3 886 0.992322756743 Henry Cohn, 2024, needs more optimization.
3 888 0.992330406551 Henry Cohn, 2024, needs more optimization.
3 889 0.992354404308 Henry Cohn, 2024, needs more optimization.
3 890 0.992359580205 Henry Cohn, 2024, needs more optimization.
3 900 0.992360793848 Henry Cohn, 2024.
3 912 0.992458117635 R. H. Hardin, N. J. A. Sloane, and W. D. Smith, Tables of spherical codes with icosahedral symmetry, 1994–2000.
3 920 0.992529804942 Henry Cohn, 2024.
3 930 0.992603658000 Henry Cohn, 2024.
3 931 0.992696378869 Henry Cohn, 2024, needs more optimization.
3 942 0.992697727936 Henry Cohn, 2024.
3 950 0.992759278250 Henry Cohn, 2024.
3 960 0.992830967656 Henry Cohn, 2024.
3 962 0.992849707370 Henry Cohn, 2024.
3 972 0.992923191999 Henry Cohn, 2024.
3 980 0.992974636259 Henry Cohn, 2024.
3 992 0.993062786669 Henry Cohn, 2024.
3 1002 0.993129515697 Henry Cohn, 2024.
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 1020 0.993235373238 R. H. Hardin, N. J. A. Sloane, and W. D. Smith, Tables of spherical codes with icosahedral symmetry, 1994–2000.
3 1022 0.993261497684 R. H. Hardin, N. J. A. Sloane, and W. D. Smith, Tables of spherical codes with icosahedral symmetry, 1994–2000.
3 1024 0.993275446250 Henry Cohn, 2024.
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 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.
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 0.722369011238 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
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 0.726684776289 Henry Cohn, 2023.
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 0.733882912083 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 0.745999226475 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
4 67 0.748969904957 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
4 68 0.751044492573 J. Wang, Finding and investigating exact spherical codes, Experiment. Math. 18 (2009), 249–256, https://projecteuclid.org/euclid.em/1259158434.
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 0.753734083742 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
4 71 0.756376010065 Henry Cohn, 2024.
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 0.759550197779 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
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 0.765202573468 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
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 0.777799422383 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
4 82 0.779757103986 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
4 83 0.781072136090 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
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 0.784955041928 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
4 87 0.785515524692 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
4 88 0.785927666189 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 0.792211352845 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
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 0.793553794017 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
4 95 0.796982807650 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
4 96 0.797981478600 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
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 0.803902192257 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
4 102 0.804700788445 Henry Cohn, 2024.
4 103 0.805093353038 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
4 104 0.806316980692 Henry Cohn, 2025.
4 105 0.807105103190 Henry Cohn, 2024.
4 106 0.807631898536 Henry Cohn, 2024.
4 107 0.808031793624 Henry Cohn, 2025.
4 108 0.808494082581 Henry Cohn, 2025.
4 109 0.808699172186 Henry Cohn, 2025.
4 110 0.808930754825 Henry Cohn, 2025.
4 111 0.809001788649 Henry Cohn, 2025.
4 112 0.809016771299 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 0.824643413914 Henry Cohn, 2024.
4 122 0.826376579266 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
4 123 0.827332082575 Henry Cohn, 2023.
4 124 0.829082798071 Henry Cohn, 2024.
4 125 0.830275233675 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
4 126 0.831282569581 Henry Cohn, 2024.
4 127 0.832258618537 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
4 128 0.833185392968 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
4 129 0.833853228231 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
4 130 0.834775628422 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
4 131 0.835560226726 Henry Cohn, 2025, needs more optimization.
4 132 0.835884092870 Henry Cohn, 2025.
4 133 0.836985790788 Henry Cohn, 2025.
4 134 0.837627700361 Henry Cohn, 2025.
4 135 0.838176006001 Henry Cohn, 2025.
4 136 0.838479552016 Henry Cohn, 2025.
4 137 0.838888930100 Henry Cohn, 2024.
4 138 0.839095930916 Henry Cohn, 2025.
4 139 0.839507625781 Henry Cohn, 2024.
4 140 0.839798108374 Henry Cohn, 2025.
4 141 0.840152855333 Henry Cohn, 2024.
4 142 0.840928862073 Henry Cohn, 2025.
4 143 0.842651920763 Henry Cohn, 2025.
4 144 0.843254231628 Henry Cohn, 2025.
4 145 0.845008421248 Henry Cohn, 2025.
4 146 0.846045194083 Henry Cohn, 2024.
4 147 0.847007565182 Henry Cohn, 2025.
4 148 0.847356034901 Henry Cohn, 2025, needs more optimization.
4 149 0.847708866977 Henry Cohn, 2025.
4 150 0.848008139501 Henry Cohn, 2025.
4 151 0.848398199561 Henry Cohn, 2025.
4 152 0.848746833410 Henry Cohn, 2024.
4 153 0.849106836683 Henry Cohn, 2024.
4 154 0.849448181031 Henry Cohn, 2024.
4 155 0.850535901046 Henry Cohn, 2025.
4 156 0.852461943923 Henry Cohn, 2025.
4 157 0.853201053249 Henry Cohn, 2025.
4 158 0.853647173508 Henry Cohn, 2025.
4 159 0.853852414168 Henry Cohn, 2025.
4 160 0.854022528612 Henry Cohn, 2025.
4 161 0.855045269236 Henry Cohn, 2025.
4 162 0.856062235978 Henry Cohn, 2024, needs more optimization.
4 163 0.856545645889 Henry Cohn, 2025.
4 164 0.856668127760 Henry Cohn, 2025.
4 165 0.856908324217 Henry Cohn, 2024.
4 166 0.857226389077 Henry Cohn, 2025.
4 167 0.857623949424 Henry Cohn, 2024.
4 168 0.859313783213 Henry Cohn, 2024.
4 169 0.860470620189 Henry Cohn, 2024, needs more optimization.
4 170 0.861395491524 Henry Cohn, 2024, needs more optimization.
4 171 0.861963021719 Henry Cohn, 2025.
4 172 0.862493564532 Henry Cohn, 2025.
4 173 0.862790116325 Henry Cohn, 2025.
4 174 0.863296180866 Henry Cohn, 2024, needs more optimization.
4 175 0.863367463185 Henry Cohn, 2025.
4 176 0.863629502475 Henry Cohn, 2024, needs more optimization.
4 177 0.863814627381 Henry Cohn, 2025.
4 178 0.863941161713 Henry Cohn, 2025.
4 179 0.864723195029 Henry Cohn, 2025.
4 180 0.865805660331 Henry Cohn, 2024, needs more optimization.
4 181 0.866600926759 Henry Cohn, 2025, needs more optimization.
4 182 0.867175044126 Henry Cohn, 2024, needs more optimization.
4 183 0.867375745581 Henry Cohn, 2024, needs more optimization.
4 184 0.867764646067 Henry Cohn, 2025.
4 185 0.868235766641 Henry Cohn, 2025.
4 186 0.868539112886 Henry Cohn, 2025.
4 187 0.868983973672 Henry Cohn, 2025.
4 188 0.869250376158 Henry Cohn, 2024.
4 189 0.869493523233 Henry Cohn, 2024, needs more optimization.
4 190 0.870057284609 Henry Cohn, 2025.
4 191 0.871104527134 Henry Cohn, 2024, needs more optimization.
4 192 0.871359261965 Henry Cohn, 2024, needs more optimization.
4 193 0.871545546243 Henry Cohn, 2025.
4 194 0.871792029869 Henry Cohn, 2025, needs more optimization.
4 195 0.872110216189 Henry Cohn, 2025.
4 196 0.872624857394 Henry Cohn, 2025.
4 197 0.873487427519 Henry Cohn, 2025.
4 198 0.874181617265 Henry Cohn, 2024, needs more optimization.
4 199 0.875069584192 Henry Cohn, 2025.
4 200 0.875749485568 Henry Cohn, 2024, needs more optimization.
4 201 0.876314814493 Henry Cohn, 2025.
4 202 0.876692218769 Henry Cohn, 2024, needs more optimization.
4 203 0.876947417589 Henry Cohn, 2024, needs more optimization.
4 204 0.877392685484 Henry Cohn, 2025.
4 205 0.877537776607 Henry Cohn, 2024, needs more optimization.
4 206 0.878017860463 Henry Cohn, 2024, needs more optimization.
4 207 0.878030418848 Henry Cohn, 2024, needs more optimization.
4 208 0.878236126718 Henry Cohn, 2024, needs more optimization.
4 209 0.878652010549 Henry Cohn, 2024, needs more optimization.
4 210 0.879214731108 Henry Cohn, 2024, needs more optimization.
4 211 0.879769460878 Henry Cohn, 2025.
4 212 0.879882006013 Henry Cohn, 2024, needs more optimization.
4 213 0.879961582933 Henry Cohn, 2024, needs more optimization.
4 214 0.879976571390 Henry Cohn, 2024, needs more optimization.
4 215 0.880272662054 Henry Cohn, 2025.
4 216 0.880912444476 Henry Cohn, 2024, needs more optimization.
4 217 0.881539806860 Henry Cohn, 2025.
4 218 0.882210786599 Henry Cohn, 2024, needs more optimization.
4 219 0.882481279113 Henry Cohn, 2024, needs more optimization.
4 220 0.882596201372 Henry Cohn, 2024, needs more optimization.
4 221 0.883068319599 Henry Cohn, 2024, needs more optimization.
4 222 0.883561228808 Henry Cohn, 2024, needs more optimization.
4 223 0.884255386876 Henry Cohn, 2024, needs more optimization.
4 224 0.884686089745 Henry Cohn, 2024, needs more optimization.
4 225 0.885236784394 Henry Cohn, 2024, needs more optimization.
4 226 0.885373603102 Henry Cohn, 2024, needs more optimization.
4 227 0.885541630029 Henry Cohn, 2024, needs more optimization.
4 228 0.885875665888 Henry Cohn, 2024, needs more optimization.
4 229 0.886312244147 Henry Cohn, 2024, needs more optimization.
4 230 0.886375168166 Henry Cohn, 2024, needs more optimization.
4 231 0.886852778794 Henry Cohn, 2024, needs more optimization.
4 232 0.887369280696 Henry Cohn, 2024, needs more optimization.
4 233 0.887405441855 Henry Cohn, 2024, needs more optimization.
4 234 0.887610594043 Henry Cohn, 2024, needs more optimization.
4 235 0.887931566287 Henry Cohn, 2024, needs more optimization.
4 236 0.888127923058 Henry Cohn, 2024, needs more optimization.
4 237 0.888458444562 Henry Cohn, 2024, needs more optimization.
4 238 0.888944992762 Henry Cohn, 2024, needs more optimization.
4 239 0.889387503952 Henry Cohn, 2024, needs more optimization.
4 240 0.889609979679 Henry Cohn, 2024, needs more optimization.
4 241 0.889887902632 Henry Cohn, 2024, needs more optimization.
4 242 0.890278312942 Henry Cohn, 2024, needs more optimization.
4 243 0.890336503434 Henry Cohn, 2025, needs more optimization.
4 244 0.890776113396 Henry Cohn, 2025, needs more optimization.
4 245 0.891046196126 Henry Cohn, 2024, needs more optimization.
4 246 0.891251467769 Henry Cohn, 2025, needs more optimization.
4 247 0.891800101613 Henry Cohn, 2024, needs more optimization.
4 248 0.892325123794 Henry Cohn, 2025, needs more optimization.
4 249 0.892362999827 Henry Cohn, 2024, needs more optimization.
4 250 0.892781145975 Henry Cohn, 2024, needs more optimization.
4 251 0.893110278625 Henry Cohn, 2024, needs more optimization.
4 252 0.893392539456 Henry Cohn, 2025, needs more optimization.
4 253 0.893785136004 Henry Cohn, 2024, needs more optimization.
4 254 0.893946035543 Henry Cohn, 2025, needs more optimization.
4 255 0.894031438903 Henry Cohn, 2025, needs more optimization.
4 256 0.894642036631 Henry Cohn, 2024, needs more optimization.
4 257 0.895506419045 Henry Cohn, 2024, needs more optimization.
4 258 0.895921105722 Henry Cohn, 2024, needs more optimization.
4 259 0.895963216248 Henry Cohn, 2024, needs more optimization.
4 260 0.896463789534 Henry Cohn, 2024, needs more optimization.
4 262 0.896731345107 Henry Cohn, 2024, needs more optimization.
4 264 0.897013899044 Henry Cohn, 2024, needs more optimization.
4 265 0.897542375096 Henry Cohn, 2024, needs more optimization.
4 266 0.897995510234 Henry Cohn, 2024, needs more optimization.
4 267 0.898027547023 Henry Cohn, 2024, needs more optimization.
4 268 0.898326647476 Henry Cohn, 2024, needs more optimization.
4 270 0.898392727058 Henry Cohn, 2024, needs more optimization.
4 272 0.898571947982 Henry Cohn, 2024, needs more optimization.
4 273 0.898987004687 Henry Cohn, 2024, needs more optimization.
4 275 0.899171296644 Henry Cohn, 2024, needs more optimization.
4 276 0.899311325170 Henry Cohn, 2024, needs more optimization.
4 280 0.899759533393 Henry Cohn, 2024, needs more optimization.
4 282 0.901640399706 Henry Cohn, 2024, needs more optimization.
4 285 0.903101045501 Henry Cohn, 2024, needs more optimization.
4 287 0.903182162103 Henry Cohn, 2024, needs more optimization.
4 289 0.903785683460 Henry Cohn, 2024, needs more optimization.
4 290 0.904326749689 Henry Cohn, 2024, needs more optimization.
4 291 0.904392951497 Henry Cohn, 2024, needs more optimization.
4 292 0.904960711978 Henry Cohn, 2024, needs more optimization.
4 293 0.904988049048 Henry Cohn, 2024, needs more optimization.
4 294 0.905258188975 Henry Cohn, 2024, needs more optimization.
4 295 0.905369748349 Henry Cohn, 2024, needs more optimization.
4 296 0.905748220040 Henry Cohn, 2024, needs more optimization.
4 297 0.906049199589 Henry Cohn, 2024, needs more optimization.
4 298 0.906097210743 Henry Cohn, 2024, needs more optimization.
4 299 0.906258231870 Henry Cohn, 2024, needs more optimization.
4 300 0.906379282667 Henry Cohn, 2024, needs more optimization.
4 301 0.906490387106 Henry Cohn, 2024, needs more optimization.
4 303 0.906728421232 Henry Cohn, 2024, needs more optimization.
4 306 0.907336286614 Henry Cohn, 2024, needs more optimization.
4 307 0.908014784148 Henry Cohn, 2024, needs more optimization.
4 308 0.908200268315 Henry Cohn, 2024, needs more optimization.
4 309 0.908524174285 Henry Cohn, 2024, needs more optimization.
4 311 0.908774780970 Henry Cohn, 2024, needs more optimization.
4 313 0.909174422955 Henry Cohn, 2024, needs more optimization.
4 315 0.909400096030 Henry Cohn, 2024, needs more optimization.
4 316 0.909591590227 Henry Cohn, 2024, needs more optimization.
4 320 0.910162393615 Henry Cohn, 2024, needs more optimization.
4 321 0.910568185365 Henry Cohn, 2024, needs more optimization.
4 322 0.910845211484 Henry Cohn, 2024, needs more optimization.
4 323 0.911072573325 Henry Cohn, 2024, needs more optimization.
4 324 0.911353633046 Henry Cohn, 2024, needs more optimization.
4 325 0.911596934979 Henry Cohn, 2024, needs more optimization.
4 326 0.911638505924 Henry Cohn, 2024, needs more optimization.
4 328 0.911674459073 Henry Cohn, 2024, needs more optimization.
4 329 0.912279518208 Henry Cohn, 2024, needs more optimization.
4 330 0.912335440508 Henry Cohn, 2024, needs more optimization.
4 332 0.912643295765 Henry Cohn, 2024, needs more optimization.
4 333 0.913024530220 Henry Cohn, 2024, needs more optimization.
4 334 0.913059192245 Henry Cohn, 2024, needs more optimization.
4 335 0.913196572690 Henry Cohn, 2024, needs more optimization.
4 337 0.913451773590 Henry Cohn, 2024, needs more optimization.
4 342 0.913523258748 Henry Cohn, 2024, needs more optimization.
4 343 0.914471393379 Henry Cohn, 2024, needs more optimization.
4 344 0.914531092841 Henry Cohn, 2024, needs more optimization.
4 345 0.914946893842 Henry Cohn, 2024, needs more optimization.
4 346 0.915037643153 Henry Cohn, 2024, needs more optimization.
4 347 0.915155460237 Henry Cohn, 2024, needs more optimization.
4 348 0.915339083137 Henry Cohn, 2024, needs more optimization.
4 349 0.915696755614 Henry Cohn, 2024, needs more optimization.
4 350 0.915830232701 Henry Cohn, 2024, needs more optimization.
4 353 0.915865414787 Henry Cohn, 2024, needs more optimization.
4 354 0.916426923601 Henry Cohn, 2024, needs more optimization.
4 355 0.916515692544 Henry Cohn, 2024, needs more optimization.
4 356 0.916719790133 Henry Cohn, 2024, needs more optimization.
4 357 0.916926018003 Henry Cohn, 2024, needs more optimization.
4 358 0.916952693380 Henry Cohn, 2024, needs more optimization.
4 359 0.917184353380 Henry Cohn, 2024, needs more optimization.
4 360 0.917256233542 Henry Cohn, 2024, needs more optimization.
4 361 0.917501268713 Henry Cohn, 2024, needs more optimization.
4 363 0.917660013513 Henry Cohn, 2024, needs more optimization.
4 364 0.917950596179 Henry Cohn, 2024, needs more optimization.
4 365 0.918000164673 Henry Cohn, 2024, needs more optimization.
4 367 0.918180724714 Henry Cohn, 2024, needs more optimization.
4 368 0.918327633022 Henry Cohn, 2024, needs more optimization.
4 369 0.918597177409 Henry Cohn, 2024, needs more optimization.
4 370 0.918672283932 Henry Cohn, 2024, needs more optimization.
4 371 0.918909811798 Henry Cohn, 2024, needs more optimization.
4 372 0.918959249241 Henry Cohn, 2024, needs more optimization.
4 373 0.919141189383 Henry Cohn, 2024, needs more optimization.
4 374 0.919345045026 Henry Cohn, 2024, needs more optimization.
4 375 0.919668591179 Henry Cohn, 2024, needs more optimization.
4 376 0.919701825386 Henry Cohn, 2024, needs more optimization.
4 377 0.919929828299 Henry Cohn, 2024, needs more optimization.
4 378 0.919952250379 Henry Cohn, 2024, needs more optimization.
4 379 0.919984049653 Henry Cohn, 2024, needs more optimization.
4 380 0.920326304335 Henry Cohn, 2024, needs more optimization.
4 381 0.920477880901 Henry Cohn, 2024, needs more optimization.
4 384 0.920515492657 Henry Cohn, 2024, needs more optimization.
4 385 0.920629091957 Henry Cohn, 2024, needs more optimization.
4 386 0.921069123557 Henry Cohn, 2024, needs more optimization.
4 387 0.921222859095 Henry Cohn, 2024, needs more optimization.
4 388 0.921329806499 Henry Cohn, 2024, needs more optimization.
4 389 0.921436998051 Henry Cohn, 2024, needs more optimization.
4 390 0.921631016949 Henry Cohn, 2024, needs more optimization.
4 391 0.921656912604 Henry Cohn, 2024, needs more optimization.
4 392 0.921833112615 Henry Cohn, 2024, needs more optimization.
4 393 0.921860416465 Henry Cohn, 2024, needs more optimization.
4 394 0.922101052747 Henry Cohn, 2024, needs more optimization.
4 397 0.922310025989 Henry Cohn, 2024, needs more optimization.
4 399 0.922680842984 Henry Cohn, 2024, needs more optimization.
4 400 0.922843424735 Henry Cohn, 2024, needs more optimization.
4 402 0.923041162887 Henry Cohn, 2024, needs more optimization.
4 403 0.923277366092 Henry Cohn, 2024, needs more optimization.
4 404 0.923374489690 Henry Cohn, 2024, needs more optimization.
4 405 0.923608403071 Henry Cohn, 2024, needs more optimization.
4 406 0.923725163017 Henry Cohn, 2024, needs more optimization.
4 407 0.923781872755 Henry Cohn, 2024, needs more optimization.
4 409 0.923931120762 Henry Cohn, 2024, needs more optimization.
4 410 0.924268226075 Henry Cohn, 2024, needs more optimization.
4 412 0.924334111010 Henry Cohn, 2024, needs more optimization.
4 413 0.924566892487 Henry Cohn, 2024, needs more optimization.
4 414 0.924685293588 Henry Cohn, 2024, needs more optimization.
4 415 0.924720372166 Henry Cohn, 2024, needs more optimization.
4 416 0.924787098694 Henry Cohn, 2024, needs more optimization.
4 417 0.924909925827 Henry Cohn, 2024, needs more optimization.
4 418 0.924982344524 Henry Cohn, 2024, needs more optimization.
4 419 0.925293424335 Henry Cohn, 2024, needs more optimization.
4 420 0.925379395961 Henry Cohn, 2024, needs more optimization.
4 421 0.925493384144 Henry Cohn, 2024, needs more optimization.
4 422 0.925696831122 Henry Cohn, 2024, needs more optimization.
4 424 0.925808711964 Henry Cohn, 2024, needs more optimization.
4 425 0.925920053739 Henry Cohn, 2024, needs more optimization.
4 426 0.926089923301 Henry Cohn, 2024, needs more optimization.
4 429 0.926209189182 Henry Cohn, 2024, needs more optimization.
4 431 0.926602305630 Henry Cohn, 2024, needs more optimization.
4 432 0.926730918922 Henry Cohn, 2024, needs more optimization.
4 433 0.926885181460 Henry Cohn, 2024, needs more optimization.
4 435 0.926903229834 Henry Cohn, 2024, needs more optimization.
4 436 0.927107835196 Henry Cohn, 2024, needs more optimization.
4 438 0.927359511761 Henry Cohn, 2024, needs more optimization.
4 439 0.927500149239 Henry Cohn, 2024, needs more optimization.
4 440 0.927680635319 Henry Cohn, 2024, needs more optimization.
4 442 0.927773460752 Henry Cohn, 2024, needs more optimization.
4 444 0.927994407780 Henry Cohn, 2024, needs more optimization.
4 445 0.928174343009 Henry Cohn, 2024, needs more optimization.
4 447 0.928269975311 Henry Cohn, 2024, needs more optimization.
4 448 0.928346764282 Henry Cohn, 2024, needs more optimization.
4 449 0.928542215442 Henry Cohn, 2024, needs more optimization.
4 450 0.928797699825 Henry Cohn, 2024, needs more optimization.
4 451 0.928889251087 Henry Cohn, 2024, needs more optimization.
4 452 0.928925951732 Henry Cohn, 2024, needs more optimization.
4 453 0.928968097840 Henry Cohn, 2024, needs more optimization.
4 455 0.929130454671 Henry Cohn, 2024, needs more optimization.
4 456 0.929448089657 Henry Cohn, 2024, needs more optimization.
4 457 0.929452803216 Henry Cohn, 2024, needs more optimization.
4 458 0.929596689524 Henry Cohn, 2024, needs more optimization.
4 459 0.929633478539 Henry Cohn, 2024, needs more optimization.
4 460 0.929745874111 Henry Cohn, 2024, needs more optimization.
4 461 0.929837411431 Henry Cohn, 2024, needs more optimization.
4 462 0.929881927065 Henry Cohn, 2024, needs more optimization.
4 463 0.930183172652 Henry Cohn, 2024, needs more optimization.
4 464 0.930229990223 Henry Cohn, 2024, needs more optimization.
4 465 0.930292726823 Henry Cohn, 2024, needs more optimization.
4 466 0.930385069612 Henry Cohn, 2024, needs more optimization.
4 467 0.930513556380 Henry Cohn, 2024, needs more optimization.
4 468 0.930534599901 Henry Cohn, 2024, needs more optimization.
4 469 0.930710596651 Henry Cohn, 2024, needs more optimization.
4 470 0.930750383881 Henry Cohn, 2024, needs more optimization.
4 471 0.930817587249 Henry Cohn, 2024, needs more optimization.
4 473 0.930977638621 Henry Cohn, 2024, needs more optimization.
4 475 0.931166730590 Henry Cohn, 2024, needs more optimization.
4 476 0.931355307171 Henry Cohn, 2024, needs more optimization.
4 478 0.931485013171 Henry Cohn, 2024, needs more optimization.
4 479 0.931708246067 Henry Cohn, 2024, needs more optimization.
4 481 0.931856524115 Henry Cohn, 2024, needs more optimization.
4 483 0.931948157734 Henry Cohn, 2024, needs more optimization.
4 484 0.932058268203 Henry Cohn, 2024, needs more optimization.
4 485 0.932210994062 Henry Cohn, 2024, needs more optimization.
4 487 0.932274161903 Henry Cohn, 2024, needs more optimization.
4 488 0.932476062079 Henry Cohn, 2024, needs more optimization.
4 489 0.932596306901 Henry Cohn, 2024, needs more optimization.
4 490 0.932721997765 Henry Cohn, 2024, needs more optimization.
4 491 0.932795362387 Henry Cohn, 2024, needs more optimization.
4 493 0.933018698660 Henry Cohn, 2024, needs more optimization.
4 494 0.933037830534 Henry Cohn, 2024, needs more optimization.
4 496 0.933156840899 Henry Cohn, 2024, needs more optimization.
4 499 0.933319415107 Henry Cohn, 2024, needs more optimization.
4 501 0.933613519113 Henry Cohn, 2024, needs more optimization.
4 502 0.933762931747 Henry Cohn, 2024, needs more optimization.
4 503 0.933834273938 Henry Cohn, 2024, needs more optimization.
4 504 0.933917979097 Henry Cohn, 2024, needs more optimization.
4 505 0.934060230136 Henry Cohn, 2024, needs more optimization.
4 506 0.934162428034 Henry Cohn, 2024, needs more optimization.
4 508 0.934259784750 Henry Cohn, 2024, needs more optimization.
4 509 0.934403247225 Henry Cohn, 2024, needs more optimization.
4 510 0.934460540569 Henry Cohn, 2024, needs more optimization.
4 512 0.934503377224 Henry Cohn, 2024, needs more optimization.
4 513 0.934763790621 Henry Cohn, 2024, needs more optimization.
4 514 0.934862891592 Henry Cohn, 2024, needs more optimization.
4 515 0.934964728304 Henry Cohn, 2024, needs more optimization.
4 517 0.935001334617 Henry Cohn, 2024, needs more optimization.
4 518 0.935009372457 Henry Cohn, 2024, needs more optimization.
4 519 0.935120262505 Henry Cohn, 2024, needs more optimization.
4 520 0.935286999828 Henry Cohn, 2024, needs more optimization.
4 521 0.935397268080 Henry Cohn, 2024, needs more optimization.
4 522 0.935464829472 Henry Cohn, 2024, needs more optimization.
4 523 0.935471858436 Henry Cohn, 2024, needs more optimization.
4 524 0.935611528967 Henry Cohn, 2024, needs more optimization.
4 525 0.935688748693 Henry Cohn, 2024, needs more optimization.
4 526 0.935802525626 Henry Cohn, 2024, needs more optimization.
4 528 0.935823807664 Henry Cohn, 2024, needs more optimization.
4 529 0.936039390281 Henry Cohn, 2024, needs more optimization.
4 530 0.936126012920 Henry Cohn, 2024, needs more optimization.
4 531 0.936200360571 Henry Cohn, 2024, needs more optimization.
4 532 0.936238746929 Henry Cohn, 2024, needs more optimization.
4 533 0.936295103921 Henry Cohn, 2024, needs more optimization.
4 535 0.936417034845 Henry Cohn, 2024, needs more optimization.
4 536 0.936647940847 Henry Cohn, 2024, needs more optimization.
4 537 0.936731570500 Henry Cohn, 2024, needs more optimization.
4 538 0.936746449910 Henry Cohn, 2024, needs more optimization.
4 539 0.936908028170 Henry Cohn, 2024, needs more optimization.
4 541 0.936918377264 Henry Cohn, 2024, needs more optimization.
4 542 0.937131969496 Henry Cohn, 2024, needs more optimization.
4 543 0.937157082228 Henry Cohn, 2024, needs more optimization.
4 544 0.937189452957 Henry Cohn, 2024, needs more optimization.
4 545 0.937222136014 Henry Cohn, 2024, needs more optimization.
4 547 0.937411350691 Henry Cohn, 2024, needs more optimization.
4 548 0.937584188766 Henry Cohn, 2024, needs more optimization.
4 549 0.937647309871 Henry Cohn, 2024, needs more optimization.
4 550 0.937651721882 Henry Cohn, 2024, needs more optimization.
4 552 0.937697963129 Henry Cohn, 2024, needs more optimization.
4 554 0.937776609003 Henry Cohn, 2024, needs more optimization.
4 556 0.937865276365 Henry Cohn, 2024, needs more optimization.
4 557 0.938157095962 Henry Cohn, 2024, needs more optimization.
4 558 0.938220630989 Henry Cohn, 2024, needs more optimization.
4 559 0.938307086856 Henry Cohn, 2024, needs more optimization.
4 560 0.938412256910 Henry Cohn, 2024, needs more optimization.
4 561 0.938492545286 Henry Cohn, 2024, needs more optimization.
4 562 0.938603381696 Henry Cohn, 2024, needs more optimization.
4 564 0.938612791036 Henry Cohn, 2024, needs more optimization.
4 565 0.938805921651 Henry Cohn, 2024, needs more optimization.
4 567 0.938873108204 Henry Cohn, 2024, needs more optimization.
4 568 0.939010375899 Henry Cohn, 2024, needs more optimization.
4 570 0.939055787733 Henry Cohn, 2024, needs more optimization.
4 571 0.939138200216 Henry Cohn, 2024, needs more optimization.
4 572 0.939325762702 Henry Cohn, 2024, needs more optimization.
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4 575 0.939519727659 Henry Cohn, 2024, needs more optimization.
4 576 0.939520115001 Henry Cohn, 2024, needs more optimization.
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4 578 0.939677067258 Henry Cohn, 2024, needs more optimization.
4 579 0.939713952351 Henry Cohn, 2024, needs more optimization.
4 580 0.939822985838 Henry Cohn, 2024, needs more optimization.
4 581 0.939839776713 Henry Cohn, 2024, needs more optimization.
4 582 0.939946428177 Henry Cohn, 2024, needs more optimization.
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4 592 0.940537409081 Henry Cohn, 2024, needs more optimization.
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4 606 0.941592633184 Henry Cohn, 2024, needs more optimization.
4 607 0.941701088451 Henry Cohn, 2024, needs more optimization.
4 608 0.941751632562 Henry Cohn, 2024, needs more optimization.
4 610 0.941856112416 Henry Cohn, 2024, needs more optimization.
4 612 0.941879298244 Henry Cohn, 2024, needs more optimization.
4 613 0.942020567161 Henry Cohn, 2024, needs more optimization.
4 614 0.942020998008 Henry Cohn, 2024, needs more optimization.
4 615 0.942061652961 Henry Cohn, 2024, needs more optimization.
4 616 0.942161304053 Henry Cohn, 2024, needs more optimization.
4 618 0.942259650617 Henry Cohn, 2024, needs more optimization.
4 619 0.942390469832 Henry Cohn, 2024, needs more optimization.
4 620 0.942496233552 Henry Cohn, 2024, needs more optimization.
4 621 0.942537980004 Henry Cohn, 2024, needs more optimization.
4 622 0.942657325798 Henry Cohn, 2024, needs more optimization.
4 623 0.942675507343 Henry Cohn, 2024, needs more optimization.
4 626 0.942738404524 Henry Cohn, 2024, needs more optimization.
4 627 0.942870798244 Henry Cohn, 2024, needs more optimization.
4 628 0.942944821753 Henry Cohn, 2024, needs more optimization.
4 629 0.943005551172 Henry Cohn, 2024, needs more optimization.
4 630 0.943023074275 Henry Cohn, 2024, needs more optimization.
4 632 0.943117258171 Henry Cohn, 2024, needs more optimization.
4 633 0.943269155431 Henry Cohn, 2024, needs more optimization.
4 634 0.943347014993 Henry Cohn, 2024, needs more optimization.
4 637 0.943353013497 Henry Cohn, 2024, needs more optimization.
4 639 0.943576044867 Henry Cohn, 2024, needs more optimization.
4 640 0.943631054456 Henry Cohn, 2024, needs more optimization.
4 642 0.943717141306 Henry Cohn, 2024, needs more optimization.
4 643 0.943870811482 Henry Cohn, 2024, needs more optimization.
4 644 0.943876018348 Henry Cohn, 2024, needs more optimization.
4 645 0.943968512529 Henry Cohn, 2024, needs more optimization.
4 647 0.944022277829 Henry Cohn, 2024, needs more optimization.
4 649 0.944124089788 Henry Cohn, 2024, needs more optimization.
4 650 0.944261879687 Henry Cohn, 2024, needs more optimization.
4 651 0.944319506522 Henry Cohn, 2024, needs more optimization.
4 652 0.944372902932 Henry Cohn, 2024, needs more optimization.
4 653 0.944425282372 Henry Cohn, 2024, needs more optimization.
4 656 0.944456640520 Henry Cohn, 2024, needs more optimization.
4 657 0.944559743325 Henry Cohn, 2024, needs more optimization.
4 658 0.944644231597 Henry Cohn, 2024, needs more optimization.
4 659 0.944727989973 Henry Cohn, 2024, needs more optimization.
4 661 0.944820343727 Henry Cohn, 2024, needs more optimization.
4 662 0.944870215174 Henry Cohn, 2024, needs more optimization.
4 663 0.944973761833 Henry Cohn, 2024, needs more optimization.
4 664 0.945040638735 Henry Cohn, 2024, needs more optimization.
4 665 0.945062359818 Henry Cohn, 2024, needs more optimization.
4 666 0.945133486687 Henry Cohn, 2024, needs more optimization.
4 667 0.945215255966 Henry Cohn, 2024, needs more optimization.
4 669 0.945297450615 Henry Cohn, 2024, needs more optimization.
4 672 0.945349042312 Henry Cohn, 2024, needs more optimization.
4 674 0.945401250054 Henry Cohn, 2024, needs more optimization.
4 675 0.945675664306 Henry Cohn, 2024, needs more optimization.
4 677 0.945716976317 Henry Cohn, 2024, needs more optimization.
4 678 0.945739263721 Henry Cohn, 2024, needs more optimization.
4 679 0.945748308940 Henry Cohn, 2024, needs more optimization.
4 680 0.945906107433 Henry Cohn, 2024, needs more optimization.
4 681 0.945924284714 Henry Cohn, 2024, needs more optimization.
4 682 0.946035429637 Henry Cohn, 2024, needs more optimization.
4 683 0.946068368634 Henry Cohn, 2024, needs more optimization.
4 686 0.946164647317 Henry Cohn, 2024, needs more optimization.
4 687 0.946239030546 Henry Cohn, 2024, needs more optimization.
4 689 0.946297396159 Henry Cohn, 2024, needs more optimization.
4 690 0.946347682760 Henry Cohn, 2024, needs more optimization.
4 691 0.946441641443 Henry Cohn, 2024, needs more optimization.
4 692 0.946570218624 Henry Cohn, 2024, needs more optimization.
4 694 0.946572146831 Henry Cohn, 2024, needs more optimization.
4 696 0.946633974711 Henry Cohn, 2024, needs more optimization.
4 697 0.946748809585 Henry Cohn, 2024, needs more optimization.
4 698 0.946827862264 Henry Cohn, 2024, needs more optimization.
4 699 0.946873111175 Henry Cohn, 2024, needs more optimization.
4 700 0.946913667844 Henry Cohn, 2024, needs more optimization.
4 701 0.946919924340 Henry Cohn, 2024, needs more optimization.
4 702 0.946967097739 Henry Cohn, 2024, needs more optimization.
4 704 0.947075199199 Henry Cohn, 2024, needs more optimization.
4 705 0.947125687941 Henry Cohn, 2024, needs more optimization.
4 706 0.947179880161 Henry Cohn, 2024, needs more optimization.
4 708 0.947225684252 Henry Cohn, 2024, needs more optimization.
4 709 0.947356569765 Henry Cohn, 2024, needs more optimization.
4 711 0.947495886619 Henry Cohn, 2024, needs more optimization.
4 713 0.947558555369 Henry Cohn, 2024, needs more optimization.
4 714 0.947575367960 Henry Cohn, 2024, needs more optimization.
4 715 0.947660334815 Henry Cohn, 2024, needs more optimization.
4 718 0.947762265614 Henry Cohn, 2024, needs more optimization.
4 719 0.947864318017 Henry Cohn, 2024, needs more optimization.
4 720 0.947868126726 Henry Cohn, 2024, needs more optimization.
4 721 0.947974163996 Henry Cohn, 2024, needs more optimization.
4 722 0.947999797189 Henry Cohn, 2024, needs more optimization.
4 724 0.948034978379 Henry Cohn, 2024, needs more optimization.
4 726 0.948118517510 Henry Cohn, 2024, needs more optimization.
4 727 0.948205944887 Henry Cohn, 2024, needs more optimization.
4 729 0.948314255602 Henry Cohn, 2024, needs more optimization.
4 731 0.948402018338 Henry Cohn, 2024, needs more optimization.
4 732 0.948463656747 Henry Cohn, 2024, needs more optimization.
4 733 0.948568171344 Henry Cohn, 2024, needs more optimization.
4 734 0.948572352575 Henry Cohn, 2024, needs more optimization.
4 735 0.948647746403 Henry Cohn, 2024, needs more optimization.
4 736 0.948710323675 Henry Cohn, 2024, needs more optimization.
4 740 0.948764602285 Henry Cohn, 2024, needs more optimization.
4 742 0.948889210791 Henry Cohn, 2024, needs more optimization.
4 744 0.949013987012 Henry Cohn, 2024, needs more optimization.
4 745 0.949097780271 Henry Cohn, 2024, needs more optimization.
4 746 0.949112572400 Henry Cohn, 2024, needs more optimization.
4 747 0.949123943411 Henry Cohn, 2024, needs more optimization.
4 748 0.949211879808 Henry Cohn, 2024, needs more optimization.
4 749 0.949301151765 Henry Cohn, 2024, needs more optimization.
4 750 0.949317977956 Henry Cohn, 2024, needs more optimization.
4 753 0.949374590018 Henry Cohn, 2024, needs more optimization.
4 755 0.949470355277 Henry Cohn, 2024, needs more optimization.
4 756 0.949570024969 Henry Cohn, 2024, needs more optimization.
4 757 0.949613955028 Henry Cohn, 2024, needs more optimization.
4 758 0.949673563999 Henry Cohn, 2024, needs more optimization.
4 760 0.949698281428 Henry Cohn, 2024, needs more optimization.
4 762 0.949808662093 Henry Cohn, 2024, needs more optimization.
4 763 0.949868987416 Henry Cohn, 2024, needs more optimization.
4 765 0.949933410138 Henry Cohn, 2024, needs more optimization.
4 768 0.950027503574 Henry Cohn, 2024, needs more optimization.
4 769 0.950117935696 Henry Cohn, 2024, needs more optimization.
4 774 0.950142456068 Henry Cohn, 2024, needs more optimization.
4 775 0.950384290160 Henry Cohn, 2024, needs more optimization.
4 777 0.950455824780 Henry Cohn, 2024, needs more optimization.
4 778 0.950464862269 Henry Cohn, 2024, needs more optimization.
4 779 0.950556681098 Henry Cohn, 2024, needs more optimization.
4 781 0.950612538691 Henry Cohn, 2024, needs more optimization.
4 782 0.950692900129 Henry Cohn, 2024, needs more optimization.
4 783 0.950714827824 Henry Cohn, 2024, needs more optimization.
4 785 0.950781459010 Henry Cohn, 2024, needs more optimization.
4 786 0.950857470732 Henry Cohn, 2024, needs more optimization.
4 787 0.950877564221 Henry Cohn, 2024, needs more optimization.
4 789 0.950951512914 Henry Cohn, 2024, needs more optimization.
4 790 0.950968600006 Henry Cohn, 2024, needs more optimization.
4 792 0.951060277944 Henry Cohn, 2024, needs more optimization.
4 793 0.951144911455 Henry Cohn, 2024, needs more optimization.
4 794 0.951196999672 Henry Cohn, 2024, needs more optimization.
4 798 0.951213307390 Henry Cohn, 2024, needs more optimization.
4 799 0.951389683657 Henry Cohn, 2024, needs more optimization.
4 800 0.951426373948 Henry Cohn, 2024, needs more optimization.
4 803 0.951508977666 Henry Cohn, 2024, needs more optimization.
4 806 0.951618708192 Henry Cohn, 2024, needs more optimization.
4 807 0.951720277853 Henry Cohn, 2024, needs more optimization.
4 808 0.951770727479 Henry Cohn, 2024, needs more optimization.
4 809 0.951803412506 Henry Cohn, 2024, needs more optimization.
4 810 0.951841539918 Henry Cohn, 2024, needs more optimization.
4 813 0.951855299747 Henry Cohn, 2024, needs more optimization.
4 815 0.951959591272 Henry Cohn, 2024, needs more optimization.
4 817 0.951992819249 Henry Cohn, 2024, needs more optimization.
4 818 0.952151901626 Henry Cohn, 2024, needs more optimization.
4 819 0.952164225642 Henry Cohn, 2024, needs more optimization.
4 821 0.952192029683 Henry Cohn, 2024, needs more optimization.
4 826 0.952297838543 Henry Cohn, 2024, needs more optimization.
4 828 0.952495439235 Henry Cohn, 2024, needs more optimization.
4 829 0.952599787112 Henry Cohn, 2024, needs more optimization.
4 831 0.952607763800 Henry Cohn, 2024, needs more optimization.
4 832 0.952664755133 Henry Cohn, 2024, needs more optimization.
4 833 0.952719201922 Henry Cohn, 2024, needs more optimization.
4 834 0.952773544720 Henry Cohn, 2024, needs more optimization.
4 836 0.952806034530 Henry Cohn, 2024, needs more optimization.
4 837 0.952856303570 Henry Cohn, 2024, needs more optimization.
4 838 0.952880720569 Henry Cohn, 2024, needs more optimization.
4 840 0.952955774312 Henry Cohn, 2024, needs more optimization.
4 841 0.953015396016 Henry Cohn, 2024, needs more optimization.
4 842 0.953019036637 Henry Cohn, 2024, needs more optimization.
4 843 0.953081881684 Henry Cohn, 2024, needs more optimization.
4 844 0.953147190762 Henry Cohn, 2024, needs more optimization.
4 845 0.953166271372 Henry Cohn, 2024, needs more optimization.
4 846 0.953237238764 Henry Cohn, 2024, needs more optimization.
4 847 0.953269901570 Henry Cohn, 2024, needs more optimization.
4 849 0.953312652154 Henry Cohn, 2024, needs more optimization.
4 850 0.953336803449 Henry Cohn, 2024, needs more optimization.
4 851 0.953385849426 Henry Cohn, 2024, needs more optimization.
4 853 0.953394325543 Henry Cohn, 2024, needs more optimization.
4 854 0.953493297216 Henry Cohn, 2024, needs more optimization.
4 858 0.953551717885 Henry Cohn, 2024, needs more optimization.
4 859 0.953615305538 Henry Cohn, 2024, needs more optimization.
4 860 0.953663585513 Henry Cohn, 2024, needs more optimization.
4 861 0.953769165311 Henry Cohn, 2024, needs more optimization.
4 862 0.953785986297 Henry Cohn, 2024, needs more optimization.
4 863 0.953806166213 Henry Cohn, 2024, needs more optimization.
4 864 0.953811425363 Henry Cohn, 2024, needs more optimization.
4 865 0.953900241964 Henry Cohn, 2024, needs more optimization.
4 866 0.953907044918 Henry Cohn, 2024, needs more optimization.
4 868 0.953978598906 Henry Cohn, 2024, needs more optimization.
4 869 0.954069160565 Henry Cohn, 2024, needs more optimization.
4 870 0.954075908588 Henry Cohn, 2024, needs more optimization.
4 873 0.954089575585 Henry Cohn, 2024, needs more optimization.
4 874 0.954174938911 Henry Cohn, 2024, needs more optimization.
4 875 0.954201508004 Henry Cohn, 2024, needs more optimization.
4 876 0.954302083495 Henry Cohn, 2024, needs more optimization.
4 879 0.954306999135 Henry Cohn, 2024, needs more optimization.
4 880 0.954433156342 Henry Cohn, 2024, needs more optimization.
4 881 0.954481885478 Henry Cohn, 2024, needs more optimization.
4 882 0.954507916806 Henry Cohn, 2024, needs more optimization.
4 883 0.954545874882 Henry Cohn, 2024, needs more optimization.
4 885 0.954547001849 Henry Cohn, 2024, needs more optimization.
4 886 0.954640689347 Henry Cohn, 2024, needs more optimization.
4 887 0.954674278735 Henry Cohn, 2024, needs more optimization.
4 888 0.954710989478 Henry Cohn, 2024, needs more optimization.
4 889 0.954730044896 Henry Cohn, 2024, needs more optimization.
4 890 0.954765733812 Henry Cohn, 2024, needs more optimization.
4 891 0.954779850741 Henry Cohn, 2024, needs more optimization.
4 892 0.954803272350 Henry Cohn, 2024, needs more optimization.
4 894 0.954818175966 Henry Cohn, 2024, needs more optimization.
4 896 0.954923249127 Henry Cohn, 2024, needs more optimization.
4 897 0.954987783425 Henry Cohn, 2024, needs more optimization.
4 898 0.955011061713 Henry Cohn, 2024, needs more optimization.
4 900 0.955052861715 Henry Cohn, 2024, needs more optimization.
4 902 0.955074900576 Henry Cohn, 2024, needs more optimization.
4 904 0.955215889833 Henry Cohn, 2024, needs more optimization.
4 905 0.955286672897 Henry Cohn, 2024, needs more optimization.
4 906 0.955311932908 Henry Cohn, 2024, needs more optimization.
4 907 0.955348240380 Henry Cohn, 2024, needs more optimization.
4 908 0.955365101478 Henry Cohn, 2024, needs more optimization.
4 909 0.955371085695 Henry Cohn, 2024, needs more optimization.
4 910 0.955414451205 Henry Cohn, 2024, needs more optimization.
4 911 0.955449796686 Henry Cohn, 2024, needs more optimization.
4 912 0.955463734593 Henry Cohn, 2024, needs more optimization.
4 914 0.955532504369 Henry Cohn, 2024, needs more optimization.
4 915 0.955598176671 Henry Cohn, 2024, needs more optimization.
4 917 0.955632294327 Henry Cohn, 2024, needs more optimization.
4 918 0.955649963189 Henry Cohn, 2024, needs more optimization.
4 919 0.955727763243 Henry Cohn, 2024, needs more optimization.
4 920 0.955764433928 Henry Cohn, 2024, needs more optimization.
4 921 0.955787907402 Henry Cohn, 2024, needs more optimization.
4 923 0.955819982179 Henry Cohn, 2024, needs more optimization.
4 924 0.955868537855 Henry Cohn, 2024, needs more optimization.
4 925 0.955869114371 Henry Cohn, 2024, needs more optimization.
4 926 0.955896280562 Henry Cohn, 2024, needs more optimization.
4 927 0.955953824953 Henry Cohn, 2024, needs more optimization.
4 928 0.956000273385 Henry Cohn, 2024, needs more optimization.
4 929 0.956054401569 Henry Cohn, 2024, needs more optimization.
4 930 0.956059740965 Henry Cohn, 2024, needs more optimization.
4 931 0.956108274375 Henry Cohn, 2024, needs more optimization.
4 933 0.956122504058 Henry Cohn, 2024, needs more optimization.
4 934 0.956195225508 Henry Cohn, 2024, needs more optimization.
4 936 0.956244121903 Henry Cohn, 2024, needs more optimization.
4 937 0.956298249830 Henry Cohn, 2024, needs more optimization.
4 939 0.956309600184 Henry Cohn, 2024, needs more optimization.
4 940 0.956386720816 Henry Cohn, 2024, needs more optimization.
4 941 0.956406067912 Henry Cohn, 2024, needs more optimization.
4 944 0.956444370893 Henry Cohn, 2024, needs more optimization.
4 945 0.956544683564 Henry Cohn, 2024, needs more optimization.
4 947 0.956550215283 Henry Cohn, 2024, needs more optimization.
4 950 0.956609598011 Henry Cohn, 2024, needs more optimization.
4 952 0.956712484074 Henry Cohn, 2024, needs more optimization.
4 953 0.956792045991 Henry Cohn, 2024, needs more optimization.
4 954 0.956806693773 Henry Cohn, 2024, needs more optimization.
4 955 0.956824088061 Henry Cohn, 2024, needs more optimization.
4 956 0.956852541004 Henry Cohn, 2024, needs more optimization.
4 957 0.956892010585 Henry Cohn, 2024, needs more optimization.
4 959 0.956901112169 Henry Cohn, 2024, needs more optimization.
4 960 0.956949581643 Henry Cohn, 2024, needs more optimization.
4 961 0.957032617114 Henry Cohn, 2024, needs more optimization.
4 962 0.957048142883 Henry Cohn, 2024, needs more optimization.
4 963 0.957064509224 Henry Cohn, 2024, needs more optimization.
4 964 0.957106230310 Henry Cohn, 2024, needs more optimization.
4 965 0.957148465347 Henry Cohn, 2024, needs more optimization.
4 966 0.957165212410 Henry Cohn, 2024, needs more optimization.
4 967 0.957178269882 Henry Cohn, 2024, needs more optimization.
4 968 0.957208958546 Henry Cohn, 2024, needs more optimization.
4 970 0.957262559683 Henry Cohn, 2024, needs more optimization.
4 971 0.957309220651 Henry Cohn, 2024, needs more optimization.
4 972 0.957336758499 Henry Cohn, 2024, needs more optimization.
4 973 0.957350659669 Henry Cohn, 2024, needs more optimization.
4 975 0.957381023833 Henry Cohn, 2024, needs more optimization.
4 976 0.957467620560 Henry Cohn, 2024, needs more optimization.
4 977 0.957489460589 Henry Cohn, 2024, needs more optimization.
4 980 0.957525124216 Henry Cohn, 2024, needs more optimization.
4 982 0.957608209286 Henry Cohn, 2024, needs more optimization.
4 983 0.957652656822 Henry Cohn, 2024, needs more optimization.
4 985 0.957654692429 Henry Cohn, 2024, needs more optimization.
4 986 0.957736958580 Henry Cohn, 2024, needs more optimization.
4 987 0.957774189270 Henry Cohn, 2024, needs more optimization.
4 991 0.957779949772 Henry Cohn, 2024, needs more optimization.
4 992 0.957893243237 Henry Cohn, 2024, needs more optimization.
4 996 0.957962501018 Henry Cohn, 2024, needs more optimization.
4 998 0.958058819199 Henry Cohn, 2024, needs more optimization.
4 999 0.958094896802 Henry Cohn, 2024, needs more optimization.
4 1001 0.958101646044 Henry Cohn, 2024, needs more optimization.
4 1003 0.958189273472 Henry Cohn, 2024, needs more optimization.
4 1004 0.958255392006 Henry Cohn, 2024, needs more optimization.
4 1006 0.958303570253 Henry Cohn, 2024, needs more optimization.
4 1007 0.958318328203 Henry Cohn, 2024, needs more optimization.
4 1008 0.958353696948 Henry Cohn, 2024, needs more optimization.
4 1009 0.958379127361 Henry Cohn, 2024, needs more optimization.
4 1010 0.958402525014 Henry Cohn, 2024, needs more optimization.
4 1011 0.958453156298 Henry Cohn, 2024, needs more optimization.
4 1013 0.958459170454 Henry Cohn, 2024, needs more optimization.
4 1015 0.958516794697 Henry Cohn, 2024, needs more optimization.
4 1016 0.958580228998 Henry Cohn, 2024, needs more optimization.
4 1017 0.958608546379 Henry Cohn, 2024, needs more optimization.
4 1019 0.958629965130 Henry Cohn, 2024, needs more optimization.
4 1020 0.958673443818 Henry Cohn, 2024, needs more optimization.
4 1021 0.958685243756 Henry Cohn, 2024, needs more optimization.
4 1024 0.958714533977 Henry Cohn, 2024, 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 0.499972875265 Henry Cohn, 2023.
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 0.540670680520 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 0.560142118522 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
5 53 0.566884877287 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
5 54 0.571075966439 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
5 55 0.574605986788 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
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 0.587022815774 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
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 0.596253477246 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
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 0.609103619699 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
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 0.615266925767 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
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 0.631407903402 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
5 77 0.636488757855 Henry Cohn, 2024.
5 78 0.640236710534 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
5 79 0.643753931686 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
5 80 0.646962010484 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
5 81 0.648895057989 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
5 82 0.651451569925 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
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 0.660931914755 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
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 0.664477235588 Henry Cohn, 2023.
5 89 0.666347999639 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
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, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
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 0.673832800816 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
5 94 0.675241739397 Henry Cohn, 2025.
5 95 0.676620972599 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
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 0.679247181253 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
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 0.683153316834 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
5 101 0.685227033891 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
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 0.688905339886 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
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 0.690732711178 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
5 106 0.692006929261 Henry Cohn, 2025.
5 107 0.693864161444 Henry Cohn, 2023.
5 108 0.695372507746 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
5 109 0.696434702697 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
5 110 0.698105081148 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
5 111 0.699318689076 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
5 112 0.700444084148 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
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 0.703017238158 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
5 115 0.704067616852 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
5 116 0.705352999078 Henry Cohn, 2023.
5 117 0.706882139184 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
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 0.709352721779 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
5 120 0.710427148894 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 0.713919145331 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
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 0.716605844513 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
5 126 0.717145190665 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
5 127 0.718613505104 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
5 128 0.719655857739 Henry Cohn, 2025.
5 129 0.720947866937 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
5 130 0.721730094738 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
5 131 0.723834031798 Henry Cohn, 2024, needs more optimization.
5 132 0.724849546170 Henry Cohn, 2025.
5 133 0.726102416252 Henry Cohn, 2025, needs more optimization.
5 134 0.726845848163 Henry Cohn, 2025.
5 135 0.727901938687 Henry Cohn, 2024.
5 136 0.728795165566 Henry Cohn, 2025.
5 137 0.730137625404 Henry Cohn, 2025.
5 138 0.730258203182 Henry Cohn, 2025.
5 139 0.731233247267 Henry Cohn, 2024, needs more optimization.
5 140 0.732079054288 Henry Cohn, 2025.
5 141 0.733438878630 Henry Cohn, 2024, needs more optimization.
5 142 0.733700667628 Henry Cohn, 2025.
5 143 0.734583692516 Henry Cohn, 2024, needs more optimization.
5 144 0.735428646221 Henry Cohn, 2025.
5 145 0.736652862664 Henry Cohn, 2025, needs more optimization.
5 146 0.736773285142 Henry Cohn, 2024, needs more optimization.
5 147 0.737456709632 Henry Cohn, 2024, needs more optimization.
5 148 0.737462993030 Henry Cohn, 2025, needs more optimization.
5 149 0.738328098648 Henry Cohn, 2025.
5 150 0.738349348874 Henry Cohn, 2024.
5 151 0.739674819120 Henry Cohn, 2024, needs more optimization.
5 152 0.739876190186 Henry Cohn, 2025.
5 153 0.740845753814 Henry Cohn, 2024, needs more optimization.
5 154 0.741806690902 Henry Cohn, 2024, needs more optimization.
5 155 0.742490254105 Henry Cohn, 2024, needs more optimization.
5 156 0.743018121151 Henry Cohn, 2024, needs more optimization.
5 157 0.743341541217 Henry Cohn, 2024, needs more optimization.
5 158 0.743505412747 Henry Cohn, 2024, needs more optimization.
5 159 0.744017236520 Henry Cohn, 2025.
5 160 0.744199738783 Henry Cohn, 2024, needs more optimization.
5 161 0.747801779476 Henry Cohn, 2024, needs more optimization.
5 162 0.748865834405 Henry Cohn, 2024, needs more optimization.
5 163 0.750226685590 Henry Cohn, 2024, needs more optimization.
5 164 0.750893520872 Henry Cohn, 2024, needs more optimization.
5 165 0.752234081839 Henry Cohn, 2024, needs more optimization.
5 166 0.752576713906 Henry Cohn, 2025.
5 167 0.753719771569 Henry Cohn, 2024, needs more optimization.
5 168 0.754280841444 Henry Cohn, 2024, needs more optimization.
5 169 0.755539175642 Henry Cohn, 2024, needs more optimization.
5 170 0.755994225479 Henry Cohn, 2024, needs more optimization.
5 171 0.757378746479 Henry Cohn, 2024, needs more optimization.
5 172 0.757391724917 Henry Cohn, 2024, needs more optimization.
5 173 0.759204089942 Henry Cohn, 2024, needs more optimization.
5 174 0.759690412111 Henry Cohn, 2025.
5 175 0.761114540131 Henry Cohn, 2024, needs more optimization.
5 176 0.761291434804 Henry Cohn, 2024, needs more optimization.
5 177 0.762879443582 Henry Cohn, 2025.
5 178 0.763376958827 Henry Cohn, 2024, needs more optimization.
5 179 0.764697635597 Henry Cohn, 2024, needs more optimization.
5 180 0.764934172446 Henry Cohn, 2024, needs more optimization.
5 181 0.765782579080 Henry Cohn, 2024, needs more optimization.
5 182 0.766075144848 Henry Cohn, 2024, needs more optimization.
5 183 0.767096396460 Henry Cohn, 2024, needs more optimization.
5 184 0.767227251599 Henry Cohn, 2024, needs more optimization.
5 185 0.767351322558 Henry Cohn, 2024, needs more optimization.
5 186 0.769133495760 Henry Cohn, 2024, needs more optimization.
5 187 0.769453923787 Henry Cohn, 2024, needs more optimization.
5 188 0.769538048912 Henry Cohn, 2024, needs more optimization.
5 189 0.770181961522 Henry Cohn, 2024, needs more optimization.
5 190 0.770226475575 Henry Cohn, 2024, needs more optimization.
5 191 0.771560866167 Henry Cohn, 2024, needs more optimization.
5 192 0.772511751593 Henry Cohn, 2024, needs more optimization.
5 193 0.772582048317 Henry Cohn, 2024, needs more optimization.
5 194 0.773685178039 Henry Cohn, 2024, needs more optimization.
5 195 0.773813006437 Henry Cohn, 2024, needs more optimization.
5 196 0.773839798481 Henry Cohn, 2024, needs more optimization.
5 197 0.774304415129 Henry Cohn, 2024, needs more optimization.
5 198 0.775175105500 Henry Cohn, 2024, needs more optimization.
5 199 0.775763545059 Henry Cohn, 2024, needs more optimization.
5 200 0.775819817125 Henry Cohn, 2024, needs more optimization.
5 201 0.776489915931 Henry Cohn, 2024, needs more optimization.
5 202 0.778031694692 Henry Cohn, 2024, needs more optimization.
5 203 0.778189170937 Henry Cohn, 2024, needs more optimization.
5 204 0.778291073852 Henry Cohn, 2024, needs more optimization.
5 205 0.779119542936 Henry Cohn, 2024, needs more optimization.
5 206 0.780197384900 Henry Cohn, 2024, needs more optimization.
5 207 0.780220103863 Henry Cohn, 2024, needs more optimization.
5 208 0.781347179606 Henry Cohn, 2024, needs more optimization.
5 209 0.781412315759 Henry Cohn, 2024, needs more optimization.
5 210 0.782473354455 Henry Cohn, 2024, needs more optimization.
5 211 0.782967740056 Henry Cohn, 2024, needs more optimization.
5 212 0.783038378207 Henry Cohn, 2024, needs more optimization.
5 213 0.783791270600 Henry Cohn, 2024, needs more optimization.
5 214 0.784433201086 Henry Cohn, 2024, needs more optimization.
5 215 0.784462292637 Henry Cohn, 2024, needs more optimization.
5 216 0.785734236790 Henry Cohn, 2024, needs more optimization.
5 217 0.786020633860 Henry Cohn, 2024, needs more optimization.
5 218 0.786047822894 Henry Cohn, 2024, needs more optimization.
5 219 0.787018742874 Henry Cohn, 2024, needs more optimization.
5 220 0.787315038866 Henry Cohn, 2024, needs more optimization.
5 221 0.787583949286 Henry Cohn, 2024, needs more optimization.
5 222 0.788141285485 Henry Cohn, 2024, needs more optimization.
5 223 0.788514294500 Henry Cohn, 2024, needs more optimization.
5 224 0.788925277780 Henry Cohn, 2024, needs more optimization.
5 225 0.789719397278 Henry Cohn, 2024, needs more optimization.
5 226 0.789848064711 Henry Cohn, 2024, needs more optimization.
5 227 0.790572742290 Henry Cohn, 2024, needs more optimization.
5 228 0.790968522452 Henry Cohn, 2024, needs more optimization.
5 229 0.791053547654 Henry Cohn, 2024, needs more optimization.
5 230 0.791825318987 Henry Cohn, 2024, needs more optimization.
5 231 0.792557652397 Henry Cohn, 2024, needs more optimization.
5 232 0.793010647854 Henry Cohn, 2024, needs more optimization.
5 233 0.793037186555 Henry Cohn, 2024, needs more optimization.
5 234 0.793698364139 Henry Cohn, 2024, needs more optimization.
5 235 0.793707865751 Henry Cohn, 2024, needs more optimization.
5 236 0.794259101081 Henry Cohn, 2024, needs more optimization.
5 237 0.794802526357 Henry Cohn, 2024, needs more optimization.
5 238 0.795033139757 Henry Cohn, 2024, needs more optimization.
5 239 0.795886833711 Henry Cohn, 2024, needs more optimization.
5 240 0.796035417113 Henry Cohn, 2024, needs more optimization.
5 241 0.796330049120 Henry Cohn, 2024, needs more optimization.
5 242 0.796945621508 Henry Cohn, 2024, needs more optimization.
5 243 0.797420976879 Henry Cohn, 2024, needs more optimization.
5 244 0.797794965711 Henry Cohn, 2024, needs more optimization.
5 245 0.798017136597 Henry Cohn, 2024, needs more optimization.
5 246 0.798309824113 Henry Cohn, 2024, needs more optimization.
5 247 0.799019810738 Henry Cohn, 2024, needs more optimization.
5 248 0.799384175795 Henry Cohn, 2024, needs more optimization.
5 249 0.799923913903 Henry Cohn, 2024, needs more optimization.
5 250 0.799940951673 Henry Cohn, 2024, needs more optimization.
5 251 0.800780764451 Henry Cohn, 2024, needs more optimization.
5 252 0.801170160271 Henry Cohn, 2024, needs more optimization.
5 253 0.801514484615 Henry Cohn, 2024, needs more optimization.
5 254 0.802087710003 Henry Cohn, 2024, needs more optimization.
5 255 0.802465141400 Henry Cohn, 2024, needs more optimization.
5 256 0.802732574778 Henry Cohn, 2024, needs more optimization.
5 257 0.803630859093 Henry Cohn, 2024, needs more optimization.
5 258 0.803652082731 Henry Cohn, 2024, needs more optimization.
5 259 0.804145530818 Henry Cohn, 2024, needs more optimization.
5 260 0.804664476281 Henry Cohn, 2024, needs more optimization.
5 261 0.804741597438 Henry Cohn, 2024, needs more optimization.
5 263 0.805477054382 Henry Cohn, 2024, needs more optimization.
5 264 0.806231284417 Henry Cohn, 2024, needs more optimization.
5 266 0.806278244936 Henry Cohn, 2024, needs more optimization.
5 267 0.807339555930 Henry Cohn, 2024, needs more optimization.
5 269 0.807438391686 Henry Cohn, 2024, needs more optimization.
5 273 0.807992893281 Henry Cohn, 2024, needs more optimization.
5 274 0.809512265665 Henry Cohn, 2024, needs more optimization.
5 276 0.809537500805 Henry Cohn, 2024, needs more optimization.
5 280 0.811088581620 Henry Cohn, 2024, needs more optimization.
5 283 0.812614508146 Henry Cohn, 2024, needs more optimization.
5 284 0.813076808704 Henry Cohn, 2024, needs more optimization.
5 286 0.813456383799 Henry Cohn, 2024, needs more optimization.
5 288 0.814119126700 Henry Cohn, 2024, needs more optimization.
5 291 0.814917952232 Henry Cohn, 2024, needs more optimization.
5 294 0.815103813312 Henry Cohn, 2024, needs more optimization.
5 296 0.816364724088 Henry Cohn, 2024, needs more optimization.
5 297 0.817080752402 Henry Cohn, 2024, needs more optimization.
5 299 0.817479885004 Henry Cohn, 2024, needs more optimization.
5 301 0.818379670150 Henry Cohn, 2024, needs more optimization.
5 302 0.818887321996 Henry Cohn, 2024, needs more optimization.
5 303 0.819220431767 Henry Cohn, 2024, needs more optimization.
5 305 0.820026472417 Henry Cohn, 2024, needs more optimization.
5 307 0.820144252540 Henry Cohn, 2024, needs more optimization.
5 308 0.820638345789 Henry Cohn, 2024, needs more optimization.
5 309 0.820900341625 Henry Cohn, 2024, needs more optimization.
5 311 0.821391117674 Henry Cohn, 2024, needs more optimization.
5 312 0.821972526406 Henry Cohn, 2024, needs more optimization.
5 313 0.822119755324 Henry Cohn, 2024, needs more optimization.
5 314 0.822514486271 Henry Cohn, 2024, needs more optimization.
5 315 0.822724427165 Henry Cohn, 2024, needs more optimization.
5 316 0.823137527884 Henry Cohn, 2024, needs more optimization.
5 317 0.823488348659 Henry Cohn, 2024, needs more optimization.
5 318 0.823660639814 Henry Cohn, 2024, needs more optimization.
5 319 0.824093152802 Henry Cohn, 2024, needs more optimization.
5 320 0.824194874505 Henry Cohn, 2024, needs more optimization.
5 321 0.824593051871 Henry Cohn, 2024, needs more optimization.
5 322 0.824806631313 Henry Cohn, 2024, needs more optimization.
5 323 0.825058145456 Henry Cohn, 2024, needs more optimization.
5 324 0.825561713091 Henry Cohn, 2024, needs more optimization.
5 325 0.825925082066 Henry Cohn, 2024, needs more optimization.
5 326 0.825994802442 Henry Cohn, 2024, needs more optimization.
5 327 0.826623580607 Henry Cohn, 2024, needs more optimization.
5 328 0.826677144046 Henry Cohn, 2024, needs more optimization.
5 329 0.826989989478 Henry Cohn, 2024, needs more optimization.
5 330 0.827290532457 Henry Cohn, 2024, needs more optimization.
5 331 0.827318975479 Henry Cohn, 2024, needs more optimization.
5 332 0.827724495826 Henry Cohn, 2024, needs more optimization.
5 333 0.827961937236 Henry Cohn, 2024, needs more optimization.
5 334 0.828307204645 Henry Cohn, 2024, needs more optimization.
5 335 0.828524239945 Henry Cohn, 2024, needs more optimization.
5 336 0.828699585269 Henry Cohn, 2024, needs more optimization.
5 337 0.828957776638 Henry Cohn, 2024, needs more optimization.
5 338 0.829186674146 Henry Cohn, 2024, needs more optimization.
5 339 0.829487418768 Henry Cohn, 2024, needs more optimization.
5 340 0.829944714161 Henry Cohn, 2024, needs more optimization.
5 341 0.829952102122 Henry Cohn, 2024, needs more optimization.
5 344 0.830356860911 Henry Cohn, 2024, needs more optimization.
5 345 0.830876159871 Henry Cohn, 2024, needs more optimization.
5 346 0.831125641368 Henry Cohn, 2024, needs more optimization.
5 348 0.831582478141 Henry Cohn, 2024, needs more optimization.
5 349 0.832052653241 Henry Cohn, 2024, needs more optimization.
5 350 0.832238682079 Henry Cohn, 2024, needs more optimization.
5 351 0.832573849774 Henry Cohn, 2024, needs more optimization.
5 352 0.832771148485 Henry Cohn, 2024, needs more optimization.
5 353 0.833014323351 Henry Cohn, 2024, needs more optimization.
5 354 0.833221752713 Henry Cohn, 2024, needs more optimization.
5 355 0.833546975148 Henry Cohn, 2024, needs more optimization.
5 356 0.833792211767 Henry Cohn, 2024, needs more optimization.
5 357 0.833915819053 Henry Cohn, 2024, needs more optimization.
5 358 0.834060570865 Henry Cohn, 2024, needs more optimization.
5 359 0.834430269447 Henry Cohn, 2024, needs more optimization.
5 360 0.834523915405 Henry Cohn, 2024, needs more optimization.
5 361 0.834786686148 Henry Cohn, 2024, needs more optimization.
5 362 0.835044047008 Henry Cohn, 2024, needs more optimization.
5 363 0.835420190450 Henry Cohn, 2024, needs more optimization.
5 364 0.835560062018 Henry Cohn, 2024, needs more optimization.
5 365 0.835679967129 Henry Cohn, 2024, needs more optimization.
5 366 0.835850323817 Henry Cohn, 2024, needs more optimization.
5 367 0.836303774293 Henry Cohn, 2024, needs more optimization.
5 368 0.836415683001 Henry Cohn, 2024, needs more optimization.
5 369 0.836636164943 Henry Cohn, 2024, needs more optimization.
5 371 0.837000241908 Henry Cohn, 2024, needs more optimization.
5 372 0.837279711599 Henry Cohn, 2024, needs more optimization.
5 373 0.837458661276 Henry Cohn, 2024, needs more optimization.
5 374 0.837763913575 Henry Cohn, 2024, needs more optimization.
5 375 0.837801935499 Henry Cohn, 2024, needs more optimization.
5 376 0.838022067031 Henry Cohn, 2024, needs more optimization.
5 378 0.838332204415 Henry Cohn, 2024, needs more optimization.
5 379 0.838728975267 Henry Cohn, 2024, needs more optimization.
5 380 0.838894224821 Henry Cohn, 2024, needs more optimization.
5 381 0.839134741746 Henry Cohn, 2024, needs more optimization.
5 382 0.839402847651 Henry Cohn, 2024, needs more optimization.
5 384 0.839566094156 Henry Cohn, 2024, needs more optimization.
5 385 0.840050635133 Henry Cohn, 2024, needs more optimization.
5 386 0.840464741395 Henry Cohn, 2024, needs more optimization.
5 387 0.840600329870 Henry Cohn, 2024, needs more optimization.
5 388 0.840602041499 Henry Cohn, 2024, needs more optimization.
5 390 0.840928236435 Henry Cohn, 2024, needs more optimization.
5 391 0.841242182169 Henry Cohn, 2024, needs more optimization.
5 392 0.841390348408 Henry Cohn, 2024, needs more optimization.
5 393 0.841546322118 Henry Cohn, 2024, needs more optimization.
5 394 0.841656225692 Henry Cohn, 2024, needs more optimization.
5 395 0.842175492233 Henry Cohn, 2024, needs more optimization.
5 397 0.842312525805 Henry Cohn, 2024, needs more optimization.
5 398 0.842821829194 Henry Cohn, 2024, needs more optimization.
5 400 0.843108412559 Henry Cohn, 2024, needs more optimization.
5 401 0.843303453627 Henry Cohn, 2024, needs more optimization.
5 402 0.843448008706 Henry Cohn, 2024, needs more optimization.
5 403 0.843760372226 Henry Cohn, 2024, needs more optimization.
5 404 0.843817069776 Henry Cohn, 2024, needs more optimization.
5 405 0.844094998240 Henry Cohn, 2024, needs more optimization.
5 406 0.844323377158 Henry Cohn, 2024, needs more optimization.
5 407 0.844485563711 Henry Cohn, 2024, needs more optimization.
5 408 0.844556001098 Henry Cohn, 2024, needs more optimization.
5 409 0.844802837321 Henry Cohn, 2024, needs more optimization.
5 410 0.845013136499 Henry Cohn, 2024, needs more optimization.
5 412 0.845363429802 Henry Cohn, 2024, needs more optimization.
5 413 0.845494443883 Henry Cohn, 2024, needs more optimization.
5 414 0.845760344945 Henry Cohn, 2024, needs more optimization.
5 415 0.845863846569 Henry Cohn, 2024, needs more optimization.
5 416 0.846017109121 Henry Cohn, 2024, needs more optimization.
5 417 0.846381638493 Henry Cohn, 2024, needs more optimization.
5 418 0.846552824540 Henry Cohn, 2024, needs more optimization.
5 419 0.846730927899 Henry Cohn, 2024, needs more optimization.
5 420 0.846821424511 Henry Cohn, 2024, needs more optimization.
5 421 0.847030147027 Henry Cohn, 2024, needs more optimization.
5 422 0.847192623432 Henry Cohn, 2024, needs more optimization.
5 423 0.847435053538 Henry Cohn, 2024, needs more optimization.
5 424 0.847591864954 Henry Cohn, 2024, needs more optimization.
5 425 0.847763910433 Henry Cohn, 2024, needs more optimization.
5 426 0.847908861685 Henry Cohn, 2024, needs more optimization.
5 428 0.848160982707 Henry Cohn, 2024, needs more optimization.
5 429 0.848390710832 Henry Cohn, 2024, needs more optimization.
5 430 0.848485508273 Henry Cohn, 2024, needs more optimization.
5 431 0.849024227625 Henry Cohn, 2024, needs more optimization.
5 433 0.849135870400 Henry Cohn, 2024, needs more optimization.
5 434 0.849355518229 Henry Cohn, 2024, needs more optimization.
5 435 0.849525528644 Henry Cohn, 2024, needs more optimization.
5 436 0.849735570113 Henry Cohn, 2024, needs more optimization.
5 437 0.849750337020 Henry Cohn, 2024, needs more optimization.
5 438 0.850063655236 Henry Cohn, 2024, needs more optimization.
5 439 0.850274420514 Henry Cohn, 2024, needs more optimization.
5 441 0.850486201575 Henry Cohn, 2024, needs more optimization.
5 442 0.850827343879 Henry Cohn, 2024, needs more optimization.
5 443 0.850935072484 Henry Cohn, 2024, needs more optimization.
5 444 0.851095868023 Henry Cohn, 2024, needs more optimization.
5 445 0.851283744106 Henry Cohn, 2024, needs more optimization.
5 446 0.851417600098 Henry Cohn, 2024, needs more optimization.
5 448 0.851432775789 Henry Cohn, 2024, needs more optimization.
5 449 0.851814400454 Henry Cohn, 2024, needs more optimization.
5 450 0.852115618095 Henry Cohn, 2024, needs more optimization.
5 451 0.852170951149 Henry Cohn, 2024, needs more optimization.
5 452 0.852425270818 Henry Cohn, 2024, needs more optimization.
5 453 0.852544124278 Henry Cohn, 2024, needs more optimization.
5 454 0.852873806138 Henry Cohn, 2024, needs more optimization.
5 456 0.852977093912 Henry Cohn, 2024, needs more optimization.
5 457 0.853054232862 Henry Cohn, 2024, needs more optimization.
5 459 0.853309316208 Henry Cohn, 2024, needs more optimization.
5 460 0.853607891027 Henry Cohn, 2024, needs more optimization.
5 461 0.853889902233 Henry Cohn, 2024, needs more optimization.
5 463 0.854134487124 Henry Cohn, 2024, needs more optimization.
5 464 0.854199545036 Henry Cohn, 2024, needs more optimization.
5 465 0.854488097243 Henry Cohn, 2024, needs more optimization.
5 466 0.854613908533 Henry Cohn, 2024, needs more optimization.
5 468 0.854810807800 Henry Cohn, 2024, needs more optimization.
5 469 0.855154626641 Henry Cohn, 2024, needs more optimization.
5 471 0.855316052997 Henry Cohn, 2024, needs more optimization.
5 473 0.855708510715 Henry Cohn, 2024, needs more optimization.
5 474 0.855914036580 Henry Cohn, 2024, needs more optimization.
5 475 0.856044320281 Henry Cohn, 2024, needs more optimization.
5 476 0.856251176730 Henry Cohn, 2024, needs more optimization.
5 477 0.856311183940 Henry Cohn, 2024, needs more optimization.
5 478 0.856593109572 Henry Cohn, 2024, needs more optimization.
5 479 0.856795015260 Henry Cohn, 2024, needs more optimization.
5 480 0.856848279845 Henry Cohn, 2024, needs more optimization.
5 481 0.857045857514 Henry Cohn, 2024, needs more optimization.
5 483 0.857101796304 Henry Cohn, 2024, needs more optimization.
5 484 0.857153369342 Henry Cohn, 2024, needs more optimization.
5 485 0.857420676450 Henry Cohn, 2024, needs more optimization.
5 486 0.857684155167 Henry Cohn, 2024, needs more optimization.
5 487 0.857792754581 Henry Cohn, 2024, needs more optimization.
5 488 0.858045587965 Henry Cohn, 2024, needs more optimization.
5 489 0.858087616773 Henry Cohn, 2024, needs more optimization.
5 490 0.858412383835 Henry Cohn, 2024, needs more optimization.
5 491 0.858504282110 Henry Cohn, 2024, needs more optimization.
5 492 0.858750770561 Henry Cohn, 2024, needs more optimization.
5 493 0.858795558487 Henry Cohn, 2024, needs more optimization.
5 494 0.859033085137 Henry Cohn, 2024, needs more optimization.
5 496 0.859051345277 Henry Cohn, 2024, needs more optimization.
5 497 0.859408304608 Henry Cohn, 2024, needs more optimization.
5 498 0.859487868753 Henry Cohn, 2024, needs more optimization.
5 499 0.859493014081 Henry Cohn, 2024, needs more optimization.
5 500 0.859673038039 Henry Cohn, 2024, needs more optimization.
5 501 0.859772123797 Henry Cohn, 2024, needs more optimization.
5 502 0.859940964715 Henry Cohn, 2024, needs more optimization.
5 503 0.860146264816 Henry Cohn, 2024, needs more optimization.
5 506 0.860274079827 Henry Cohn, 2024, needs more optimization.
5 507 0.860678561599 Henry Cohn, 2024, needs more optimization.
5 508 0.860759360076 Henry Cohn, 2024, needs more optimization.
5 509 0.860881787214 Henry Cohn, 2024, needs more optimization.
5 510 0.861046974263 Henry Cohn, 2024, needs more optimization.
5 512 0.861183078039 Henry Cohn, 2024, needs more optimization.
5 513 0.861244572197 Henry Cohn, 2024, needs more optimization.
5 514 0.861625503796 Henry Cohn, 2024, needs more optimization.
5 515 0.861742083113 Henry Cohn, 2024, needs more optimization.
5 516 0.861993992163 Henry Cohn, 2024, needs more optimization.
5 517 0.862167092691 Henry Cohn, 2024, needs more optimization.
5 518 0.862273900242 Henry Cohn, 2024, needs more optimization.
5 520 0.862325868568 Henry Cohn, 2024, needs more optimization.
5 521 0.862426469177 Henry Cohn, 2024, needs more optimization.
5 522 0.862717053747 Henry Cohn, 2024, needs more optimization.
5 523 0.862743700127 Henry Cohn, 2024, needs more optimization.
5 524 0.862747890463 Henry Cohn, 2024, needs more optimization.
5 525 0.863041567481 Henry Cohn, 2024, needs more optimization.
5 526 0.863100633608 Henry Cohn, 2024, needs more optimization.
5 527 0.863259247880 Henry Cohn, 2024, needs more optimization.
5 528 0.863511073342 Henry Cohn, 2024, needs more optimization.
5 529 0.863591944919 Henry Cohn, 2024, needs more optimization.
5 530 0.863743087066 Henry Cohn, 2024, needs more optimization.
5 531 0.863845584375 Henry Cohn, 2024, needs more optimization.
5 534 0.864011290034 Henry Cohn, 2024, needs more optimization.
5 535 0.864307945238 Henry Cohn, 2024, needs more optimization.
5 536 0.864462980256 Henry Cohn, 2024, needs more optimization.
5 537 0.864681360896 Henry Cohn, 2024, needs more optimization.
5 538 0.864763768541 Henry Cohn, 2024, needs more optimization.
5 539 0.864963899451 Henry Cohn, 2024, needs more optimization.
5 541 0.865150496144 Henry Cohn, 2024, needs more optimization.
5 542 0.865171273961 Henry Cohn, 2024, needs more optimization.
5 543 0.865431271794 Henry Cohn, 2024, needs more optimization.
5 544 0.865480762229 Henry Cohn, 2024, needs more optimization.
5 546 0.865533256541 Henry Cohn, 2024, needs more optimization.
5 547 0.865983140110 Henry Cohn, 2024, needs more optimization.
5 548 0.866045826282 Henry Cohn, 2024, needs more optimization.
5 550 0.866116874581 Henry Cohn, 2024, needs more optimization.
5 551 0.866258048697 Henry Cohn, 2024, needs more optimization.
5 552 0.866440792158 Henry Cohn, 2024, needs more optimization.
5 553 0.866688525579 Henry Cohn, 2024, needs more optimization.
5 554 0.866814701705 Henry Cohn, 2024, needs more optimization.
5 555 0.866837487961 Henry Cohn, 2024, needs more optimization.
5 556 0.866927561370 Henry Cohn, 2024, needs more optimization.
5 557 0.867093206587 Henry Cohn, 2024, needs more optimization.
5 558 0.867151103958 Henry Cohn, 2024, needs more optimization.
5 559 0.867275706665 Henry Cohn, 2024, needs more optimization.
5 560 0.867392144344 Henry Cohn, 2024, needs more optimization.
5 561 0.867654791888 Henry Cohn, 2024, needs more optimization.
5 562 0.867754993003 Henry Cohn, 2024, needs more optimization.
5 563 0.867896583003 Henry Cohn, 2024, needs more optimization.
5 565 0.867918044756 Henry Cohn, 2024, needs more optimization.
5 566 0.867930075223 Henry Cohn, 2024, needs more optimization.
5 567 0.868154739433 Henry Cohn, 2024, needs more optimization.
5 569 0.868427827779 Henry Cohn, 2024, needs more optimization.
5 572 0.868700450314 Henry Cohn, 2024, needs more optimization.
5 573 0.869006716768 Henry Cohn, 2024, needs more optimization.
5 575 0.869063129917 Henry Cohn, 2024, needs more optimization.
5 576 0.869189760749 Henry Cohn, 2024, needs more optimization.
5 577 0.869357553262 Henry Cohn, 2024, needs more optimization.
5 579 0.869376734154 Henry Cohn, 2024, needs more optimization.
5 580 0.869715916888 Henry Cohn, 2024, needs more optimization.
5 581 0.869885323351 Henry Cohn, 2024, needs more optimization.
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5 583 0.870068063619 Henry Cohn, 2024, needs more optimization.
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5 586 0.870351175241 Henry Cohn, 2024, needs more optimization.
5 587 0.870546353949 Henry Cohn, 2024, needs more optimization.
5 588 0.870549506069 Henry Cohn, 2024, needs more optimization.
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5 590 0.870829286630 Henry Cohn, 2024, needs more optimization.
5 591 0.870873097654 Henry Cohn, 2024, needs more optimization.
5 592 0.871137571124 Henry Cohn, 2024, needs more optimization.
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5 594 0.871333471942 Henry Cohn, 2024, needs more optimization.
5 595 0.871467952940 Henry Cohn, 2024, needs more optimization.
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5 600 0.871914356253 Henry Cohn, 2024, needs more optimization.
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5 605 0.872403334736 Henry Cohn, 2024, needs more optimization.
5 606 0.872547887133 Henry Cohn, 2024, needs more optimization.
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5 613 0.873256545581 Henry Cohn, 2024, needs more optimization.
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5 616 0.873602601431 Henry Cohn, 2024, needs more optimization.
5 617 0.873694927318 Henry Cohn, 2024, needs more optimization.
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5 620 0.874014428541 Henry Cohn, 2024, needs more optimization.
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5 622 0.874337637915 Henry Cohn, 2024, needs more optimization.
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5 624 0.874396187666 Henry Cohn, 2024, needs more optimization.
5 625 0.874420396380 Henry Cohn, 2024, needs more optimization.
5 626 0.874571402032 Henry Cohn, 2024, needs more optimization.
5 628 0.874714925477 Henry Cohn, 2024, needs more optimization.
5 629 0.874957547010 Henry Cohn, 2024, needs more optimization.
5 630 0.875128737036 Henry Cohn, 2024, needs more optimization.
5 631 0.875133452902 Henry Cohn, 2024, needs more optimization.
5 632 0.875202575937 Henry Cohn, 2024, needs more optimization.
5 633 0.875315069185 Henry Cohn, 2024, needs more optimization.
5 635 0.875373259173 Henry Cohn, 2024, needs more optimization.
5 636 0.875611155528 Henry Cohn, 2024, needs more optimization.
5 638 0.875711170884 Henry Cohn, 2024, needs more optimization.
5 640 0.875852396517 Henry Cohn, 2024, needs more optimization.
5 641 0.876030693225 Henry Cohn, 2024, needs more optimization.
5 642 0.876138670712 Henry Cohn, 2024, needs more optimization.
5 644 0.876293400090 Henry Cohn, 2024, needs more optimization.
5 645 0.876532500971 Henry Cohn, 2024, needs more optimization.
5 646 0.876577955287 Henry Cohn, 2024, needs more optimization.
5 647 0.876646095916 Henry Cohn, 2024, needs more optimization.
5 648 0.876762649138 Henry Cohn, 2024, needs more optimization.
5 649 0.876783420376 Henry Cohn, 2024, needs more optimization.
5 651 0.876942670839 Henry Cohn, 2024, needs more optimization.
5 652 0.877157740745 Henry Cohn, 2024, needs more optimization.
5 654 0.877341948000 Henry Cohn, 2024, needs more optimization.
5 655 0.877487906152 Henry Cohn, 2024, needs more optimization.
5 656 0.877590475147 Henry Cohn, 2024, needs more optimization.
5 657 0.877617572810 Henry Cohn, 2024, needs more optimization.
5 658 0.877619210720 Henry Cohn, 2024, needs more optimization.
5 659 0.877763475717 Henry Cohn, 2024, needs more optimization.
5 660 0.877887494621 Henry Cohn, 2024, needs more optimization.
5 661 0.877972134247 Henry Cohn, 2024, needs more optimization.
5 663 0.878009254707 Henry Cohn, 2024, needs more optimization.
5 664 0.878188655276 Henry Cohn, 2024, needs more optimization.
5 665 0.878305184484 Henry Cohn, 2024, needs more optimization.
5 666 0.878380405179 Henry Cohn, 2024, needs more optimization.
5 667 0.878485599017 Henry Cohn, 2024, needs more optimization.
5 668 0.878618794532 Henry Cohn, 2024, needs more optimization.
5 669 0.878678213552 Henry Cohn, 2024, needs more optimization.
5 670 0.878825425526 Henry Cohn, 2024, needs more optimization.
5 671 0.878962663408 Henry Cohn, 2024, needs more optimization.
5 672 0.878989807514 Henry Cohn, 2024, needs more optimization.
5 674 0.879169553714 Henry Cohn, 2024, needs more optimization.
5 675 0.879343847959 Henry Cohn, 2024, needs more optimization.
5 676 0.879382063628 Henry Cohn, 2024, needs more optimization.
5 678 0.879452118947 Henry Cohn, 2024, needs more optimization.
5 679 0.879594895841 Henry Cohn, 2024, needs more optimization.
5 681 0.879713860312 Henry Cohn, 2024, needs more optimization.
5 682 0.879906459711 Henry Cohn, 2024, needs more optimization.
5 683 0.879962151626 Henry Cohn, 2024, needs more optimization.
5 684 0.880126685542 Henry Cohn, 2024, needs more optimization.
5 686 0.880185138246 Henry Cohn, 2024, needs more optimization.
5 687 0.880287258597 Henry Cohn, 2024, needs more optimization.
5 688 0.880399472049 Henry Cohn, 2024, needs more optimization.
5 691 0.880569275227 Henry Cohn, 2024, needs more optimization.
5 693 0.880782935964 Henry Cohn, 2024, needs more optimization.
5 694 0.880868056473 Henry Cohn, 2024, needs more optimization.
5 695 0.881121874422 Henry Cohn, 2024, needs more optimization.
5 697 0.881151663214 Henry Cohn, 2024, needs more optimization.
5 698 0.881307594158 Henry Cohn, 2024, needs more optimization.
5 701 0.881441027180 Henry Cohn, 2024, needs more optimization.
5 704 0.881682980873 Henry Cohn, 2024, needs more optimization.
5 705 0.881895885820 Henry Cohn, 2024, needs more optimization.
5 708 0.882003704004 Henry Cohn, 2024, needs more optimization.
5 709 0.882202800275 Henry Cohn, 2024, needs more optimization.
5 710 0.882260826311 Henry Cohn, 2024, needs more optimization.
5 711 0.882411304212 Henry Cohn, 2024, needs more optimization.
5 712 0.882478866731 Henry Cohn, 2024, needs more optimization.
5 713 0.882488454047 Henry Cohn, 2024, needs more optimization.
5 714 0.882559295184 Henry Cohn, 2024, needs more optimization.
5 715 0.882664837861 Henry Cohn, 2024, needs more optimization.
5 716 0.882776825715 Henry Cohn, 2024, needs more optimization.
5 718 0.882875424928 Henry Cohn, 2024, needs more optimization.
5 719 0.883024266389 Henry Cohn, 2024, needs more optimization.
5 720 0.883180423876 Henry Cohn, 2024, needs more optimization.
5 721 0.883219842994 Henry Cohn, 2024, needs more optimization.
5 722 0.883226047184 Henry Cohn, 2024, needs more optimization.
5 723 0.883276992636 Henry Cohn, 2024, needs more optimization.
5 725 0.883437265048 Henry Cohn, 2024, needs more optimization.
5 726 0.883555994316 Henry Cohn, 2024, needs more optimization.
5 728 0.883656454263 Henry Cohn, 2024, needs more optimization.
5 731 0.883849962842 Henry Cohn, 2024, needs more optimization.
5 733 0.884051438759 Henry Cohn, 2024, needs more optimization.
5 734 0.884232429039 Henry Cohn, 2024, needs more optimization.
5 735 0.884245745635 Henry Cohn, 2024, needs more optimization.
5 736 0.884402793224 Henry Cohn, 2024, needs more optimization.
5 738 0.884421975221 Henry Cohn, 2024, needs more optimization.
5 739 0.884537682167 Henry Cohn, 2024, needs more optimization.
5 741 0.884612007344 Henry Cohn, 2024, needs more optimization.
5 742 0.884728811561 Henry Cohn, 2024, needs more optimization.
5 744 0.884931378298 Henry Cohn, 2024, needs more optimization.
5 745 0.884979651390 Henry Cohn, 2024, needs more optimization.
5 746 0.885105626925 Henry Cohn, 2024, needs more optimization.
5 747 0.885243528634 Henry Cohn, 2024, needs more optimization.
5 748 0.885302401486 Henry Cohn, 2024, needs more optimization.
5 750 0.885337542079 Henry Cohn, 2024, needs more optimization.
5 751 0.885469552611 Henry Cohn, 2024, needs more optimization.
5 752 0.885588240547 Henry Cohn, 2024, needs more optimization.
5 753 0.885669470504 Henry Cohn, 2024, needs more optimization.
5 754 0.885734650099 Henry Cohn, 2024, needs more optimization.
5 755 0.885852192406 Henry Cohn, 2024, needs more optimization.
5 757 0.885909162204 Henry Cohn, 2024, needs more optimization.
5 758 0.885928981107 Henry Cohn, 2024, needs more optimization.
5 759 0.886132281390 Henry Cohn, 2024, needs more optimization.
5 760 0.886217820320 Henry Cohn, 2024, needs more optimization.
5 761 0.886275655751 Henry Cohn, 2024, needs more optimization.
5 762 0.886280660119 Henry Cohn, 2024, needs more optimization.
5 763 0.886482522214 Henry Cohn, 2024, needs more optimization.
5 764 0.886497941376 Henry Cohn, 2024, needs more optimization.
5 765 0.886590713325 Henry Cohn, 2024, needs more optimization.
5 768 0.886671289046 Henry Cohn, 2024, needs more optimization.
5 769 0.886813576202 Henry Cohn, 2024, needs more optimization.
5 770 0.886871421978 Henry Cohn, 2024, needs more optimization.
5 772 0.887069683254 Henry Cohn, 2024, needs more optimization.
5 774 0.887150646356 Henry Cohn, 2024, needs more optimization.
5 775 0.887262591516 Henry Cohn, 2024, needs more optimization.
5 777 0.887395747281 Henry Cohn, 2024, needs more optimization.
5 778 0.887574308533 Henry Cohn, 2024, needs more optimization.
5 780 0.887602025499 Henry Cohn, 2024, needs more optimization.
5 781 0.887706303584 Henry Cohn, 2024, needs more optimization.
5 783 0.887811222711 Henry Cohn, 2024, needs more optimization.
5 784 0.887817661934 Henry Cohn, 2024, needs more optimization.
5 786 0.888027869955 Henry Cohn, 2024, needs more optimization.
5 787 0.888182950825 Henry Cohn, 2024, needs more optimization.
5 788 0.888230031335 Henry Cohn, 2024, needs more optimization.
5 789 0.888270403855 Henry Cohn, 2024, needs more optimization.
5 790 0.888379209515 Henry Cohn, 2024, needs more optimization.
5 791 0.888397775887 Henry Cohn, 2024, needs more optimization.
5 793 0.888621421699 Henry Cohn, 2024, needs more optimization.
5 794 0.888713851464 Henry Cohn, 2024, needs more optimization.
5 795 0.888770473237 Henry Cohn, 2024, needs more optimization.
5 796 0.888829768067 Henry Cohn, 2024, needs more optimization.
5 797 0.888862067869 Henry Cohn, 2024, needs more optimization.
5 798 0.888969354507 Henry Cohn, 2024, needs more optimization.
5 800 0.888977985876 Henry Cohn, 2024, needs more optimization.
5 801 0.889115008528 Henry Cohn, 2024, needs more optimization.
5 802 0.889186386850 Henry Cohn, 2024, needs more optimization.
5 803 0.889283196715 Henry Cohn, 2024, needs more optimization.
5 804 0.889442323202 Henry Cohn, 2024, needs more optimization.
5 805 0.889471506750 Henry Cohn, 2024, needs more optimization.
5 807 0.889499578559 Henry Cohn, 2024, needs more optimization.
5 808 0.889649407936 Henry Cohn, 2024, needs more optimization.
5 809 0.889709704986 Henry Cohn, 2024, needs more optimization.
5 811 0.889763734183 Henry Cohn, 2024, needs more optimization.
5 812 0.889909164306 Henry Cohn, 2024, needs more optimization.
5 813 0.889979956355 Henry Cohn, 2024, needs more optimization.
5 814 0.890046635657 Henry Cohn, 2024, needs more optimization.
5 815 0.890059337317 Henry Cohn, 2024, needs more optimization.
5 817 0.890108868183 Henry Cohn, 2024, needs more optimization.
5 818 0.890266868567 Henry Cohn, 2024, needs more optimization.
5 819 0.890385996844 Henry Cohn, 2024, needs more optimization.
5 820 0.890451054767 Henry Cohn, 2024, needs more optimization.
5 823 0.890630859080 Henry Cohn, 2024, needs more optimization.
5 824 0.890734758693 Henry Cohn, 2024, needs more optimization.
5 825 0.890847244891 Henry Cohn, 2024, needs more optimization.
5 826 0.890903780680 Henry Cohn, 2024, needs more optimization.
5 827 0.890923963777 Henry Cohn, 2024, needs more optimization.
5 829 0.890971959102 Henry Cohn, 2024, needs more optimization.
5 830 0.891098680158 Henry Cohn, 2024, needs more optimization.
5 832 0.891126553040 Henry Cohn, 2024, needs more optimization.
5 833 0.891288239667 Henry Cohn, 2024, needs more optimization.
5 834 0.891378704132 Henry Cohn, 2024, needs more optimization.
5 835 0.891467646866 Henry Cohn, 2024, needs more optimization.
5 836 0.891552695835 Henry Cohn, 2024, needs more optimization.
5 837 0.891554083247 Henry Cohn, 2024, needs more optimization.
5 838 0.891562625354 Henry Cohn, 2024, needs more optimization.
5 839 0.891757359878 Henry Cohn, 2024, needs more optimization.
5 840 0.891794463631 Henry Cohn, 2024, needs more optimization.
5 842 0.891805118856 Henry Cohn, 2024, needs more optimization.
5 845 0.892003657647 Henry Cohn, 2024, needs more optimization.
5 846 0.892125077493 Henry Cohn, 2024, needs more optimization.
5 847 0.892129416853 Henry Cohn, 2024, needs more optimization.
5 851 0.892267206698 Henry Cohn, 2024, needs more optimization.
5 852 0.892425916059 Henry Cohn, 2024, needs more optimization.
5 853 0.892613078203 Henry Cohn, 2024, needs more optimization.
5 854 0.892683379112 Henry Cohn, 2024, needs more optimization.
5 855 0.892710031206 Henry Cohn, 2024, needs more optimization.
5 856 0.892865430148 Henry Cohn, 2024, needs more optimization.
5 857 0.892912051380 Henry Cohn, 2024, needs more optimization.
5 858 0.892920122869 Henry Cohn, 2024, needs more optimization.
5 859 0.892941336994 Henry Cohn, 2024, needs more optimization.
5 861 0.893037052557 Henry Cohn, 2024, needs more optimization.
5 862 0.893122874927 Henry Cohn, 2024, needs more optimization.
5 863 0.893246401962 Henry Cohn, 2024, needs more optimization.
5 864 0.893350487836 Henry Cohn, 2024, needs more optimization.
5 866 0.893392065409 Henry Cohn, 2024, needs more optimization.
5 867 0.893423920470 Henry Cohn, 2024, needs more optimization.
5 868 0.893488420859 Henry Cohn, 2024, needs more optimization.
5 869 0.893602500416 Henry Cohn, 2024, needs more optimization.
5 870 0.893621876837 Henry Cohn, 2024, needs more optimization.
5 871 0.893747231780 Henry Cohn, 2024, needs more optimization.
5 872 0.893774305089 Henry Cohn, 2024, needs more optimization.
5 873 0.893822219690 Henry Cohn, 2024, needs more optimization.
5 876 0.893890180337 Henry Cohn, 2024, needs more optimization.
5 877 0.894014232502 Henry Cohn, 2024, needs more optimization.
5 880 0.894142258873 Henry Cohn, 2024, needs more optimization.
5 881 0.894211711664 Henry Cohn, 2024, needs more optimization.
5 882 0.894285244595 Henry Cohn, 2024, needs more optimization.
5 884 0.894425815143 Henry Cohn, 2024, needs more optimization.
5 885 0.894564551460 Henry Cohn, 2024, needs more optimization.
5 886 0.894646001125 Henry Cohn, 2024, needs more optimization.
5 888 0.894686608921 Henry Cohn, 2024, needs more optimization.
5 889 0.894771044581 Henry Cohn, 2024, needs more optimization.
5 890 0.894879750200 Henry Cohn, 2024, needs more optimization.
5 892 0.894898856619 Henry Cohn, 2024, needs more optimization.
5 893 0.894961547473 Henry Cohn, 2024, needs more optimization.
5 894 0.895067499505 Henry Cohn, 2024, needs more optimization.
5 896 0.895086375676 Henry Cohn, 2024, needs more optimization.
5 897 0.895213205466 Henry Cohn, 2024, needs more optimization.
5 898 0.895347107199 Henry Cohn, 2024, needs more optimization.
5 900 0.895362940204 Henry Cohn, 2024, needs more optimization.
5 901 0.895492500840 Henry Cohn, 2024, needs more optimization.
5 902 0.895525698938 Henry Cohn, 2024, needs more optimization.
5 904 0.895579314721 Henry Cohn, 2024, needs more optimization.
5 905 0.895717812833 Henry Cohn, 2024, needs more optimization.
5 906 0.895771032812 Henry Cohn, 2024, needs more optimization.
5 908 0.895804048281 Henry Cohn, 2024, needs more optimization.
5 909 0.895892149706 Henry Cohn, 2024, needs more optimization.
5 910 0.896003227321 Henry Cohn, 2024, needs more optimization.
5 911 0.896075744042 Henry Cohn, 2024, needs more optimization.
5 913 0.896177219775 Henry Cohn, 2024, needs more optimization.
5 914 0.896178036717 Henry Cohn, 2024, needs more optimization.
5 916 0.896238597511 Henry Cohn, 2024, needs more optimization.
5 917 0.896384835112 Henry Cohn, 2024, needs more optimization.
5 918 0.896394924234 Henry Cohn, 2024, needs more optimization.
5 920 0.896607363347 Henry Cohn, 2024, needs more optimization.
5 921 0.896608530216 Henry Cohn, 2024, needs more optimization.
5 922 0.896724763861 Henry Cohn, 2024, needs more optimization.
5 924 0.896728989736 Henry Cohn, 2024, needs more optimization.
5 926 0.896918210136 Henry Cohn, 2024, needs more optimization.
5 927 0.896998267669 Henry Cohn, 2024, needs more optimization.
5 928 0.897002630462 Henry Cohn, 2024, needs more optimization.
5 929 0.897061439607 Henry Cohn, 2024, needs more optimization.
5 930 0.897128660140 Henry Cohn, 2024, needs more optimization.
5 931 0.897160788569 Henry Cohn, 2024, needs more optimization.
5 932 0.897201485510 Henry Cohn, 2024, needs more optimization.
5 934 0.897297497448 Henry Cohn, 2024, needs more optimization.
5 935 0.897392576854 Henry Cohn, 2024, needs more optimization.
5 936 0.897487482650 Henry Cohn, 2024, needs more optimization.
5 937 0.897536023496 Henry Cohn, 2024, needs more optimization.
5 939 0.897571860936 Henry Cohn, 2024, needs more optimization.
5 940 0.897676099453 Henry Cohn, 2024, needs more optimization.
5 941 0.897737257871 Henry Cohn, 2024, needs more optimization.
5 942 0.897800231577 Henry Cohn, 2024, needs more optimization.
5 943 0.897851682146 Henry Cohn, 2024, needs more optimization.
5 944 0.897868716036 Henry Cohn, 2024, needs more optimization.
5 945 0.897923343424 Henry Cohn, 2024, needs more optimization.
5 946 0.897955883457 Henry Cohn, 2024, needs more optimization.
5 948 0.898075522532 Henry Cohn, 2024, needs more optimization.
5 951 0.898272343571 Henry Cohn, 2024, needs more optimization.
5 952 0.898289512999 Henry Cohn, 2024, needs more optimization.
5 953 0.898431564165 Henry Cohn, 2024, needs more optimization.
5 954 0.898438607429 Henry Cohn, 2024, needs more optimization.
5 956 0.898532537887 Henry Cohn, 2024, needs more optimization.
5 957 0.898584436884 Henry Cohn, 2024, needs more optimization.
5 959 0.898656912344 Henry Cohn, 2024, needs more optimization.
5 960 0.898657455112 Henry Cohn, 2024, needs more optimization.
5 961 0.898836053619 Henry Cohn, 2024, needs more optimization.
5 962 0.898890715135 Henry Cohn, 2024, needs more optimization.
5 963 0.898892304163 Henry Cohn, 2024, needs more optimization.
5 964 0.898906142850 Henry Cohn, 2024, needs more optimization.
5 965 0.899002119483 Henry Cohn, 2024, needs more optimization.
5 966 0.899116480632 Henry Cohn, 2024, needs more optimization.
5 968 0.899160899922 Henry Cohn, 2024, needs more optimization.
5 969 0.899198568421 Henry Cohn, 2024, needs more optimization.
5 970 0.899277172527 Henry Cohn, 2024, needs more optimization.
5 972 0.899355800752 Henry Cohn, 2024, needs more optimization.
5 974 0.899432663991 Henry Cohn, 2024, needs more optimization.
5 976 0.899542355852 Henry Cohn, 2024, needs more optimization.
5 977 0.899663069146 Henry Cohn, 2024, needs more optimization.
5 978 0.899758993949 Henry Cohn, 2024, needs more optimization.
5 979 0.899793677393 Henry Cohn, 2024, needs more optimization.
5 980 0.899833388600 Henry Cohn, 2024, needs more optimization.
5 981 0.899879432042 Henry Cohn, 2024, needs more optimization.
5 982 0.899885161457 Henry Cohn, 2024, needs more optimization.
5 983 0.899895404869 Henry Cohn, 2024, needs more optimization.
5 984 0.899930504225 Henry Cohn, 2024, needs more optimization.
5 986 0.899989950487 Henry Cohn, 2024, needs more optimization.
5 987 0.900065471715 Henry Cohn, 2024, needs more optimization.
5 988 0.900189901389 Henry Cohn, 2024, needs more optimization.
5 990 0.900263543609 Henry Cohn, 2024, needs more optimization.
5 991 0.900344316663 Henry Cohn, 2024, needs more optimization.
5 992 0.900360346031 Henry Cohn, 2024, needs more optimization.
5 994 0.900503427199 Henry Cohn, 2024, needs more optimization.
5 995 0.900538703204 Henry Cohn, 2024, needs more optimization.
5 996 0.900602679430 Henry Cohn, 2024, needs more optimization.
5 997 0.900657346509 Henry Cohn, 2024, needs more optimization.
5 998 0.900707454091 Henry Cohn, 2024, needs more optimization.
5 999 0.900759814121 Henry Cohn, 2024, needs more optimization.
5 1000 0.900788083273 Henry Cohn, 2024, needs more optimization.
5 1001 0.900817500206 Henry Cohn, 2024, needs more optimization.
5 1002 0.900896290815 Henry Cohn, 2024, needs more optimization.
5 1003 0.900933731572 Henry Cohn, 2024, needs more optimization.
5 1004 0.900971917805 Henry Cohn, 2024, needs more optimization.
5 1005 0.901047050635 Henry Cohn, 2024, needs more optimization.
5 1006 0.901094167480 Henry Cohn, 2024, needs more optimization.
5 1007 0.901140387647 Henry Cohn, 2024, needs more optimization.
5 1008 0.901149120061 Henry Cohn, 2024, needs more optimization.
5 1013 0.901329439554 Henry Cohn, 2024, needs more optimization.
5 1014 0.901484467356 Henry Cohn, 2024, needs more optimization.
5 1015 0.901521326498 Henry Cohn, 2024, needs more optimization.
5 1016 0.901641751114 Henry Cohn, 2024, needs more optimization.
5 1018 0.901644032208 Henry Cohn, 2024, needs more optimization.
5 1020 0.901671297591 Henry Cohn, 2024, needs more optimization.
5 1021 0.901748681317 Henry Cohn, 2024, needs more optimization.
5 1024 0.901852772510 Henry Cohn, 2024, 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 0.426943929412 Henry Cohn, 2023.
6 46 0.435728619792 J. Wang, Finding and investigating exact spherical codes, Experiment. Math. 18 (2009), 249–256, https://projecteuclid.org/euclid.em/1259158434.
6 47 0.441277260126 Henry Cohn, 2023.
24⁢x3+16⁢x2−14⁢x+1
6 48 0.443652559533 Henry Cohn, 2023.
6 49 0.446060501890 Henry Cohn, 2023.
6 50 0.446739131277 Henry Cohn, 2023.
58⁢x3−50⁢x2+13⁢x−1
6 51 0.456559101176 Henry Cohn, 2024.
6 52 0.458253528717 Henry Cohn, 2023.
6 53 0.459152260492 Henry Cohn, 2023.
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 0.479818012263 Henry Cohn, 2023.
6 58 0.482548584905 Henry Cohn, 2024.
20⁢x2+9⁢x−9
6 59 0.486119746833 Henry Cohn, 2023.
6 60 0.486877257533 Henry Cohn, 2023.
6 61 0.491751789653 Henry Cohn, 2023.
6 62 0.495376595904 Henry Cohn, 2023.
6 63 0.498122491823 Henry Cohn, 2023.
6 64 0.498526182118 Henry Cohn, 2023.
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 0.517792073302 Bram Cohen, 2023.
Minimal polynomial listed in plain text data
6 74 0.524331921924 Bram Cohen, 2023.
6 75 0.527712280585 Henry Cohn, 2024.
6 76 0.530523879593 Henry Cohn, 2023.
6 77 0.531821471743 Henry Cohn, 2024.
6 79 0.533954283180 Henry Cohn, 2024.
6 80 0.536674173959 Henry Cohn, 2024.
6 81 0.539327575295 Henry Cohn, 2025.
6 82 0.542045389727 Henry Cohn, 2025.
6 83 0.543869792291 Henry Cohn, 2025.
6 84 0.546970222275 Henry Cohn, 2024.
6 85 0.549385704407 Henry Cohn, 2024.
6 86 0.550314646242 Henry Cohn, 2023.
6 87 0.551714767476 Henry Cohn, 2023.
6 88 0.552456763833 Henry Cohn, 2024.
6 89 0.556214421895 Henry Cohn, 2025.
6 91 0.557603429720 Henry Cohn, 2024.
6 92 0.560998442664 Henry Cohn, 2023.
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.
6 104 0.583764775420 Henry Cohn, 2025.
6 105 0.584090776742 Henry Cohn, 2025.
6 106 0.586276471960 Henry Cohn, 2025.
6 107 0.586428828400 Henry Cohn, 2025.
6 110 0.586596917770 Henry Cohn, 2025.
6 111 0.587632666644 Henry Cohn, 2025.
6 112 0.587657648892 Henry Cohn, 2024.
6 114 0.588109690133 Henry Cohn, 2023.
6 115 0.596007597445 Henry Cohn, 2025, needs more optimization.
6 116 0.598226276508 Henry Cohn, 2025.
6 117 0.599162939132 Henry Cohn, 2025, needs more optimization.
6 118 0.599245397179 Henry Cohn, 2025.
6 119 0.599290283257 Henry Cohn, 2025, needs more optimization.
6 120 0.599317371092 Henry Cohn, 2024.
6 121 0.605179180329 Henry Cohn, 2025.
6 122 0.606689340567 Henry Cohn, 2025, needs more optimization.
6 123 0.607115797651 Henry Cohn, 2025.
6 125 0.607974063065 Henry Cohn, 2024, needs more optimization.
6 126 0.610431849202 Henry Cohn, 2024.
6 127 0.616601953906 Henry Cohn, 2025, needs more optimization.
6 128 0.619159679425 Henry Cohn, 2025, needs more optimization.
6 129 0.620265668376 Henry Cohn, 2025, needs more optimization.
6 130 0.623641846517 Henry Cohn, 2025, needs more optimization.
6 131 0.624699873954 Henry Cohn, 2024, needs more optimization.
6 132 0.624700782851 Henry Cohn, 2024, needs more optimization.
6 133 0.628272863539 Henry Cohn, 2024, needs more optimization.
6 134 0.629038278513 Henry Cohn, 2024, needs more optimization.
6 135 0.630970129578 Henry Cohn, 2024, needs more optimization.
6 136 0.631874875582 Henry Cohn, 2024, needs more optimization.
6 137 0.633404247764 Henry Cohn, 2024, needs more optimization.
6 138 0.634799118997 Henry Cohn, 2024, needs more optimization.
6 139 0.637009870842 Henry Cohn, 2024, needs more optimization.
6 140 0.637601758571 Henry Cohn, 2024, needs more optimization.
6 141 0.639689060506 Henry Cohn, 2024, needs more optimization.
6 142 0.640106345397 Henry Cohn, 2024, needs more optimization.
6 143 0.641918964542 Henry Cohn, 2024, needs more optimization.
6 144 0.642557048262 Henry Cohn, 2024, needs more optimization.
6 145 0.644531046308 Henry Cohn, 2024, needs more optimization.
6 146 0.644980390551 Henry Cohn, 2024, needs more optimization.
6 147 0.646474185890 Henry Cohn, 2024, needs more optimization.
6 148 0.646885686260 Henry Cohn, 2024, needs more optimization.
6 149 0.648910786680 Henry Cohn, 2024, 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 0.651472728170 Henry Cohn, 2024, needs more optimization.
6 153 0.652219004325 Henry Cohn, 2024, needs more optimization.
6 154 0.653276789190 Henry Cohn, 2024, needs more optimization.
6 155 0.654140457971 Henry Cohn, 2025.
6 156 0.654967854425 Henry Cohn, 2024, needs more optimization.
6 157 0.655952564295 Henry Cohn, 2024, needs more optimization.
6 158 0.656490997508 Henry Cohn, 2024, needs more optimization.
6 159 0.657297444240 Henry Cohn, 2024, needs more optimization.
6 160 0.658421788265 Henry Cohn, 2024, needs more optimization.
6 161 0.659148909926 Henry Cohn, 2024, needs more optimization.
6 162 0.659974223237 Henry Cohn, 2024, needs more optimization.
6 163 0.660657844536 Henry Cohn, 2024, needs more optimization.
6 164 0.661102846593 Henry Cohn, 2024, needs more optimization.
6 165 0.662275167972 Henry Cohn, 2024, needs more optimization.
6 166 0.662887250500 Henry Cohn, 2024, needs more optimization.
6 167 0.664103556470 Henry Cohn, 2024, needs more optimization.
6 168 0.664638529355 Henry Cohn, 2024, needs more optimization.
6 169 0.664933654764 Henry Cohn, 2024, needs more optimization.
6 170 0.665719376863 Henry Cohn, 2024, needs more optimization.
6 171 0.666505733547 Henry Cohn, 2024, needs more optimization.
6 172 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
6 173 0.666843022728 Henry Cohn, 2024, needs more optimization.
6 174 0.669495969360 Henry Cohn, 2024, needs more optimization.
6 175 0.669846695305 Henry Cohn, 2024, needs more optimization.
6 176 0.670657714864 Henry Cohn, 2024, needs more optimization.
6 177 0.671462802949 Henry Cohn, 2024, needs more optimization.
6 178 0.672090486997 Henry Cohn, 2024, needs more optimization.
6 179 0.672116417279 Henry Cohn, 2024, needs more optimization.
6 180 0.673670633944 Henry Cohn, 2024, needs more optimization.
6 181 0.674385774058 Henry Cohn, 2024, needs more optimization.
6 182 0.674861105323 Henry Cohn, 2024, needs more optimization.
6 183 0.676168019474 Henry Cohn, 2024, needs more optimization.
6 184 0.676222362335 Henry Cohn, 2024, needs more optimization.
6 185 0.677383532812 Henry Cohn, 2024, needs more optimization.
6 186 0.678125681892 Henry Cohn, 2024, needs more optimization.
6 187 0.678997598593 Henry Cohn, 2024, needs more optimization.
6 188 0.679604697812 Henry Cohn, 2024, needs more optimization.
6 189 0.680283637195 Henry Cohn, 2024, needs more optimization.
6 190 0.681121072009 Henry Cohn, 2024, needs more optimization.
6 191 0.681826750372 Henry Cohn, 2024, needs more optimization.
6 192 0.682168722212 Henry Cohn, 2024, needs more optimization.
6 193 0.683009964330 Henry Cohn, 2024, needs more optimization.
6 194 0.683996793833 Henry Cohn, 2024, needs more optimization.
6 195 0.684715373686 Henry Cohn, 2024, needs more optimization.
6 196 0.685103818367 Henry Cohn, 2024, needs more optimization.
6 197 0.685682689871 Henry Cohn, 2024, needs more optimization.
6 198 0.686447437948 Henry Cohn, 2024, needs more optimization.
6 199 0.687030212507 Henry Cohn, 2024, needs more optimization.
6 200 0.687462969287 Henry Cohn, 2024, needs more optimization.
6 201 0.688187440577 Henry Cohn, 2024, needs more optimization.
6 202 0.688401371909 Henry Cohn, 2024, needs more optimization.
6 203 0.688802922098 Henry Cohn, 2024, needs more optimization.
6 204 0.688915971680 Henry Cohn, 2024, needs more optimization.
6 205 0.689067368438 Henry Cohn, 2024, needs more optimization.
6 206 0.689166617627 Henry Cohn, 2024, needs more optimization.
6 207 0.689193313118 Henry Cohn, 2024, needs more optimization.
6 208 0.689229393912 Henry Cohn, 2024, needs more optimization.
6 209 0.693090647103 Henry Cohn, 2024, needs more optimization.
6 210 0.693708151091 Henry Cohn, 2024, needs more optimization.
6 211 0.693815034585 Henry Cohn, 2024, needs more optimization.
6 212 0.694538944930 Henry Cohn, 2024, needs more optimization.
6 213 0.695358313158 Henry Cohn, 2024, needs more optimization.
6 214 0.695363898891 Henry Cohn, 2024, needs more optimization.
6 215 0.696037822586 Henry Cohn, 2024, needs more optimization.
6 216 0.696584925283 Henry Cohn, 2024, needs more optimization.
6 217 0.697276834869 Henry Cohn, 2024, 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 0.699230526477 Henry Cohn, 2024, 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 0.711560605742 Henry Cohn, 2024, needs more optimization.
6 245 0.712023928070 Henry Cohn, 2024, needs more optimization.
6 246 0.712470150490 Henry Cohn, 2024, needs more optimization.
6 247 0.712775578797 Henry Cohn, 2024, needs more optimization.
6 248 0.713435087282 Henry Cohn, 2024, needs more optimization.
6 249 0.713844431253 Henry Cohn, 2024, needs more optimization.
6 250 0.714709048662 Henry Cohn, 2024, needs more optimization.
6 251 0.715178755122 Henry Cohn, 2024, needs more optimization.
6 252 0.715511232601 Henry Cohn, 2024, needs more optimization.
6 253 0.715777453837 Henry Cohn, 2024, needs more optimization.
6 254 0.716537798518 Henry Cohn, 2024, needs more optimization.
6 255 0.716554399508 Henry Cohn, 2024, needs more optimization.
6 256 0.717229018586 Henry Cohn, 2024, needs more optimization.
6 257 0.718329779779 Henry Cohn, 2024, needs more optimization.
6 258 0.718893170767 Henry Cohn, 2024, needs more optimization.
6 259 0.719368177318 Henry Cohn, 2024, needs more optimization.
6 260 0.719684920078 Henry Cohn, 2024, needs more optimization.
6 261 0.720159098445 Henry Cohn, 2024, needs more optimization.
6 262 0.720663575468 Henry Cohn, 2024, needs more optimization.
6 263 0.720790517196 Henry Cohn, 2024, needs more optimization.
6 264 0.721547118564 Henry Cohn, 2024, needs more optimization.
6 265 0.722041770260 Henry Cohn, 2024, needs more optimization.
6 266 0.722391741963 Henry Cohn, 2024, needs more optimization.
6 268 0.722905745539 Henry Cohn, 2024, needs more optimization.
6 269 0.723474757327 Henry Cohn, 2024, needs more optimization.
6 270 0.724013408954 Henry Cohn, 2024, needs more optimization.
6 271 0.724318644370 Henry Cohn, 2024, needs more optimization.
6 272 0.724908812114 Henry Cohn, 2024, needs more optimization.
6 273 0.725288773828 Henry Cohn, 2024, needs more optimization.
6 274 0.725629732309 Henry Cohn, 2024, needs more optimization.
6 275 0.726227646112 Henry Cohn, 2024, needs more optimization.
6 276 0.726473275540 Henry Cohn, 2024, needs more optimization.
6 277 0.727338457753 Henry Cohn, 2024, needs more optimization.
6 278 0.727501321100 Henry Cohn, 2024, needs more optimization.
6 279 0.728080967418 Henry Cohn, 2024, needs more optimization.
6 281 0.728496233560 Henry Cohn, 2024, needs more optimization.
6 282 0.728856316860 Henry Cohn, 2024, needs more optimization.
6 283 0.729588201847 Henry Cohn, 2024, needs more optimization.
6 285 0.730155456352 Henry Cohn, 2024, needs more optimization.
6 286 0.730351462534 Henry Cohn, 2024, needs more optimization.
6 288 0.730779001660 Henry Cohn, 2024, needs more optimization.
6 289 0.731875981400 Henry Cohn, 2024, needs more optimization.
6 290 0.732010104762 Henry Cohn, 2024, needs more optimization.
6 291 0.732452285322 Henry Cohn, 2024, needs more optimization.
6 292 0.732718003921 Henry Cohn, 2024, needs more optimization.
6 295 0.732956473776 Henry Cohn, 2024, needs more optimization.
6 296 0.733369483130 Henry Cohn, 2024, needs more optimization.
6 297 0.734429673583 Henry Cohn, 2024, needs more optimization.
6 298 0.734886010843 Henry Cohn, 2024, needs more optimization.
6 299 0.735378314946 Henry Cohn, 2024, needs more optimization.
6 301 0.735512037518 Henry Cohn, 2024, needs more optimization.
6 302 0.735969971368 Henry Cohn, 2024, needs more optimization.
6 303 0.736900208314 Henry Cohn, 2024, needs more optimization.
6 304 0.736917446854 Henry Cohn, 2024, needs more optimization.
6 305 0.737045062205 Henry Cohn, 2024, needs more optimization.
6 308 0.737857011615 Henry Cohn, 2024, needs more optimization.
6 309 0.738370539520 Henry Cohn, 2024, needs more optimization.
6 310 0.739076934892 Henry Cohn, 2024, needs more optimization.
6 311 0.739632798137 Henry Cohn, 2024, needs more optimization.
6 312 0.739722086479 Henry Cohn, 2024, needs more optimization.
6 313 0.739833712572 Henry Cohn, 2024, needs more optimization.
6 314 0.740548906417 Henry Cohn, 2024, needs more optimization.
6 316 0.740860575302 Henry Cohn, 2024, needs more optimization.
6 318 0.741228524101 Henry Cohn, 2024, needs more optimization.
6 320 0.742285478564 Henry Cohn, 2024, needs more optimization.
6 321 0.742489872692 Henry Cohn, 2024, needs more optimization.
6 323 0.743048686458 Henry Cohn, 2024, needs more optimization.
6 325 0.743525548095 Henry Cohn, 2024, needs more optimization.
6 326 0.744385183719 Henry Cohn, 2024, needs more optimization.
6 327 0.744528143108 Henry Cohn, 2024, needs more optimization.
6 328 0.744820191363 Henry Cohn, 2024, needs more optimization.
6 329 0.745304364964 Henry Cohn, 2024, needs more optimization.
6 330 0.745506766623 Henry Cohn, 2024, needs more optimization.
6 331 0.745928456524 Henry Cohn, 2024, needs more optimization.
6 332 0.746314759104 Henry Cohn, 2024, needs more optimization.
6 333 0.746617257267 Henry Cohn, 2024, needs more optimization.
6 342 0.746790391073 Henry Cohn, 2023, needs more optimization.
6 343 0.749879992123 Henry Cohn, 2024, needs more optimization.
6 344 0.750121199015 Henry Cohn, 2024, needs more optimization.
6 345 0.750137851748 Henry Cohn, 2024, needs more optimization.
6 346 0.750462455816 Henry Cohn, 2024, needs more optimization.
6 347 0.750849499383 Henry Cohn, 2024, needs more optimization.
6 348 0.751007359200 Henry Cohn, 2024, needs more optimization.
6 349 0.751567071326 Henry Cohn, 2024, needs more optimization.
6 350 0.751733828588 Henry Cohn, 2024, needs more optimization.
6 352 0.751988740709 Henry Cohn, 2024, needs more optimization.
6 353 0.752804382650 Henry Cohn, 2024, needs more optimization.
6 354 0.753023091407 Henry Cohn, 2024, needs more optimization.
6 355 0.753207744809 Henry Cohn, 2024, needs more optimization.
6 356 0.753588009375 Henry Cohn, 2024, needs more optimization.
6 357 0.753857233122 Henry Cohn, 2024, needs more optimization.
6 358 0.753961875499 Henry Cohn, 2024, needs more optimization.
6 359 0.754370696908 Henry Cohn, 2024, needs more optimization.
6 360 0.754771680847 Henry Cohn, 2024, needs more optimization.
6 361 0.755138999793 Henry Cohn, 2024, needs more optimization.
6 362 0.755352184542 Henry Cohn, 2024, needs more optimization.
6 363 0.755582234120 Henry Cohn, 2024, needs more optimization.
6 364 0.755815196064 Henry Cohn, 2024, needs more optimization.
6 365 0.755886559719 Henry Cohn, 2024, needs more optimization.
6 366 0.755924204293 Henry Cohn, 2024, needs more optimization.
6 367 0.756425644381 Henry Cohn, 2024, needs more optimization.
6 368 0.756677745853 Henry Cohn, 2024, needs more optimization.
6 369 0.757083082826 Henry Cohn, 2024, needs more optimization.
6 370 0.757445865071 Henry Cohn, 2024, needs more optimization.
6 371 0.757718262362 Henry Cohn, 2024, needs more optimization.
6 372 0.757870319779 Henry Cohn, 2024, needs more optimization.
6 373 0.758086199146 Henry Cohn, 2024, needs more optimization.
6 374 0.758459159130 Henry Cohn, 2024, needs more optimization.
6 375 0.758923061357 Henry Cohn, 2024, needs more optimization.
6 376 0.759053524329 Henry Cohn, 2024, needs more optimization.
6 377 0.759210707487 Henry Cohn, 2024, needs more optimization.
6 380 0.759377793292 Henry Cohn, 2024, needs more optimization.
6 381 0.760196912898 Henry Cohn, 2024, needs more optimization.
6 382 0.760550808143 Henry Cohn, 2024, needs more optimization.
6 384 0.760743441807 Henry Cohn, 2024, needs more optimization.
6 385 0.760751216946 Henry Cohn, 2024, needs more optimization.
6 386 0.761409132115 Henry Cohn, 2024, needs more optimization.
6 387 0.761752012292 Henry Cohn, 2024, needs more optimization.
6 388 0.761827451806 Henry Cohn, 2024, needs more optimization.
6 389 0.762188679066 Henry Cohn, 2024, needs more optimization.
6 390 0.762353995011 Henry Cohn, 2024, needs more optimization.
6 391 0.762997719049 Henry Cohn, 2024, needs more optimization.
6 392 0.763223867977 Henry Cohn, 2024, needs more optimization.
6 393 0.763227312819 Henry Cohn, 2024, needs more optimization.
6 394 0.763306564923 Henry Cohn, 2024, needs more optimization.
6 395 0.763604648554 Henry Cohn, 2024, needs more optimization.
6 397 0.763982070793 Henry Cohn, 2024, needs more optimization.
6 398 0.764408956285 Henry Cohn, 2024, needs more optimization.
6 400 0.764630214122 Henry Cohn, 2024, needs more optimization.
6 401 0.765115947998 Henry Cohn, 2024, needs more optimization.
6 402 0.765316081848 Henry Cohn, 2024, needs more optimization.
6 403 0.765618499592 Henry Cohn, 2024, needs more optimization.
6 404 0.765786415860 Henry Cohn, 2024, needs more optimization.
6 406 0.766182324167 Henry Cohn, 2024, needs more optimization.
6 407 0.766458995820 Henry Cohn, 2024, needs more optimization.
6 408 0.766621937326 Henry Cohn, 2024, needs more optimization.
6 409 0.766707609872 Henry Cohn, 2024, needs more optimization.
6 412 0.767128083885 Henry Cohn, 2024, needs more optimization.
6 414 0.767849275050 Henry Cohn, 2024, needs more optimization.
6 415 0.768181070291 Henry Cohn, 2024, needs more optimization.
6 416 0.768510511721 Henry Cohn, 2024, needs more optimization.
6 417 0.768816715774 Henry Cohn, 2024, needs more optimization.
6 418 0.768926298340 Henry Cohn, 2024, needs more optimization.
6 419 0.769241472031 Henry Cohn, 2024, needs more optimization.
6 420 0.769431304395 Henry Cohn, 2024, needs more optimization.
6 421 0.769576803387 Henry Cohn, 2024, needs more optimization.
6 422 0.769970777566 Henry Cohn, 2024, needs more optimization.
6 423 0.770038912152 Henry Cohn, 2024, needs more optimization.
6 424 0.770142912845 Henry Cohn, 2024, needs more optimization.
6 425 0.770565145673 Henry Cohn, 2024, needs more optimization.
6 426 0.770614398803 Henry Cohn, 2024, needs more optimization.
6 427 0.770839222781 Henry Cohn, 2024, needs more optimization.
6 428 0.771137170438 Henry Cohn, 2024, needs more optimization.
6 429 0.771413291790 Henry Cohn, 2024, needs more optimization.
6 430 0.771598248235 Henry Cohn, 2024, needs more optimization.
6 431 0.772060665594 Henry Cohn, 2024, needs more optimization.
6 432 0.772111575039 Henry Cohn, 2024, needs more optimization.
6 434 0.772166224945 Henry Cohn, 2024, needs more optimization.
6 435 0.772678484693 Henry Cohn, 2024, needs more optimization.
6 436 0.773042507014 Henry Cohn, 2024, needs more optimization.
6 437 0.773165657025 Henry Cohn, 2024, needs more optimization.
6 438 0.773262137087 Henry Cohn, 2024, needs more optimization.
6 439 0.773567208298 Henry Cohn, 2024, needs more optimization.
6 440 0.773680684565 Henry Cohn, 2024, needs more optimization.
6 441 0.773925312184 Henry Cohn, 2024, needs more optimization.
6 443 0.774198574213 Henry Cohn, 2024, needs more optimization.
6 445 0.774788449836 Henry Cohn, 2024, needs more optimization.
6 446 0.774887492836 Henry Cohn, 2024, needs more optimization.
6 448 0.775092016852 Henry Cohn, 2024, needs more optimization.
6 449 0.775524001223 Henry Cohn, 2024, needs more optimization.
6 450 0.775888171873 Henry Cohn, 2024, needs more optimization.
6 451 0.776121670523 Henry Cohn, 2024, needs more optimization.
6 452 0.776354640513 Henry Cohn, 2024, needs more optimization.
6 453 0.776498881964 Henry Cohn, 2024, needs more optimization.
6 454 0.776513452273 Henry Cohn, 2024, needs more optimization.
6 455 0.776948483114 Henry Cohn, 2024, needs more optimization.
6 456 0.777038085436 Henry Cohn, 2024, needs more optimization.
6 457 0.777200611192 Henry Cohn, 2024, needs more optimization.
6 458 0.777360741822 Henry Cohn, 2024, needs more optimization.
6 459 0.777520171983 Henry Cohn, 2024, needs more optimization.
6 460 0.777717875412 Henry Cohn, 2024, needs more optimization.
6 461 0.778009540430 Henry Cohn, 2024, needs more optimization.
6 462 0.778165257022 Henry Cohn, 2024, needs more optimization.
6 463 0.778189142286 Henry Cohn, 2024, needs more optimization.
6 464 0.778489557015 Henry Cohn, 2024, needs more optimization.
6 465 0.778711486135 Henry Cohn, 2024, needs more optimization.
6 466 0.778925230425 Henry Cohn, 2024, needs more optimization.
6 467 0.778979746482 Henry Cohn, 2024, needs more optimization.
6 468 0.779396460222 Henry Cohn, 2024, needs more optimization.
6 469 0.779560756746 Henry Cohn, 2024, needs more optimization.
6 470 0.779780910564 Henry Cohn, 2024, needs more optimization.
6 471 0.779896054611 Henry Cohn, 2024, needs more optimization.
6 472 0.780038293080 Henry Cohn, 2024, needs more optimization.
6 473 0.780171543918 Henry Cohn, 2024, needs more optimization.
6 474 0.780558857566 Henry Cohn, 2024, needs more optimization.
6 475 0.780574998598 Henry Cohn, 2024, needs more optimization.
6 476 0.780771765302 Henry Cohn, 2024, needs more optimization.
6 478 0.780947939746 Henry Cohn, 2024, needs more optimization.
6 479 0.781349633857 Henry Cohn, 2024, needs more optimization.
6 481 0.781726324258 Henry Cohn, 2024, needs more optimization.
6 482 0.781741947033 Henry Cohn, 2024, needs more optimization.
6 483 0.781982348349 Henry Cohn, 2024, needs more optimization.
6 485 0.782524290320 Henry Cohn, 2024, needs more optimization.
6 486 0.782581618334 Henry Cohn, 2024, needs more optimization.
6 487 0.782783290799 Henry Cohn, 2024, needs more optimization.
6 489 0.783015313663 Henry Cohn, 2024, needs more optimization.
6 490 0.783522672841 Henry Cohn, 2024, needs more optimization.
6 491 0.783732361437 Henry Cohn, 2024, needs more optimization.
6 493 0.783787835780 Henry Cohn, 2024, needs more optimization.
6 494 0.784025430368 Henry Cohn, 2024, needs more optimization.
6 495 0.784376711434 Henry Cohn, 2024, needs more optimization.
6 496 0.784586534841 Henry Cohn, 2024, needs more optimization.
6 497 0.784588806604 Henry Cohn, 2024, needs more optimization.
6 499 0.784707747423 Henry Cohn, 2024, needs more optimization.
6 500 0.784892746736 Henry Cohn, 2024, needs more optimization.
6 501 0.785128241298 Henry Cohn, 2024, needs more optimization.
6 503 0.785435622175 Henry Cohn, 2024, needs more optimization.
6 504 0.785794694945 Henry Cohn, 2024, needs more optimization.
6 505 0.785927349565 Henry Cohn, 2024, needs more optimization.
6 506 0.786407290796 Henry Cohn, 2024, needs more optimization.
6 507 0.786411278671 Henry Cohn, 2024, needs more optimization.
6 509 0.786513919006 Henry Cohn, 2024, needs more optimization.
6 510 0.786790552180 Henry Cohn, 2024, needs more optimization.
6 512 0.786833495928 Henry Cohn, 2024, needs more optimization.
6 513 0.787272027541 Henry Cohn, 2024, needs more optimization.
6 514 0.787450071394 Henry Cohn, 2024, needs more optimization.
6 516 0.787567057474 Henry Cohn, 2024, needs more optimization.
6 517 0.787776658723 Henry Cohn, 2024, needs more optimization.
6 518 0.788165586341 Henry Cohn, 2024, needs more optimization.
6 521 0.788328135631 Henry Cohn, 2024, needs more optimization.
6 522 0.788935899456 Henry Cohn, 2024, needs more optimization.
6 523 0.789042690069 Henry Cohn, 2024, needs more optimization.
6 525 0.789220941439 Henry Cohn, 2024, needs more optimization.
6 527 0.789300152202 Henry Cohn, 2024, needs more optimization.
6 528 0.789660081881 Henry Cohn, 2024, needs more optimization.
6 530 0.790032323896 Henry Cohn, 2024, needs more optimization.
6 531 0.790044213486 Henry Cohn, 2024, needs more optimization.
6 532 0.790318339039 Henry Cohn, 2024, needs more optimization.
6 533 0.790592404591 Henry Cohn, 2024, needs more optimization.
6 535 0.790617421219 Henry Cohn, 2024, needs more optimization.
6 536 0.791059013745 Henry Cohn, 2024, needs more optimization.
6 537 0.791255911617 Henry Cohn, 2024, needs more optimization.
6 538 0.791275934732 Henry Cohn, 2024, needs more optimization.
6 539 0.791425942755 Henry Cohn, 2024, needs more optimization.
6 540 0.791650394497 Henry Cohn, 2024, needs more optimization.
6 542 0.791768800007 Henry Cohn, 2024, needs more optimization.
6 543 0.792057339770 Henry Cohn, 2024, needs more optimization.
6 545 0.792354435253 Henry Cohn, 2024, needs more optimization.
6 546 0.792662820534 Henry Cohn, 2024, needs more optimization.
6 547 0.792756030515 Henry Cohn, 2024, needs more optimization.
6 548 0.792770879781 Henry Cohn, 2024, needs more optimization.
6 549 0.793036778341 Henry Cohn, 2024, needs more optimization.
6 550 0.793316066022 Henry Cohn, 2024, needs more optimization.
6 551 0.793326577761 Henry Cohn, 2024, needs more optimization.
6 553 0.793404782573 Henry Cohn, 2024, needs more optimization.
6 554 0.793752174481 Henry Cohn, 2024, needs more optimization.
6 555 0.793998545972 Henry Cohn, 2024, needs more optimization.
6 556 0.794006939769 Henry Cohn, 2024, needs more optimization.
6 558 0.794269661975 Henry Cohn, 2024, needs more optimization.
6 559 0.794611140739 Henry Cohn, 2024, needs more optimization.
6 560 0.794683647970 Henry Cohn, 2024, needs more optimization.
6 561 0.794838516374 Henry Cohn, 2024, needs more optimization.
6 563 0.795259924097 Henry Cohn, 2024, needs more optimization.
6 565 0.795380158724 Henry Cohn, 2024, needs more optimization.
6 566 0.795563780746 Henry Cohn, 2024, needs more optimization.
6 567 0.795617480958 Henry Cohn, 2024, needs more optimization.
6 568 0.795681791942 Henry Cohn, 2024, needs more optimization.
6 569 0.795883821257 Henry Cohn, 2024, needs more optimization.
6 570 0.796075509679 Henry Cohn, 2024, needs more optimization.
6 571 0.796384791296 Henry Cohn, 2024, needs more optimization.
6 572 0.796517572046 Henry Cohn, 2024, needs more optimization.
6 574 0.796719181603 Henry Cohn, 2024, needs more optimization.
6 576 0.796870926518 Henry Cohn, 2024, needs more optimization.
6 577 0.797254816465 Henry Cohn, 2024, needs more optimization.
6 578 0.797417937429 Henry Cohn, 2024, needs more optimization.
6 580 0.797583613782 Henry Cohn, 2024, needs more optimization.
6 581 0.797865682204 Henry Cohn, 2024, needs more optimization.
6 583 0.797923168282 Henry Cohn, 2024, needs more optimization.
6 584 0.798055440351 Henry Cohn, 2024, needs more optimization.
6 585 0.798219760589 Henry Cohn, 2024, needs more optimization.
6 586 0.798392606965 Henry Cohn, 2024, needs more optimization.
6 587 0.798497762280 Henry Cohn, 2024, needs more optimization.
6 588 0.798773944776 Henry Cohn, 2024, needs more optimization.
6 590 0.798783796601 Henry Cohn, 2024, needs more optimization.
6 591 0.799186611311 Henry Cohn, 2024, needs more optimization.
6 593 0.799279677702 Henry Cohn, 2024, needs more optimization.
6 594 0.799431353162 Henry Cohn, 2024, needs more optimization.
6 595 0.799749917541 Henry Cohn, 2024, needs more optimization.
6 596 0.799838882310 Henry Cohn, 2024, needs more optimization.
6 597 0.799973510033 Henry Cohn, 2024, needs more optimization.
6 599 0.800117480921 Henry Cohn, 2024, needs more optimization.
6 601 0.800378802385 Henry Cohn, 2024, needs more optimization.
6 602 0.800470557131 Henry Cohn, 2024, needs more optimization.
6 603 0.800810518656 Henry Cohn, 2024, needs more optimization.
6 604 0.801007265645 Henry Cohn, 2024, needs more optimization.
6 605 0.801047409160 Henry Cohn, 2024, needs more optimization.
6 606 0.801215777010 Henry Cohn, 2024, needs more optimization.
6 607 0.801330435984 Henry Cohn, 2024, needs more optimization.
6 608 0.801546585635 Henry Cohn, 2024, needs more optimization.
6 610 0.801558206675 Henry Cohn, 2024, needs more optimization.
6 611 0.801651597274 Henry Cohn, 2024, needs more optimization.
6 612 0.801905101705 Henry Cohn, 2024, needs more optimization.
6 613 0.802089915164 Henry Cohn, 2024, needs more optimization.
6 614 0.802273502070 Henry Cohn, 2024, needs more optimization.
6 615 0.802354542134 Henry Cohn, 2024, needs more optimization.
6 616 0.802442064726 Henry Cohn, 2024, needs more optimization.
6 617 0.802468490476 Henry Cohn, 2024, needs more optimization.
6 618 0.802581505669 Henry Cohn, 2024, needs more optimization.
6 619 0.802875465835 Henry Cohn, 2024, needs more optimization.
6 620 0.803058034461 Henry Cohn, 2024, needs more optimization.
6 622 0.803165761641 Henry Cohn, 2024, needs more optimization.
6 623 0.803437141332 Henry Cohn, 2024, needs more optimization.
6 624 0.803528991377 Henry Cohn, 2024, needs more optimization.
6 625 0.803533852398 Henry Cohn, 2024, needs more optimization.
6 626 0.803756110992 Henry Cohn, 2024, needs more optimization.
6 627 0.803830463261 Henry Cohn, 2024, needs more optimization.
6 628 0.804102157694 Henry Cohn, 2024, needs more optimization.
6 629 0.804169288734 Henry Cohn, 2024, needs more optimization.
6 630 0.804325055030 Henry Cohn, 2024, needs more optimization.
6 632 0.804448274058 Henry Cohn, 2024, needs more optimization.
6 633 0.804623382498 Henry Cohn, 2024, needs more optimization.
6 635 0.804733187955 Henry Cohn, 2024, needs more optimization.
6 637 0.804901371340 Henry Cohn, 2024, needs more optimization.
6 638 0.805189589547 Henry Cohn, 2024, needs more optimization.
6 640 0.805274739564 Henry Cohn, 2024, needs more optimization.
6 641 0.805410065187 Henry Cohn, 2024, needs more optimization.
6 643 0.805773239367 Henry Cohn, 2024, needs more optimization.
6 644 0.805939773655 Henry Cohn, 2024, needs more optimization.
6 646 0.806192571730 Henry Cohn, 2024, needs more optimization.
6 647 0.806230808156 Henry Cohn, 2024, needs more optimization.
6 648 0.806389195822 Henry Cohn, 2024, needs more optimization.
6 649 0.806417386260 Henry Cohn, 2024, needs more optimization.
6 650 0.806754705955 Henry Cohn, 2024, needs more optimization.
6 651 0.806817101024 Henry Cohn, 2024, needs more optimization.
6 652 0.806847407606 Henry Cohn, 2024, needs more optimization.
6 653 0.806929939766 Henry Cohn, 2024, needs more optimization.
6 654 0.807230953565 Henry Cohn, 2024, needs more optimization.
6 656 0.807265224351 Henry Cohn, 2024, needs more optimization.
6 657 0.807452344179 Henry Cohn, 2024, needs more optimization.
6 658 0.807696395481 Henry Cohn, 2024, needs more optimization.
6 659 0.807715558675 Henry Cohn, 2024, needs more optimization.
6 660 0.807789369190 Henry Cohn, 2024, needs more optimization.
6 662 0.807913156556 Henry Cohn, 2024, needs more optimization.
6 665 0.808271199857 Henry Cohn, 2024, needs more optimization.
6 667 0.808514318335 Henry Cohn, 2024, needs more optimization.
6 668 0.808711714740 Henry Cohn, 2024, needs more optimization.
6 669 0.808834105194 Henry Cohn, 2024, needs more optimization.
6 670 0.809115108237 Henry Cohn, 2024, needs more optimization.
6 671 0.809126717918 Henry Cohn, 2024, needs more optimization.
6 672 0.809284992426 Henry Cohn, 2024, needs more optimization.
6 675 0.809415599688 Henry Cohn, 2024, needs more optimization.
6 676 0.809573031769 Henry Cohn, 2024, needs more optimization.
6 678 0.809747988531 Henry Cohn, 2024, needs more optimization.
6 679 0.810077082354 Henry Cohn, 2024, needs more optimization.
6 680 0.810133597607 Henry Cohn, 2024, needs more optimization.
6 681 0.810245994111 Henry Cohn, 2024, needs more optimization.
6 683 0.810342730915 Henry Cohn, 2024, needs more optimization.
6 684 0.810416904386 Henry Cohn, 2024, needs more optimization.
6 685 0.810606598968 Henry Cohn, 2024, needs more optimization.
6 686 0.810693231691 Henry Cohn, 2024, needs more optimization.
6 687 0.810924662999 Henry Cohn, 2024, needs more optimization.
6 688 0.811016962104 Henry Cohn, 2024, needs more optimization.
6 689 0.811080031219 Henry Cohn, 2024, needs more optimization.
6 690 0.811348551582 Henry Cohn, 2024, needs more optimization.
6 692 0.811356845688 Henry Cohn, 2024, needs more optimization.
6 694 0.811626838940 Henry Cohn, 2024, needs more optimization.
6 695 0.811705970501 Henry Cohn, 2024, needs more optimization.
6 697 0.812037114176 Henry Cohn, 2024, needs more optimization.
6 698 0.812089400510 Henry Cohn, 2024, needs more optimization.
6 699 0.812244001250 Henry Cohn, 2024, needs more optimization.
6 701 0.812280691246 Henry Cohn, 2024, needs more optimization.
6 702 0.812387031987 Henry Cohn, 2024, needs more optimization.
6 704 0.812509666386 Henry Cohn, 2024, needs more optimization.
6 705 0.812887006452 Henry Cohn, 2024, needs more optimization.
6 706 0.812920534753 Henry Cohn, 2024, needs more optimization.
6 709 0.813176096715 Henry Cohn, 2024, needs more optimization.
6 712 0.813470223657 Henry Cohn, 2024, needs more optimization.
6 713 0.813718977001 Henry Cohn, 2024, needs more optimization.
6 716 0.813899222311 Henry Cohn, 2024, needs more optimization.
6 717 0.814026757759 Henry Cohn, 2024, needs more optimization.
6 718 0.814232994617 Henry Cohn, 2024, needs more optimization.
6 719 0.814416603044 Henry Cohn, 2024, needs more optimization.
6 720 0.814478984086 Henry Cohn, 2024, needs more optimization.
6 721 0.814493562162 Henry Cohn, 2024, needs more optimization.
6 722 0.814603783745 Henry Cohn, 2024, needs more optimization.
6 723 0.814625521037 Henry Cohn, 2024, needs more optimization.
6 724 0.814877077758 Henry Cohn, 2024, needs more optimization.
6 725 0.815086369043 Henry Cohn, 2024, needs more optimization.
6 726 0.815114321382 Henry Cohn, 2024, needs more optimization.
6 727 0.815117948024 Henry Cohn, 2024, needs more optimization.
6 728 0.815142356677 Henry Cohn, 2024, needs more optimization.
6 730 0.815435896549 Henry Cohn, 2024, needs more optimization.
6 732 0.815598150967 Henry Cohn, 2024, needs more optimization.
6 735 0.815881057025 Henry Cohn, 2024, needs more optimization.
6 740 0.816154514992 Henry Cohn, 2024, needs more optimization.
6 742 0.816582131472 Henry Cohn, 2024, needs more optimization.
6 743 0.816799937509 Henry Cohn, 2024, needs more optimization.
6 745 0.816990733769 Henry Cohn, 2024, needs more optimization.
6 746 0.817138526527 Henry Cohn, 2024, needs more optimization.
6 747 0.817339855476 Henry Cohn, 2024, needs more optimization.
6 748 0.817386221644 Henry Cohn, 2024, needs more optimization.
6 750 0.817500968152 Henry Cohn, 2024, needs more optimization.
6 751 0.817562863996 Henry Cohn, 2024, needs more optimization.
6 752 0.817816752730 Henry Cohn, 2024, needs more optimization.
6 754 0.817824440950 Henry Cohn, 2024, needs more optimization.
6 755 0.817951987228 Henry Cohn, 2024, needs more optimization.
6 756 0.818045427870 Henry Cohn, 2024, needs more optimization.
6 757 0.818162675825 Henry Cohn, 2024, needs more optimization.
6 758 0.818336569538 Henry Cohn, 2024, needs more optimization.
6 760 0.818467874351 Henry Cohn, 2024, needs more optimization.
6 763 0.818632642432 Henry Cohn, 2024, needs more optimization.
6 764 0.818910698301 Henry Cohn, 2024, needs more optimization.
6 766 0.819074683469 Henry Cohn, 2024, needs more optimization.
6 768 0.819086134261 Henry Cohn, 2024, needs more optimization.
6 769 0.819469432793 Henry Cohn, 2024, needs more optimization.
6 771 0.819540326258 Henry Cohn, 2024, needs more optimization.
6 772 0.819681198782 Henry Cohn, 2024, needs more optimization.
6 773 0.819783993026 Henry Cohn, 2024, needs more optimization.
6 774 0.819908319943 Henry Cohn, 2024, needs more optimization.
6 775 0.819943874478 Henry Cohn, 2024, needs more optimization.
6 776 0.819977070685 Henry Cohn, 2024, needs more optimization.
6 778 0.820087469567 Henry Cohn, 2024, needs more optimization.
6 779 0.820227106914 Henry Cohn, 2024, needs more optimization.
6 780 0.820543769091 Henry Cohn, 2024, needs more optimization.
6 781 0.820553663036 Henry Cohn, 2024, needs more optimization.
6 782 0.820573409469 Henry Cohn, 2024, needs more optimization.
6 784 0.820636659913 Henry Cohn, 2024, needs more optimization.
6 786 0.820914123814 Henry Cohn, 2024, needs more optimization.
6 788 0.821119808351 Henry Cohn, 2024, needs more optimization.
6 789 0.821244496475 Henry Cohn, 2024, needs more optimization.
6 790 0.821259271427 Henry Cohn, 2024, needs more optimization.
6 793 0.821484309876 Henry Cohn, 2024, needs more optimization.
6 794 0.821680842350 Henry Cohn, 2024, needs more optimization.
6 795 0.821808190634 Henry Cohn, 2024, needs more optimization.
6 796 0.821835981475 Henry Cohn, 2024, needs more optimization.
6 797 0.821908259665 Henry Cohn, 2024, needs more optimization.
6 798 0.822038484952 Henry Cohn, 2024, needs more optimization.
6 799 0.822127424056 Henry Cohn, 2024, needs more optimization.
6 800 0.822243653565 Henry Cohn, 2024, needs more optimization.
6 801 0.822337579624 Henry Cohn, 2024, needs more optimization.
6 805 0.822447873393 Henry Cohn, 2024, needs more optimization.
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6 808 0.822817696143 Henry Cohn, 2024, needs more optimization.
6 812 0.823023655260 Henry Cohn, 2024, needs more optimization.
6 814 0.823379111105 Henry Cohn, 2024, needs more optimization.
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6 819 0.823849067181 Henry Cohn, 2024, needs more optimization.
6 820 0.823982730613 Henry Cohn, 2024, needs more optimization.
6 822 0.824104399397 Henry Cohn, 2024, needs more optimization.
6 823 0.824149617317 Henry Cohn, 2024, needs more optimization.
6 825 0.824320736304 Henry Cohn, 2024, needs more optimization.
6 826 0.824494116905 Henry Cohn, 2024, needs more optimization.
6 828 0.824623964069 Henry Cohn, 2024, needs more optimization.
6 830 0.824818002101 Henry Cohn, 2024, needs more optimization.
6 831 0.824881745988 Henry Cohn, 2024, needs more optimization.
6 832 0.824928977667 Henry Cohn, 2024, needs more optimization.
6 833 0.824948641172 Henry Cohn, 2024, needs more optimization.
6 835 0.825197502192 Henry Cohn, 2024, needs more optimization.
6 836 0.825383158132 Henry Cohn, 2024, needs more optimization.
6 837 0.825462202860 Henry Cohn, 2024, needs more optimization.
6 839 0.825548458727 Henry Cohn, 2024, needs more optimization.
6 840 0.825830816655 Henry Cohn, 2024, needs more optimization.
6 841 0.825845868678 Henry Cohn, 2024, needs more optimization.
6 842 0.825943499306 Henry Cohn, 2024, needs more optimization.
6 843 0.825973861433 Henry Cohn, 2024, needs more optimization.
6 844 0.826061089692 Henry Cohn, 2024, needs more optimization.
6 846 0.826149668626 Henry Cohn, 2024, needs more optimization.
6 847 0.826215463539 Henry Cohn, 2024, needs more optimization.
6 848 0.826427648852 Henry Cohn, 2024, needs more optimization.
6 849 0.826437561333 Henry Cohn, 2024, needs more optimization.
6 850 0.826484357303 Henry Cohn, 2024, needs more optimization.
6 852 0.826596210045 Henry Cohn, 2024, needs more optimization.
6 853 0.826692100376 Henry Cohn, 2024, needs more optimization.
6 854 0.826870697291 Henry Cohn, 2024, needs more optimization.
6 855 0.826954459622 Henry Cohn, 2024, needs more optimization.
6 856 0.827010972640 Henry Cohn, 2024, needs more optimization.
6 857 0.827108696752 Henry Cohn, 2024, needs more optimization.
6 858 0.827150513933 Henry Cohn, 2024, needs more optimization.
6 859 0.827209182078 Henry Cohn, 2024, needs more optimization.
6 860 0.827294523925 Henry Cohn, 2024, needs more optimization.
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6 864 0.827585678376 Henry Cohn, 2024, needs more optimization.
6 866 0.827746415957 Henry Cohn, 2024, needs more optimization.
6 867 0.827834078859 Henry Cohn, 2024, needs more optimization.
6 869 0.828027127434 Henry Cohn, 2024, needs more optimization.
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6 874 0.828514684271 Henry Cohn, 2024, needs more optimization.
6 875 0.828567307860 Henry Cohn, 2024, needs more optimization.
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6 878 0.828725865418 Henry Cohn, 2024, needs more optimization.
6 880 0.828794180424 Henry Cohn, 2024, needs more optimization.
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6 883 0.829045635367 Henry Cohn, 2024, needs more optimization.
6 884 0.829312010687 Henry Cohn, 2024, needs more optimization.
6 885 0.829337515925 Henry Cohn, 2024, needs more optimization.
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6 898 0.830322018300 Henry Cohn, 2024, needs more optimization.
6 899 0.830355791946 Henry Cohn, 2024, needs more optimization.
6 901 0.830388269708 Henry Cohn, 2024, needs more optimization.
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6 918 0.831667787882 Henry Cohn, 2024, needs more optimization.
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6 923 0.832122655403 Henry Cohn, 2024, needs more optimization.
6 924 0.832222604666 Henry Cohn, 2024, needs more optimization.
6 925 0.832286947776 Henry Cohn, 2024, needs more optimization.
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6 927 0.832383771671 Henry Cohn, 2024, needs more optimization.
6 928 0.832519540435 Henry Cohn, 2024, needs more optimization.
6 930 0.832613438935 Henry Cohn, 2024, needs more optimization.
6 931 0.832755568349 Henry Cohn, 2024, needs more optimization.
6 932 0.832767674850 Henry Cohn, 2024, needs more optimization.
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6 934 0.832909963990 Henry Cohn, 2024, needs more optimization.
6 935 0.832917737478 Henry Cohn, 2024, needs more optimization.
6 936 0.832950521217 Henry Cohn, 2024, needs more optimization.
6 937 0.833049788401 Henry Cohn, 2024, needs more optimization.
6 939 0.833293167428 Henry Cohn, 2024, 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 0.836842330777 Henry Cohn, 2024, needs more optimization.
6 992 0.836972901917 Henry Cohn, 2024, needs more optimization.
6 994 0.837010741893 Henry Cohn, 2024, needs more optimization.
6 995 0.837031225550 Henry Cohn, 2024, needs more optimization.
6 996 0.837178926110 Henry Cohn, 2024, needs more optimization.
6 997 0.837279549211 Henry Cohn, 2024, needs more optimization.
6 998 0.837287551904 Henry Cohn, 2024, needs more optimization.
6 999 0.837385525179 Henry Cohn, 2024, needs more optimization.
6 1002 0.837510069244 Henry Cohn, 2024, needs more optimization.
6 1003 0.837726162212 Henry Cohn, 2024, needs more optimization.
6 1004 0.837747524647 Henry Cohn, 2024, needs more optimization.
6 1006 0.837791935654 Henry Cohn, 2024, needs more optimization.
6 1007 0.837858119397 Henry Cohn, 2024, needs more optimization.
6 1008 0.838059782197 Henry Cohn, 2024, needs more optimization.
6 1009 0.838129767394 Henry Cohn, 2024, needs more optimization.
6 1010 0.838214052131 Henry Cohn, 2024, needs more optimization.
6 1013 0.838224914483 Henry Cohn, 2024, needs more optimization.
6 1015 0.838375231790 Henry Cohn, 2024, needs more optimization.
6 1016 0.838425816244 Henry Cohn, 2024, needs more optimization.
6 1018 0.838487873629 Henry Cohn, 2024, needs more optimization.
6 1019 0.838714883491 Henry Cohn, 2024, needs more optimization.
6 1020 0.838745985229 Henry Cohn, 2024, needs more optimization.
6 1021 0.838818648101 Henry Cohn, 2024, needs more optimization.
6 1024 0.838887649318 Henry Cohn, 2024, 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 0.248933041753 H. Cohn, Small spherical and projective codes, data set, updated 2024, 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 0.310458216649 Henry Cohn, 2023.
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 0.329085633548 Henry Cohn, 2023.
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 0.333300834322 Henry Cohn, 2025.
7 46 0.333328638256 Henry Cohn, 2025.
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 0.389652998168 Henry Cohn, 2024.
7 58 0.393749423280 Henry Cohn, 2023.
7 59 0.403218749805 Henry Cohn, 2024.
7 60 0.407983549048 Henry Cohn, 2023.
7 61 0.412356098716 Henry Cohn, 2024.
7 62 0.415090060680 Henry Cohn, 2023.
7 63 0.415615281080 Henry Cohn, 2025.
7 64 0.420205850438 Henry Cohn, 2024.
7 67 0.421258543571 Henry Cohn, 2024.
622⁢x3−771⁢x2+288⁢x−31
7 68 0.428438543151 Henry Cohn, 2024.
7 78 0.428571428572 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001, Appendix D.7.9. There seems to be an error in Appendix D.7: it lists the code as having 80 points, but the construction describes only 78 points.
7⁢x−3
7 79 0.453278412444 Henry Cohn, 2024.
7 80 0.453887992064 Henry Cohn, 2024.
7 81 0.459721836628 Henry Cohn, 2024.
7 82 0.461281986472 Henry Cohn, 2024.
7 83 0.461669205843 Henry Cohn, 2024.
7 84 0.465073032663 Henry Cohn, 2025.
7 86 0.468426723770 Henry Cohn, 2024.
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 0.486324406204 Henry Cohn, 2025, needs more optimization.
7 92 0.486538940995 Henry Cohn, 2025, needs more optimization.
7 93 0.487115740749 Henry Cohn, 2025, needs more optimization.
7 94 0.487134413911 Henry Cohn, 2025, needs more optimization.
7 95 0.487417621542 Henry Cohn, 2025, needs more optimization.
7 96 0.489128966703 Henry Cohn, 2025.
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 0.511248407917 Henry Cohn, 2023.
1875⁢x9−27025⁢x8−9900⁢x7+10500⁢x6+14418⁢x5+4698⁢x4−3564⁢x3−1404⁢x2+243⁢x−81
7 128 0.518389380677 Henry Cohn, 2025.
7 129 0.519163695355 Henry Cohn, 2025.
7 130 0.519163776671 Henry Cohn, 2025, needs more optimization.
7 134 0.519751518195 Henry Cohn, 2024.
7 135 0.520084944184 Henry Cohn, 2025.
7 136 0.520104626378 Henry Cohn, 2024, needs more optimization.
7 137 0.520112926332 Henry Cohn, 2024, needs more optimization.
7 138 0.527218738805 Henry Cohn, 2025.
7 139 0.531666456750 Henry Cohn, 2024, needs more optimization.
7 140 0.531667726797 Henry Cohn, 2024, needs more optimization.
7 142 0.531823100330 Henry Cohn, 2024.
7 143 0.532391622875 Henry Cohn, 2025.
7 144 0.532532803692 Henry Cohn, 2024.
7 145 0.532883690322 Henry Cohn, 2024.
7 146 0.533294143823 Henry Cohn, 2025.
7 147 0.533479772596 Henry Cohn, 2024.
7 148 0.534209256490 Henry Cohn, 2023.
49⁢x4−10⁢x2−4⁢x+1
7 151 0.547644839664 Henry Cohn, 2024.
7 152 0.548216963141 Henry Cohn, 2024, needs more optimization.
7 153 0.555355872921 Henry Cohn, 2024, needs more optimization.
7 154 0.555459550087 Henry Cohn, 2024, needs more optimization.
7 155 0.557657983960 Henry Cohn, 2024, needs more optimization.
7 156 0.558984457904 Henry Cohn, 2024, needs more optimization.
7 157 0.559583705905 Henry Cohn, 2024, needs more optimization.
7 158 0.560493112032 Henry Cohn, 2024, needs more optimization.
7 159 0.561804622283 Henry Cohn, 2024, needs more optimization.
7 160 0.562359030153 Henry Cohn, 2024, needs more optimization.
7 161 0.562827007450 Henry Cohn, 2024, needs more optimization.
7 162 0.563634632161 Henry Cohn, 2024, needs more optimization.
7 163 0.565644204894 Henry Cohn, 2025, needs more optimization.
7 164 0.566152767933 Henry Cohn, 2024, needs more optimization.
7 165 0.566369193581 Henry Cohn, 2024, needs more optimization.
7 166 0.567452350562 Henry Cohn, 2024, needs more optimization.
7 167 0.568184743291 Henry Cohn, 2024, needs more optimization.
7 168 0.568219738951 Henry Cohn, 2024, needs more optimization.
7 169 0.569945344808 Henry Cohn, 2024, needs more optimization.
7 170 0.570018008784 Henry Cohn, 2024, needs more optimization.
7 171 0.570426139136 Henry Cohn, 2024, needs more optimization.
7 172 0.570484508469 Henry Cohn, 2024, needs more optimization.
7 173 0.570491186346 Henry Cohn, 2024, needs more optimization.
7 174 0.571646493655 Henry Cohn, 2024, needs more optimization.
7 175 0.571964146780 Henry Cohn, 2024, needs more optimization.
7 176 0.571975305781 Henry Cohn, 2024, needs more optimization.
7 177 0.572133679517 Henry Cohn, 2024, needs more optimization.
7 178 0.572352072992 Henry Cohn, 2024, needs more optimization.
7 179 0.572419645219 Henry Cohn, 2024, needs more optimization.
7 180 0.572866503409 Henry Cohn, 2024, needs more optimization.
7 181 0.573146880912 Henry Cohn, 2024, 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 0.589247262696 Henry Cohn, 2024, needs more optimization.
7 184 0.590395029876 Henry Cohn, 2024, needs more optimization.
7 185 0.592031258395 Henry Cohn, 2024, needs more optimization.
7 186 0.592738680493 Henry Cohn, 2024, needs more optimization.
7 187 0.594039666475 Henry Cohn, 2024, needs more optimization.
7 188 0.594044098991 Henry Cohn, 2023, needs more optimization.
7 189 0.594975255997 Henry Cohn, 2024, needs more optimization.
7 190 0.594975390242 Henry Cohn, 2024, needs more optimization.
7 191 0.594996705698 Henry Cohn, 2024, needs more optimization.
7 192 0.596206334481 Henry Cohn, 2024, needs more optimization.
7 193 0.599330079987 Henry Cohn, 2024, 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 0.603939282844 Henry Cohn, 2024, needs more optimization.
7 198 0.604006862944 Henry Cohn, 2024, 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 0.607821295375 Henry Cohn, 2024, needs more optimization.
7 202 0.609205391056 Henry Cohn, 2024, needs more optimization.
7 203 0.609371850932 Henry Cohn, 2024, 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 0.616440614340 Henry Cohn, 2024, needs more optimization.
7 213 0.617073701156 Henry Cohn, 2024, needs more optimization.
7 214 0.618555878917 Henry Cohn, 2024, needs more optimization.
7 215 0.619475011483 Henry Cohn, 2024, needs more optimization.
7 216 0.619599983206 Henry Cohn, 2024, needs more optimization.
7 217 0.620628900569 Henry Cohn, 2024, needs more optimization.
7 218 0.621368072363 Henry Cohn, 2024, needs more optimization.
7 219 0.621976267786 Henry Cohn, 2024, 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 0.624615364020 Henry Cohn, 2024, needs more optimization.
7 223 0.625218440392 Henry Cohn, 2024, needs more optimization.
7 224 0.625389348023 Henry Cohn, 2024, needs more optimization.
7 225 0.625872966956 Henry Cohn, 2024, needs more optimization.
7 226 0.627448261170 Henry Cohn, 2024, needs more optimization.
7 227 0.628342740769 Henry Cohn, 2024, needs more optimization.
7 228 0.628556042731 Henry Cohn, 2024, needs more optimization.
7 229 0.629525364974 Henry Cohn, 2024, 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 0.633282013602 Henry Cohn, 2024, needs more optimization.
7 236 0.633943127321 Henry Cohn, 2024, needs more optimization.
7 237 0.634380828579 Henry Cohn, 2024, 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 0.638594592401 Henry Cohn, 2024, needs more optimization.
7 246 0.638787946080 Henry Cohn, 2024, needs more optimization.
7 247 0.639353744539 Henry Cohn, 2024, needs more optimization.
7 248 0.640032835036 Henry Cohn, 2024, needs more optimization.
7 249 0.640412938510 Henry Cohn, 2024, needs more optimization.
7 250 0.640989667764 Henry Cohn, 2024, needs more optimization.
7 251 0.641172114031 Henry Cohn, 2024, needs more optimization.
7 252 0.641660493863 Henry Cohn, 2024, needs more optimization.
7 253 0.641883851623 Henry Cohn, 2024, needs more optimization.
7 254 0.642966537938 Henry Cohn, 2024, needs more optimization.
7 255 0.643277334366 Henry Cohn, 2024, needs more optimization.
7 256 0.643616294186 Henry Cohn, 2024, needs more optimization.
7 257 0.644984904266 Henry Cohn, 2024, needs more optimization.
7 258 0.645750633121 Henry Cohn, 2024, needs more optimization.
7 259 0.646245885471 Henry Cohn, 2024, needs more optimization.
7 260 0.646357884026 Henry Cohn, 2024, needs more optimization.
7 261 0.646805640627 Henry Cohn, 2024, needs more optimization.
7 262 0.647526347761 Henry Cohn, 2024, needs more optimization.
7 263 0.647868215289 Henry Cohn, 2024, needs more optimization.
7 264 0.648270824677 Henry Cohn, 2024, needs more optimization.
7 265 0.648896862550 Henry Cohn, 2024, needs more optimization.
7 266 0.649113231054 Henry Cohn, 2024, needs more optimization.
7 267 0.649805118030 Henry Cohn, 2024, needs more optimization.
7 268 0.650284413398 Henry Cohn, 2024, needs more optimization.
7 269 0.650630270583 Henry Cohn, 2024, needs more optimization.
7 270 0.651193710334 Henry Cohn, 2024, needs more optimization.
7 271 0.651442013421 Henry Cohn, 2024, needs more optimization.
7 272 0.651996401436 Henry Cohn, 2024, needs more optimization.
7 273 0.652344839985 Henry Cohn, 2024, needs more optimization.
7 274 0.652790449452 Henry Cohn, 2024, needs more optimization.
7 275 0.653203189273 Henry Cohn, 2024, needs more optimization.
7 276 0.653760033807 Henry Cohn, 2024, needs more optimization.
7 277 0.654176748996 Henry Cohn, 2024, needs more optimization.
7 278 0.654485132392 Henry Cohn, 2024, needs more optimization.
7 279 0.654932759344 Henry Cohn, 2024, needs more optimization.
7 280 0.655565550230 Henry Cohn, 2024, needs more optimization.
7 281 0.656040622698 Henry Cohn, 2024, needs more optimization.
7 282 0.656157037096 Henry Cohn, 2024, needs more optimization.
7 284 0.657116575229 Henry Cohn, 2024, needs more optimization.
7 285 0.657474275960 Henry Cohn, 2024, needs more optimization.
7 286 0.658263625477 Henry Cohn, 2024, needs more optimization.
7 287 0.658592809387 Henry Cohn, 2024, needs more optimization.
7 288 0.658924583777 Henry Cohn, 2024, needs more optimization.
7 289 0.659455202756 Henry Cohn, 2024, needs more optimization.
7 290 0.659729082178 Henry Cohn, 2024, needs more optimization.
7 291 0.660259144241 Henry Cohn, 2024, needs more optimization.
7 292 0.660702306732 Henry Cohn, 2024, needs more optimization.
7 293 0.660832005667 Henry Cohn, 2024, needs more optimization.
7 296 0.661782404071 Henry Cohn, 2024, needs more optimization.
7 297 0.662573822494 Henry Cohn, 2024, needs more optimization.
7 298 0.662654553316 Henry Cohn, 2024, needs more optimization.
7 299 0.663116905420 Henry Cohn, 2024, needs more optimization.
7 300 0.663737653209 Henry Cohn, 2024, needs more optimization.
7 301 0.664096575358 Henry Cohn, 2024, needs more optimization.
7 302 0.664430719434 Henry Cohn, 2024, needs more optimization.
7 303 0.664784684586 Henry Cohn, 2024, needs more optimization.
7 304 0.665314197837 Henry Cohn, 2024, needs more optimization.
7 306 0.665713515109 Henry Cohn, 2024, needs more optimization.
7 307 0.666248705545 Henry Cohn, 2024, needs more optimization.
7 308 0.666556538352 Henry Cohn, 2024, 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 0.683598699275 Henry Cohn, 2024, needs more optimization.
7 361 0.684115397972 Henry Cohn, 2024, needs more optimization.
7 362 0.684305135925 Henry Cohn, 2024, needs more optimization.
7 363 0.684569965607 Henry Cohn, 2024, needs more optimization.
7 364 0.685163900542 Henry Cohn, 2024, needs more optimization.
7 365 0.685560952235 Henry Cohn, 2024, needs more optimization.
7 366 0.685994848503 Henry Cohn, 2024, needs more optimization.
7 367 0.686055499852 Henry Cohn, 2024, needs more optimization.
7 369 0.686305682812 Henry Cohn, 2024, needs more optimization.
7 370 0.686656724310 Henry Cohn, 2024, needs more optimization.
7 371 0.686972747399 Henry Cohn, 2024, needs more optimization.
7 372 0.687130932401 Henry Cohn, 2024, needs more optimization.
7 373 0.687491157587 Henry Cohn, 2024, needs more optimization.
7 374 0.688123657407 Henry Cohn, 2024, needs more optimization.
7 375 0.688183357601 Henry Cohn, 2024, needs more optimization.
7 376 0.688641461208 Henry Cohn, 2024, needs more optimization.
7 377 0.688810477266 Henry Cohn, 2024, needs more optimization.
7 378 0.689267551188 Henry Cohn, 2024, needs more optimization.
7 379 0.689288601793 Henry Cohn, 2024, needs more optimization.
7 380 0.689622575065 Henry Cohn, 2024, needs more optimization.
7 381 0.689895992272 Henry Cohn, 2024, needs more optimization.
7 383 0.690251954521 Henry Cohn, 2024, needs more optimization.
7 384 0.690573345805 Henry Cohn, 2024, needs more optimization.
7 385 0.690791965235 Henry Cohn, 2024, needs more optimization.
7 386 0.691289464766 Henry Cohn, 2024, needs more optimization.
7 387 0.691762326516 Henry Cohn, 2024, needs more optimization.
7 388 0.691766837832 Henry Cohn, 2024, needs more optimization.
7 389 0.692205687043 Henry Cohn, 2024, needs more optimization.
7 390 0.692577800851 Henry Cohn, 2024, needs more optimization.
7 391 0.692626676743 Henry Cohn, 2024, needs more optimization.
7 392 0.692835486146 Henry Cohn, 2024, needs more optimization.
7 393 0.693377100541 Henry Cohn, 2024, needs more optimization.
7 394 0.693408898188 Henry Cohn, 2024, needs more optimization.
7 395 0.693744655004 Henry Cohn, 2024, needs more optimization.
7 396 0.693943596071 Henry Cohn, 2024, needs more optimization.
7 397 0.694256718671 Henry Cohn, 2024, needs more optimization.
7 398 0.694527180018 Henry Cohn, 2024, needs more optimization.
7 399 0.694849658274 Henry Cohn, 2024, needs more optimization.
7 400 0.695030695163 Henry Cohn, 2024, needs more optimization.
7 401 0.695436644475 Henry Cohn, 2024, needs more optimization.
7 402 0.695463468893 Henry Cohn, 2024, needs more optimization.
7 404 0.695839557726 Henry Cohn, 2024, needs more optimization.
7 405 0.696517210960 Henry Cohn, 2024, needs more optimization.
7 406 0.696677896359 Henry Cohn, 2024, needs more optimization.
7 407 0.696810094521 Henry Cohn, 2024, needs more optimization.
7 408 0.697034837518 Henry Cohn, 2024, needs more optimization.
7 409 0.697356553628 Henry Cohn, 2024, needs more optimization.
7 410 0.697362696546 Henry Cohn, 2024, needs more optimization.
7 411 0.697666703937 Henry Cohn, 2024, needs more optimization.
7 412 0.698143657897 Henry Cohn, 2024, needs more optimization.
7 413 0.698593622217 Henry Cohn, 2024, needs more optimization.
7 415 0.698806502130 Henry Cohn, 2024, needs more optimization.
7 416 0.699398216050 Henry Cohn, 2024, needs more optimization.
7 417 0.699524321582 Henry Cohn, 2024, needs more optimization.
7 418 0.699576314773 Henry Cohn, 2024, needs more optimization.
7 419 0.699931299472 Henry Cohn, 2024, needs more optimization.
7 420 0.700085163682 Henry Cohn, 2024, needs more optimization.
7 421 0.700247682761 Henry Cohn, 2024, needs more optimization.
7 422 0.700597612285 Henry Cohn, 2024, needs more optimization.
7 423 0.700793778789 Henry Cohn, 2024, needs more optimization.
7 424 0.701176796581 Henry Cohn, 2024, needs more optimization.
7 426 0.701379781075 Henry Cohn, 2024, needs more optimization.
7 427 0.701794294830 Henry Cohn, 2024, needs more optimization.
7 428 0.702176824141 Henry Cohn, 2024, needs more optimization.
7 429 0.702294591192 Henry Cohn, 2024, needs more optimization.
7 430 0.702569801664 Henry Cohn, 2024, needs more optimization.
7 431 0.702642744454 Henry Cohn, 2024, needs more optimization.
7 432 0.703091014993 Henry Cohn, 2024, needs more optimization.
7 433 0.703359481859 Henry Cohn, 2024, needs more optimization.
7 434 0.703493752289 Henry Cohn, 2024, needs more optimization.
7 435 0.703830779391 Henry Cohn, 2024, needs more optimization.
7 436 0.703836340269 Henry Cohn, 2024, needs more optimization.
7 437 0.704187761756 Henry Cohn, 2024, needs more optimization.
7 438 0.704483564225 Henry Cohn, 2024, needs more optimization.
7 440 0.704568397316 Henry Cohn, 2024, needs more optimization.
7 441 0.705056623324 Henry Cohn, 2024, needs more optimization.
7 442 0.705278871354 Henry Cohn, 2024, needs more optimization.
7 443 0.705348458225 Henry Cohn, 2024, needs more optimization.
7 444 0.705764032805 Henry Cohn, 2024, needs more optimization.
7 445 0.706061072523 Henry Cohn, 2024, needs more optimization.
7 446 0.706401653173 Henry Cohn, 2024, needs more optimization.
7 447 0.706422067659 Henry Cohn, 2024, needs more optimization.
7 448 0.706585010245 Henry Cohn, 2024, needs more optimization.
7 449 0.706988355871 Henry Cohn, 2024, needs more optimization.
7 450 0.707025523073 Henry Cohn, 2024, needs more optimization.
7 451 0.707131608392 Henry Cohn, 2024, needs more optimization.
7 452 0.707612942218 Henry Cohn, 2024, needs more optimization.
7 453 0.707806549057 Henry Cohn, 2024, needs more optimization.
7 455 0.708151871564 Henry Cohn, 2024, needs more optimization.
7 456 0.708322631803 Henry Cohn, 2024, needs more optimization.
7 457 0.708599972317 Henry Cohn, 2024, needs more optimization.
7 458 0.708948671528 Henry Cohn, 2024, needs more optimization.
7 459 0.709114128449 Henry Cohn, 2024, needs more optimization.
7 460 0.709283746909 Henry Cohn, 2024, needs more optimization.
7 462 0.709487504460 Henry Cohn, 2024, needs more optimization.
7 463 0.710200865686 Henry Cohn, 2024, needs more optimization.
7 464 0.710349500170 Henry Cohn, 2024, needs more optimization.
7 465 0.710359694081 Henry Cohn, 2024, needs more optimization.
7 466 0.710666640310 Henry Cohn, 2024, needs more optimization.
7 467 0.710806256387 Henry Cohn, 2024, needs more optimization.
7 468 0.711067399827 Henry Cohn, 2024, needs more optimization.
7 470 0.711430014246 Henry Cohn, 2024, needs more optimization.
7 471 0.711595744939 Henry Cohn, 2024, needs more optimization.
7 472 0.711697362262 Henry Cohn, 2024, needs more optimization.
7 473 0.711947461841 Henry Cohn, 2024, needs more optimization.
7 474 0.712318924458 Henry Cohn, 2024, needs more optimization.
7 475 0.712459275022 Henry Cohn, 2024, needs more optimization.
7 476 0.712748467419 Henry Cohn, 2024, needs more optimization.
7 477 0.713023754860 Henry Cohn, 2024, needs more optimization.
7 478 0.713074394621 Henry Cohn, 2024, needs more optimization.
7 479 0.713269045236 Henry Cohn, 2024, needs more optimization.
7 480 0.713661215479 Henry Cohn, 2024, needs more optimization.
7 481 0.713700184386 Henry Cohn, 2024, needs more optimization.
7 482 0.714149742898 Henry Cohn, 2024, needs more optimization.
7 483 0.714170594256 Henry Cohn, 2024, 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 0.739292715971 Henry Cohn, 2024, needs more optimization.
7 634 0.739508445070 Henry Cohn, 2024, needs more optimization.
7 635 0.739523076449 Henry Cohn, 2024, needs more optimization.
7 636 0.739677289469 Henry Cohn, 2024, needs more optimization.
7 637 0.739915434163 Henry Cohn, 2024, needs more optimization.
7 638 0.739964201719 Henry Cohn, 2024, needs more optimization.
7 639 0.740061428104 Henry Cohn, 2024, needs more optimization.
7 640 0.740116617230 Henry Cohn, 2024, needs more optimization.
7 641 0.740281042659 Henry Cohn, 2024, needs more optimization.
7 642 0.740674814577 Henry Cohn, 2024, needs more optimization.
7 643 0.740732436213 Henry Cohn, 2024, needs more optimization.
7 644 0.740834029819 Henry Cohn, 2024, needs more optimization.
7 645 0.740997000264 Henry Cohn, 2024, needs more optimization.
7 646 0.741163877533 Henry Cohn, 2024, needs more optimization.
7 647 0.741305305665 Henry Cohn, 2024, needs more optimization.
7 650 0.741369174358 Henry Cohn, 2024, needs more optimization.
7 651 0.741498078951 Henry Cohn, 2024, needs more optimization.
7 652 0.741764283454 Henry Cohn, 2024, needs more optimization.
7 653 0.741972533339 Henry Cohn, 2024, needs more optimization.
7 654 0.742141008208 Henry Cohn, 2024, needs more optimization.
7 657 0.742420901077 Henry Cohn, 2024, needs more optimization.
7 658 0.742833475825 Henry Cohn, 2024, needs more optimization.
7 659 0.742837064094 Henry Cohn, 2024, needs more optimization.
7 660 0.743187659223 Henry Cohn, 2024, needs more optimization.
7 662 0.743191927054 Henry Cohn, 2024, needs more optimization.
7 664 0.743326634875 Henry Cohn, 2024, needs more optimization.
7 665 0.743524219734 Henry Cohn, 2024, needs more optimization.
7 666 0.743574352274 Henry Cohn, 2024, needs more optimization.
7 668 0.743779619515 Henry Cohn, 2024, needs more optimization.
7 669 0.744037585104 Henry Cohn, 2024, needs more optimization.
7 670 0.744203422426 Henry Cohn, 2024, needs more optimization.
7 671 0.744394648865 Henry Cohn, 2024, needs more optimization.
7 673 0.744647066886 Henry Cohn, 2024, needs more optimization.
7 675 0.744683946888 Henry Cohn, 2024, needs more optimization.
7 677 0.745148827678 Henry Cohn, 2024, needs more optimization.
7 678 0.745291923912 Henry Cohn, 2024, needs more optimization.
7 679 0.745385219453 Henry Cohn, 2024, needs more optimization.
7 680 0.745460450784 Henry Cohn, 2024, needs more optimization.
7 681 0.745796392353 Henry Cohn, 2024, needs more optimization.
7 683 0.745923435043 Henry Cohn, 2024, needs more optimization.
7 684 0.746000097978 Henry Cohn, 2024, needs more optimization.
7 685 0.746158289700 Henry Cohn, 2024, needs more optimization.
7 686 0.746319371766 Henry Cohn, 2024, needs more optimization.
7 687 0.746464406132 Henry Cohn, 2024, needs more optimization.
7 689 0.746603310606 Henry Cohn, 2024, needs more optimization.
7 690 0.746897138407 Henry Cohn, 2024, needs more optimization.
7 691 0.747082299137 Henry Cohn, 2024, needs more optimization.
7 692 0.747135610954 Henry Cohn, 2024, needs more optimization.
7 693 0.747211598939 Henry Cohn, 2024, needs more optimization.
7 694 0.747300445156 Henry Cohn, 2024, needs more optimization.
7 695 0.747416641959 Henry Cohn, 2024, needs more optimization.
7 696 0.747519376787 Henry Cohn, 2024, needs more optimization.
7 697 0.747758205333 Henry Cohn, 2024, needs more optimization.
7 698 0.747810652054 Henry Cohn, 2024, needs more optimization.
7 699 0.747934317800 Henry Cohn, 2024, needs more optimization.
7 700 0.747974463303 Henry Cohn, 2024, needs more optimization.
7 701 0.748091038537 Henry Cohn, 2024, needs more optimization.
7 702 0.748172200576 Henry Cohn, 2024, needs more optimization.
7 704 0.748459552018 Henry Cohn, 2024, needs more optimization.
7 705 0.748618780251 Henry Cohn, 2024, needs more optimization.
7 706 0.748897497164 Henry Cohn, 2024, needs more optimization.
7 707 0.748933225793 Henry Cohn, 2024, needs more optimization.
7 708 0.749050571127 Henry Cohn, 2024, needs more optimization.
7 709 0.749261924866 Henry Cohn, 2024, needs more optimization.
7 710 0.749344679741 Henry Cohn, 2024, needs more optimization.
7 712 0.749404040360 Henry Cohn, 2024, needs more optimization.
7 713 0.749576633677 Henry Cohn, 2024, needs more optimization.
7 714 0.749866831728 Henry Cohn, 2024, needs more optimization.
7 715 0.749903254315 Henry Cohn, 2024, needs more optimization.
7 716 0.749986414453 Henry Cohn, 2024, 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 0.767060892838 Henry Cohn, 2024, needs more optimization.
7 884 0.767238581074 Henry Cohn, 2024, needs more optimization.
7 885 0.767411680061 Henry Cohn, 2024, needs more optimization.
7 887 0.767472153769 Henry Cohn, 2024, needs more optimization.
7 890 0.767596028907 Henry Cohn, 2024, needs more optimization.
7 891 0.767932521521 Henry Cohn, 2024, needs more optimization.
7 893 0.767995856674 Henry Cohn, 2024, needs more optimization.
7 894 0.768169302475 Henry Cohn, 2024, needs more optimization.
7 895 0.768207090952 Henry Cohn, 2024, needs more optimization.
7 897 0.768298172456 Henry Cohn, 2024, needs more optimization.
7 898 0.768597865714 Henry Cohn, 2024, needs more optimization.
7 899 0.768612842560 Henry Cohn, 2024, needs more optimization.
7 902 0.768700838570 Henry Cohn, 2024, needs more optimization.
7 903 0.768812942032 Henry Cohn, 2024, needs more optimization.
7 904 0.768988184659 Henry Cohn, 2024, needs more optimization.
7 907 0.769201583067 Henry Cohn, 2024, needs more optimization.
7 908 0.769301163833 Henry Cohn, 2024, needs more optimization.
7 909 0.769511981952 Henry Cohn, 2024, needs more optimization.
7 910 0.769526704485 Henry Cohn, 2024, needs more optimization.
7 912 0.769615033026 Henry Cohn, 2024, needs more optimization.
7 913 0.769844993405 Henry Cohn, 2024, needs more optimization.
7 915 0.769922679941 Henry Cohn, 2024, needs more optimization.
7 916 0.770107198587 Henry Cohn, 2024, needs more optimization.
7 918 0.770160918087 Henry Cohn, 2024, needs more optimization.
7 919 0.770317162459 Henry Cohn, 2024, needs more optimization.
7 921 0.770425707193 Henry Cohn, 2024, needs more optimization.
7 923 0.770480877799 Henry Cohn, 2024, needs more optimization.
7 924 0.770681114946 Henry Cohn, 2024, needs more optimization.
7 925 0.770870572742 Henry Cohn, 2024, needs more optimization.
7 927 0.770992342058 Henry Cohn, 2024, needs more optimization.
7 928 0.771104602322 Henry Cohn, 2024, needs more optimization.
7 930 0.771187235643 Henry Cohn, 2024, needs more optimization.
7 931 0.771313097173 Henry Cohn, 2024, needs more optimization.
7 932 0.771418036781 Henry Cohn, 2024, needs more optimization.
7 935 0.771599846854 Henry Cohn, 2024, needs more optimization.
7 937 0.771615740458 Henry Cohn, 2024, needs more optimization.
7 938 0.771897838820 Henry Cohn, 2024, needs more optimization.
7 939 0.772023691824 Henry Cohn, 2024, needs more optimization.
7 940 0.772100090275 Henry Cohn, 2024, needs more optimization.
7 942 0.772210712544 Henry Cohn, 2024, needs more optimization.
7 944 0.772297958334 Henry Cohn, 2024, needs more optimization.
7 947 0.772480240042 Henry Cohn, 2024, needs more optimization.
7 948 0.772740120557 Henry Cohn, 2024, needs more optimization.
7 950 0.772850657420 Henry Cohn, 2024, needs more optimization.
7 951 0.772906672486 Henry Cohn, 2024, needs more optimization.
7 952 0.772953143848 Henry Cohn, 2024, needs more optimization.
7 955 0.773220531820 Henry Cohn, 2024, needs more optimization.
7 957 0.773347122306 Henry Cohn, 2024, needs more optimization.
7 958 0.773422625084 Henry Cohn, 2024, needs more optimization.
7 959 0.773476415121 Henry Cohn, 2024, needs more optimization.
7 960 0.773623874685 Henry Cohn, 2024, needs more optimization.
7 961 0.773686964002 Henry Cohn, 2024, needs more optimization.
7 962 0.773867219218 Henry Cohn, 2024, needs more optimization.
7 963 0.773871780630 Henry Cohn, 2024, needs more optimization.
7 964 0.774006425747 Henry Cohn, 2024, needs more optimization.
7 965 0.774050445987 Henry Cohn, 2024, needs more optimization.
7 966 0.774088853994 Henry Cohn, 2024, needs more optimization.
7 967 0.774169467478 Henry Cohn, 2024, needs more optimization.
7 968 0.774218886802 Henry Cohn, 2024, needs more optimization.
7 969 0.774457350410 Henry Cohn, 2024, needs more optimization.
7 971 0.774544687420 Henry Cohn, 2024, needs more optimization.
7 972 0.774618589112 Henry Cohn, 2024, needs more optimization.
7 973 0.774732791296 Henry Cohn, 2024, needs more optimization.
7 975 0.774766518635 Henry Cohn, 2024, needs more optimization.
7 977 0.775025977566 Henry Cohn, 2024, needs more optimization.
7 979 0.775089596308 Henry Cohn, 2024, needs more optimization.
7 980 0.775139652843 Henry Cohn, 2024, needs more optimization.
7 981 0.775300607654 Henry Cohn, 2024, needs more optimization.
7 982 0.775392446609 Henry Cohn, 2024, needs more optimization.
7 984 0.775464088285 Henry Cohn, 2024, needs more optimization.
7 986 0.775708628890 Henry Cohn, 2024, needs more optimization.
7 987 0.775780504643 Henry Cohn, 2024, needs more optimization.
7 988 0.775785902192 Henry Cohn, 2024, needs more optimization.
7 989 0.775879831205 Henry Cohn, 2024, needs more optimization.
7 991 0.776038139602 Henry Cohn, 2024, needs more optimization.
7 992 0.776064644899 Henry Cohn, 2024, needs more optimization.
7 994 0.776317074545 Henry Cohn, 2024, needs more optimization.
7 995 0.776477937794 Henry Cohn, 2024, needs more optimization.
7 996 0.776526667767 Henry Cohn, 2024, needs more optimization.
7 998 0.776588787946 Henry Cohn, 2024, needs more optimization.
7 1000 0.776813126135 Henry Cohn, 2024, needs more optimization.
7 1001 0.776941017209 Henry Cohn, 2024, needs more optimization.
7 1003 0.776977207323 Henry Cohn, 2024, needs more optimization.
7 1005 0.777049538048 Henry Cohn, 2024, needs more optimization.
7 1006 0.777104886076 Henry Cohn, 2024, needs more optimization.
7 1008 0.777333015028 Henry Cohn, 2024, needs more optimization.
7 1010 0.777413707073 Henry Cohn, 2024, needs more optimization.
7 1011 0.777548776751 Henry Cohn, 2024, needs more optimization.
7 1012 0.777579694773 Henry Cohn, 2024, needs more optimization.
7 1013 0.777738655072 Henry Cohn, 2024, needs more optimization.
7 1014 0.777837747577 Henry Cohn, 2024, needs more optimization.
7 1015 0.777919592938 Henry Cohn, 2024, needs more optimization.
7 1016 0.778029251833 Henry Cohn, 2024, needs more optimization.
7 1017 0.778135524939 Henry Cohn, 2024, needs more optimization.
7 1019 0.778251999034 Henry Cohn, 2024, needs more optimization.
7 1020 0.778291251091 Henry Cohn, 2024, needs more optimization.
7 1021 0.778379427260 Henry Cohn, 2024, needs more optimization.
7 1024 0.778503809700 Henry Cohn, 2024, 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 0.265123725370 Henry Cohn, 2023.
8 41 0.269595854246 Henry Cohn, 2023.
8 42 0.276791074187 Henry Cohn, 2023.
8 43 0.285393498373 Henry Cohn, 2023.
8 44 0.288917068041 Henry Cohn, 2024.
8 45 0.293536733639 Henry Cohn, 2024.
8 46 0.298272580160 Henry Cohn, 2024.
8 47 0.301071641398 Henry Cohn, 2024.
8 48 0.306887170187 Henry Cohn, 2024.
8 49 0.310567741349 Henry Cohn, 2024.
8 50 0.315289580845 Henry Cohn, 2023.
8 51 0.316850575857 Henry Cohn, 2023.
8 52 0.317163413684 Henry Cohn, 2023.
8 53 0.323178575759 Henry Cohn, 2023.
8 54 0.326168059066 Henry Cohn, 2023.
8 55 0.328647504144 Henry Cohn, 2024.
8 56 0.330635803908 Henry Cohn, 2024.
8 57 0.332158960610 Henry Cohn, 2024.
8 58 0.332764123593 Henry Cohn, 2024.
8 59 0.333074199695 Henry Cohn, 2025.
8 60 0.333203664191 Henry Cohn, 2025.
8 61 0.333268531100 Henry Cohn, 2025.
8 62 0.333282393236 Henry Cohn, 2025.
8 63 0.333330430501 Henry Cohn, 2025, needs more optimization.
8 64 0.333333333334 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.
3⁢x−1
8 65 0.340297736367 Henry Cohn, 2025.
8 66 0.348779612155 Henry Cohn, 2023.
8 67 0.350802261970 Henry Cohn, 2024.
8 68 0.352462830866 Henry Cohn, 2024.
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 0.375030122156 Henry Cohn, 2024.
8 75 0.380147254829 Henry Cohn, 2024.
8 76 0.383280469013 Henry Cohn, 2023.
8 77 0.386336871922 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 0.401779725035 Henry Cohn, 2025, needs more optimization.
8 82 0.402310972296 Henry Cohn, 2025.
8 83 0.408258291015 Henry Cohn, 2025.
8 84 0.409508840421 Henry Cohn, 2024.
8 85 0.413778907224 Henry Cohn, 2025.
8 86 0.416887254507 Henry Cohn, 2025.
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 0.424840475614 Henry Cohn, 2025.
8 90 0.425699225544 Henry Cohn, 2025, needs more optimization.
8 91 0.425947075562 Henry Cohn, 2025.
8 92 0.426045181792 Henry Cohn, 2025, needs more optimization.
8 93 0.426378552695 Henry Cohn, 2025, needs more optimization.
8 94 0.426827036863 Henry Cohn, 2025.
8 95 0.427085423997 Henry Cohn, 2025, needs more optimization.
8 96 0.427640050834 Henry Cohn, 2025, 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 0.455563363107 Henry Cohn, 2025, 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 0.466199642504 Henry Cohn, 2025.
8 138 0.495133859264 Henry Cohn, 2024, needs more optimization.
8 139 0.495346136161 Henry Cohn, 2024, needs more optimization.
8 140 0.495519009315 Henry Cohn, 2024, needs more optimization.
8 141 0.495802641354 Henry Cohn, 2024, needs more optimization.
8 142 0.495914409995 Henry Cohn, 2024, needs more optimization.
8 143 0.496071818612 Henry Cohn, 2024, needs more optimization.
8 144 0.496204768427 Henry Cohn, 2024, needs more optimization.
8 145 0.497175789573 Henry Cohn, 2024, needs more optimization.
8 146 0.497369754589 Henry Cohn, 2024, needs more optimization.
8 147 0.497473811674 Henry Cohn, 2024, needs more optimization.
8 148 0.497733816721 Henry Cohn, 2024, needs more optimization.
8 149 0.497910351536 Henry Cohn, 2024, needs more optimization.
8 150 0.498180414827 Henry Cohn, 2024, needs more optimization.
8 151 0.498344087202 Henry Cohn, 2024, needs more optimization.
8 152 0.498439619657 Henry Cohn, 2024, needs more optimization.
8 153 0.498517950005 Henry Cohn, 2024, needs more optimization.
8 154 0.498617727588 Henry Cohn, 2024, needs more optimization.
8 155 0.498668170201 Henry Cohn, 2024, needs more optimization.
8 156 0.498765872920 Henry Cohn, 2024, needs more optimization.
8 157 0.498790754612 Henry Cohn, 2024, needs more optimization.
8 158 0.498854801715 Henry Cohn, 2024, needs more optimization.
8 159 0.498895065085 Henry Cohn, 2024, needs more optimization.
8 160 0.498964092556 Henry Cohn, 2024, needs more optimization.
8 162 0.498989670922 Henry Cohn, 2024, needs more optimization.
8 163 0.499040173619 Henry Cohn, 2024, needs more optimization.
8 164 0.499178666546 Henry Cohn, 2024, 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 0.550117627631 Henry Cohn, 2025, needs more optimization.
8 245 0.553653350879 Henry Cohn, 2025, needs more optimization.
8 246 0.554780227297 Henry Cohn, 2025, needs more optimization.
8 247 0.557476262905 Henry Cohn, 2025, needs more optimization.
8 248 0.558436003482 Henry Cohn, 2025, needs more optimization.
8 249 0.559791293809 Henry Cohn, 2025, needs more optimization.
8 250 0.561384867308 Henry Cohn, 2024, needs more optimization.
8 251 0.562313426667 Henry Cohn, 2024, needs more optimization.
8 252 0.564960366219 Henry Cohn, 2024, needs more optimization.
8 253 0.565615812754 Henry Cohn, 2024, needs more optimization.
8 254 0.565974682831 Henry Cohn, 2024, needs more optimization.
8 255 0.567647127049 Henry Cohn, 2025, needs more optimization.
8 256 0.568990360141 Henry Cohn, 2024, needs more optimization.
8 257 0.571348993401 Henry Cohn, 2024, needs more optimization.
8 258 0.574951988763 Henry Cohn, 2024, needs more optimization.
8 259 0.575843814238 Henry Cohn, 2024, needs more optimization.
8 262 0.576819926282 Henry Cohn, 2024, needs more optimization.
8 265 0.577799958189 Henry Cohn, 2024, needs more optimization.
8 267 0.581535858738 Henry Cohn, 2024, needs more optimization.
8 269 0.583227955002 Henry Cohn, 2024, needs more optimization.
8 271 0.583557291857 Henry Cohn, 2024, needs more optimization.
8 272 0.584841909820 Henry Cohn, 2024, needs more optimization.
8 273 0.586964009874 Henry Cohn, 2024, needs more optimization.
8 274 0.587033099504 Henry Cohn, 2024, needs more optimization.
8 276 0.587894094819 Henry Cohn, 2024, needs more optimization.
8 277 0.589521964491 Henry Cohn, 2024, needs more optimization.
8 278 0.591713618663 Henry Cohn, 2024, needs more optimization.
8 279 0.592078248163 Henry Cohn, 2024, needs more optimization.
8 310 0.592250069349 Henry Cohn, 2024, needs more optimization.
8 312 0.606140016216 Henry Cohn, 2024, needs more optimization.
8 313 0.606443949009 Henry Cohn, 2024, needs more optimization.
8 314 0.607167356632 Henry Cohn, 2024, needs more optimization.
8 315 0.607471912045 Henry Cohn, 2024, needs more optimization.
8 316 0.607886185611 Henry Cohn, 2024, needs more optimization.
8 319 0.607936086933 Henry Cohn, 2024, needs more optimization.
8 320 0.609150991920 Henry Cohn, 2024, needs more optimization.
8 321 0.609884003090 Henry Cohn, 2024, needs more optimization.
8 322 0.610186962870 Henry Cohn, 2024, needs more optimization.
8 323 0.610309852377 Henry Cohn, 2024, needs more optimization.
8 324 0.610950175534 Henry Cohn, 2024, needs more optimization.
8 325 0.611406702911 Henry Cohn, 2024, needs more optimization.
8 326 0.611598268237 Henry Cohn, 2024, needs more optimization.
8 327 0.611773278571 Henry Cohn, 2024, needs more optimization.
8 328 0.612338415205 Henry Cohn, 2024, needs more optimization.
8 329 0.612757437555 Henry Cohn, 2024, needs more optimization.
8 330 0.612883430828 Henry Cohn, 2024, needs more optimization.
8 331 0.613599740948 Henry Cohn, 2024, needs more optimization.
8 332 0.613763849886 Henry Cohn, 2024, needs more optimization.
8 333 0.614058126605 Henry Cohn, 2024, needs more optimization.
8 334 0.614808784463 Henry Cohn, 2024, needs more optimization.
8 335 0.615079834019 Henry Cohn, 2024, needs more optimization.
8 336 0.615384340884 Henry Cohn, 2024, needs more optimization.
8 337 0.615493068462 Henry Cohn, 2024, needs more optimization.
8 338 0.615840351932 Henry Cohn, 2024, needs more optimization.
8 339 0.616125937791 Henry Cohn, 2024, needs more optimization.
8 340 0.616764410332 Henry Cohn, 2024, needs more optimization.
8 341 0.617285255062 Henry Cohn, 2024, needs more optimization.
8 342 0.617540253381 Henry Cohn, 2024, needs more optimization.
8 343 0.617685024505 Henry Cohn, 2024, needs more optimization.
8 344 0.618170241059 Henry Cohn, 2024, needs more optimization.
8 345 0.618188474683 Henry Cohn, 2024, needs more optimization.
8 346 0.618759449731 Henry Cohn, 2024, needs more optimization.
8 347 0.618989152205 Henry Cohn, 2024, needs more optimization.
8 349 0.619278586435 Henry Cohn, 2024, needs more optimization.
8 350 0.620248070936 Henry Cohn, 2024, needs more optimization.
8 351 0.620434795573 Henry Cohn, 2024, needs more optimization.
8 352 0.620862610668 Henry Cohn, 2024, needs more optimization.
8 354 0.620865192742 Henry Cohn, 2024, needs more optimization.
8 355 0.621710604124 Henry Cohn, 2024, needs more optimization.
8 357 0.622109284913 Henry Cohn, 2024, needs more optimization.
8 358 0.622816239560 Henry Cohn, 2024, needs more optimization.
8 359 0.623026635274 Henry Cohn, 2024, needs more optimization.
8 360 0.623512045663 Henry Cohn, 2024, needs more optimization.
8 362 0.623803418634 Henry Cohn, 2024, needs more optimization.
8 363 0.624145303445 Henry Cohn, 2024, needs more optimization.
8 364 0.624710021438 Henry Cohn, 2024, needs more optimization.
8 365 0.624830447739 Henry Cohn, 2024, needs more optimization.
8 366 0.625324865670 Henry Cohn, 2024, needs more optimization.
8 367 0.625767122291 Henry Cohn, 2024, needs more optimization.
8 368 0.626040496057 Henry Cohn, 2024, needs more optimization.
8 369 0.626238774917 Henry Cohn, 2024, needs more optimization.
8 370 0.626587586225 Henry Cohn, 2024, needs more optimization.
8 371 0.626748911367 Henry Cohn, 2024, needs more optimization.
8 373 0.627104718576 Henry Cohn, 2024, needs more optimization.
8 375 0.627929576021 Henry Cohn, 2024, needs more optimization.
8 376 0.628361562453 Henry Cohn, 2024, needs more optimization.
8 377 0.628418917251 Henry Cohn, 2024, needs more optimization.
8 378 0.628496953656 Henry Cohn, 2024, needs more optimization.
8 379 0.629211604979 Henry Cohn, 2024, needs more optimization.
8 380 0.629473886215 Henry Cohn, 2024, needs more optimization.
8 381 0.629525993318 Henry Cohn, 2024, needs more optimization.
8 382 0.630123698447 Henry Cohn, 2024, needs more optimization.
8 383 0.630146036255 Henry Cohn, 2024, needs more optimization.
8 384 0.630462719347 Henry Cohn, 2024, needs more optimization.
8 386 0.631133875234 Henry Cohn, 2024, needs more optimization.
8 387 0.631402786306 Henry Cohn, 2024, needs more optimization.
8 388 0.631667727393 Henry Cohn, 2024, needs more optimization.
8 389 0.632161481481 Henry Cohn, 2024, needs more optimization.
8 391 0.632523058051 Henry Cohn, 2024, needs more optimization.
8 392 0.633059778292 Henry Cohn, 2024, needs more optimization.
8 393 0.633206464575 Henry Cohn, 2024, needs more optimization.
8 394 0.633212224277 Henry Cohn, 2024, needs more optimization.
8 395 0.633724521566 Henry Cohn, 2024, needs more optimization.
8 396 0.633836605862 Henry Cohn, 2024, needs more optimization.
8 397 0.634291527353 Henry Cohn, 2024, needs more optimization.
8 398 0.634592316005 Henry Cohn, 2024, needs more optimization.
8 400 0.634662910613 Henry Cohn, 2024, needs more optimization.
8 401 0.635433531717 Henry Cohn, 2024, needs more optimization.
8 402 0.635585123600 Henry Cohn, 2024, needs more optimization.
8 403 0.636032299770 Henry Cohn, 2024, needs more optimization.
8 404 0.636260844754 Henry Cohn, 2024, needs more optimization.
8 405 0.636480195129 Henry Cohn, 2024, needs more optimization.
8 406 0.636785638147 Henry Cohn, 2024, needs more optimization.
8 407 0.636947926692 Henry Cohn, 2024, needs more optimization.
8 408 0.637365777260 Henry Cohn, 2024, needs more optimization.
8 409 0.637556484002 Henry Cohn, 2024, needs more optimization.
8 410 0.637717019875 Henry Cohn, 2024, needs more optimization.
8 416 0.637917796226 Henry Cohn, 2024, needs more optimization.
8 417 0.639381636865 Henry Cohn, 2024, needs more optimization.
8 418 0.639644680913 Henry Cohn, 2024, needs more optimization.
8 420 0.640358100336 Henry Cohn, 2024, needs more optimization.
8 422 0.640587620515 Henry Cohn, 2024, needs more optimization.
8 424 0.641166620426 Henry Cohn, 2024, needs more optimization.
8 425 0.641444466419 Henry Cohn, 2024, needs more optimization.
8 426 0.641885690658 Henry Cohn, 2024, needs more optimization.
8 427 0.642141409548 Henry Cohn, 2024, needs more optimization.
8 428 0.642221658027 Henry Cohn, 2024, needs more optimization.
8 429 0.642326434683 Henry Cohn, 2024, needs more optimization.
8 430 0.642624295910 Henry Cohn, 2024, needs more optimization.
8 431 0.642922437751 Henry Cohn, 2024, needs more optimization.
8 432 0.643353495130 Henry Cohn, 2024, needs more optimization.
8 433 0.643856043582 Henry Cohn, 2024, needs more optimization.
8 435 0.644020579723 Henry Cohn, 2024, needs more optimization.
8 436 0.644267979035 Henry Cohn, 2024, needs more optimization.
8 437 0.644534181575 Henry Cohn, 2024, needs more optimization.
8 438 0.644644010247 Henry Cohn, 2024, needs more optimization.
8 439 0.644892510952 Henry Cohn, 2024, needs more optimization.
8 441 0.645391846216 Henry Cohn, 2024, needs more optimization.
8 442 0.645824066667 Henry Cohn, 2024, needs more optimization.
8 443 0.646164899517 Henry Cohn, 2024, needs more optimization.
8 446 0.646320201756 Henry Cohn, 2024, needs more optimization.
8 448 0.646914003433 Henry Cohn, 2024, needs more optimization.
8 449 0.647350870345 Henry Cohn, 2024, needs more optimization.
8 450 0.647397058925 Henry Cohn, 2024, needs more optimization.
8 451 0.648037462877 Henry Cohn, 2024, needs more optimization.
8 452 0.648087612016 Henry Cohn, 2024, needs more optimization.
8 454 0.648227839911 Henry Cohn, 2024, needs more optimization.
8 455 0.648612340129 Henry Cohn, 2024, needs more optimization.
8 456 0.648897395711 Henry Cohn, 2024, needs more optimization.
8 457 0.649226365197 Henry Cohn, 2024, needs more optimization.
8 459 0.649368907594 Henry Cohn, 2024, needs more optimization.
8 460 0.649811095129 Henry Cohn, 2024, needs more optimization.
8 461 0.649901277200 Henry Cohn, 2024, needs more optimization.
8 463 0.650362543604 Henry Cohn, 2024, needs more optimization.
8 464 0.650564071432 Henry Cohn, 2024, needs more optimization.
8 465 0.650999711027 Henry Cohn, 2024, needs more optimization.
8 467 0.651363085561 Henry Cohn, 2024, needs more optimization.
8 468 0.651600450489 Henry Cohn, 2024, needs more optimization.
8 469 0.652107027901 Henry Cohn, 2024, needs more optimization.
8 470 0.652206952494 Henry Cohn, 2024, needs more optimization.
8 471 0.652352358326 Henry Cohn, 2024, needs more optimization.
8 472 0.652523158312 Henry Cohn, 2024, needs more optimization.
8 473 0.652627527427 Henry Cohn, 2024, needs more optimization.
8 474 0.653068231662 Henry Cohn, 2024, needs more optimization.
8 475 0.653297187658 Henry Cohn, 2024, needs more optimization.
8 476 0.653513975909 Henry Cohn, 2024, needs more optimization.
8 478 0.653883669782 Henry Cohn, 2024, needs more optimization.
8 479 0.653943385613 Henry Cohn, 2024, needs more optimization.
8 480 0.654283731981 Henry Cohn, 2024, needs more optimization.
8 481 0.654732416343 Henry Cohn, 2024, needs more optimization.
8 482 0.654845248860 Henry Cohn, 2024, needs more optimization.
8 483 0.654945259730 Henry Cohn, 2024, needs more optimization.
8 484 0.655254719862 Henry Cohn, 2024, needs more optimization.
8 485 0.655495392494 Henry Cohn, 2024, needs more optimization.
8 486 0.655608574913 Henry Cohn, 2024, needs more optimization.
8 487 0.656008192612 Henry Cohn, 2024, needs more optimization.
8 488 0.656181556315 Henry Cohn, 2024, needs more optimization.
8 490 0.656403719328 Henry Cohn, 2024, needs more optimization.
8 491 0.656450876216 Henry Cohn, 2024, needs more optimization.
8 492 0.656611679455 Henry Cohn, 2024, needs more optimization.
8 493 0.656959843788 Henry Cohn, 2024, needs more optimization.
8 494 0.657052159544 Henry Cohn, 2024, needs more optimization.
8 496 0.657253461010 Henry Cohn, 2024, needs more optimization.
8 498 0.657923164268 Henry Cohn, 2024, needs more optimization.
8 499 0.658264262947 Henry Cohn, 2024, needs more optimization.
8 500 0.658453361914 Henry Cohn, 2024, needs more optimization.
8 501 0.658678648782 Henry Cohn, 2024, needs more optimization.
8 502 0.658941718292 Henry Cohn, 2024, needs more optimization.
8 503 0.658960790720 Henry Cohn, 2024, needs more optimization.
8 504 0.659310715698 Henry Cohn, 2024, needs more optimization.
8 505 0.659518417447 Henry Cohn, 2024, needs more optimization.
8 506 0.659902909692 Henry Cohn, 2024, needs more optimization.
8 507 0.659930531436 Henry Cohn, 2024, needs more optimization.
8 508 0.660198102557 Henry Cohn, 2024, needs more optimization.
8 509 0.660279961813 Henry Cohn, 2024, needs more optimization.
8 510 0.660534939054 Henry Cohn, 2024, needs more optimization.
8 511 0.660737681639 Henry Cohn, 2024, needs more optimization.
8 512 0.660883799091 Henry Cohn, 2024, needs more optimization.
8 514 0.661036085944 Henry Cohn, 2024, needs more optimization.
8 515 0.661672337915 Henry Cohn, 2024, needs more optimization.
8 516 0.661681002402 Henry Cohn, 2024, needs more optimization.
8 517 0.662076944299 Henry Cohn, 2024, needs more optimization.
8 518 0.662295612713 Henry Cohn, 2024, needs more optimization.
8 519 0.662516854205 Henry Cohn, 2024, needs more optimization.
8 521 0.662581032608 Henry Cohn, 2024, needs more optimization.
8 522 0.662823480048 Henry Cohn, 2024, needs more optimization.
8 523 0.663097264908 Henry Cohn, 2024, needs more optimization.
8 524 0.663105137621 Henry Cohn, 2024, needs more optimization.
8 525 0.663619627806 Henry Cohn, 2024, needs more optimization.
8 527 0.663654485585 Henry Cohn, 2024, needs more optimization.
8 528 0.663899602518 Henry Cohn, 2024, needs more optimization.
8 530 0.664110598247 Henry Cohn, 2024, needs more optimization.
8 531 0.664396350968 Henry Cohn, 2024, needs more optimization.
8 532 0.664630363457 Henry Cohn, 2024, needs more optimization.
8 533 0.664889640562 Henry Cohn, 2024, needs more optimization.
8 534 0.665042712640 Henry Cohn, 2024, needs more optimization.
8 535 0.665188203709 Henry Cohn, 2024, needs more optimization.
8 537 0.665272929622 Henry Cohn, 2024, needs more optimization.
8 538 0.665782468787 Henry Cohn, 2024, needs more optimization.
8 539 0.665962830029 Henry Cohn, 2024, needs more optimization.
8 540 0.666168697101 Henry Cohn, 2024, needs more optimization.
8 541 0.666221271585 Henry Cohn, 2024, needs more optimization.
8 542 0.666381161462 Henry Cohn, 2024, needs more optimization.
8 592 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
8 594 0.675359927082 Henry Cohn, 2024, needs more optimization.
8 595 0.675498380667 Henry Cohn, 2024, needs more optimization.
8 596 0.675705378034 Henry Cohn, 2024, needs more optimization.
8 597 0.675810710310 Henry Cohn, 2024, needs more optimization.
8 598 0.676196262250 Henry Cohn, 2024, needs more optimization.
8 599 0.676338773094 Henry Cohn, 2024, needs more optimization.
8 600 0.676524754238 Henry Cohn, 2024, needs more optimization.
8 601 0.676577347595 Henry Cohn, 2024, needs more optimization.
8 603 0.676825593797 Henry Cohn, 2024, needs more optimization.
8 606 0.677235384527 Henry Cohn, 2024, needs more optimization.
8 607 0.677536105789 Henry Cohn, 2024, needs more optimization.
8 608 0.677750311280 Henry Cohn, 2024, needs more optimization.
8 609 0.677998411382 Henry Cohn, 2024, needs more optimization.
8 610 0.678076222061 Henry Cohn, 2024, needs more optimization.
8 611 0.678252806754 Henry Cohn, 2024, needs more optimization.
8 613 0.678342006719 Henry Cohn, 2024, needs more optimization.
8 615 0.678838392958 Henry Cohn, 2024, needs more optimization.
8 616 0.679057676281 Henry Cohn, 2024, needs more optimization.
8 619 0.679127972439 Henry Cohn, 2024, needs more optimization.
8 621 0.679506532027 Henry Cohn, 2024, needs more optimization.
8 622 0.679848151046 Henry Cohn, 2024, needs more optimization.
8 624 0.680069197917 Henry Cohn, 2024, needs more optimization.
8 625 0.680180058207 Henry Cohn, 2024, needs more optimization.
8 626 0.680350499855 Henry Cohn, 2024, needs more optimization.
8 627 0.680468746844 Henry Cohn, 2024, needs more optimization.
8 628 0.680756297826 Henry Cohn, 2024, needs more optimization.
8 629 0.680779104082 Henry Cohn, 2024, needs more optimization.
8 630 0.680989561514 Henry Cohn, 2024, needs more optimization.
8 632 0.681301792943 Henry Cohn, 2024, needs more optimization.
8 634 0.681539572040 Henry Cohn, 2024, needs more optimization.
8 635 0.681689548471 Henry Cohn, 2024, needs more optimization.
8 636 0.681957300787 Henry Cohn, 2024, needs more optimization.
8 638 0.682186142540 Henry Cohn, 2024, needs more optimization.
8 640 0.682252960387 Henry Cohn, 2024, needs more optimization.
8 642 0.682627396534 Henry Cohn, 2024, needs more optimization.
8 644 0.682987511844 Henry Cohn, 2024, needs more optimization.
8 645 0.683255081578 Henry Cohn, 2024, needs more optimization.
8 646 0.683343588105 Henry Cohn, 2024, needs more optimization.
8 647 0.683592918825 Henry Cohn, 2024, needs more optimization.
8 648 0.683668902312 Henry Cohn, 2024, needs more optimization.
8 649 0.683943722547 Henry Cohn, 2024, needs more optimization.
8 650 0.683986133419 Henry Cohn, 2024, needs more optimization.
8 651 0.684075836396 Henry Cohn, 2024, needs more optimization.
8 654 0.684426202451 Henry Cohn, 2024, needs more optimization.
8 656 0.684699545033 Henry Cohn, 2024, needs more optimization.
8 657 0.684844024046 Henry Cohn, 2024, needs more optimization.
8 658 0.685066223726 Henry Cohn, 2024, needs more optimization.
8 660 0.685289468253 Henry Cohn, 2024, needs more optimization.
8 661 0.685347358250 Henry Cohn, 2024, needs more optimization.
8 662 0.685782461241 Henry Cohn, 2024, needs more optimization.
8 663 0.685816695445 Henry Cohn, 2024, needs more optimization.
8 665 0.685980754867 Henry Cohn, 2024, needs more optimization.
8 668 0.686371487707 Henry Cohn, 2024, needs more optimization.
8 669 0.686646284566 Henry Cohn, 2024, needs more optimization.
8 672 0.686742479256 Henry Cohn, 2024, needs more optimization.
8 673 0.687306107718 Henry Cohn, 2024, needs more optimization.
8 674 0.687386703264 Henry Cohn, 2024, needs more optimization.
8 676 0.687479849470 Henry Cohn, 2024, needs more optimization.
8 677 0.687728291551 Henry Cohn, 2024, needs more optimization.
8 678 0.687869048948 Henry Cohn, 2024, needs more optimization.
8 679 0.688009232816 Henry Cohn, 2024, needs more optimization.
8 682 0.688250615003 Henry Cohn, 2024, needs more optimization.
8 683 0.688552005096 Henry Cohn, 2024, needs more optimization.
8 684 0.688582976835 Henry Cohn, 2024, needs more optimization.
8 686 0.688685461787 Henry Cohn, 2024, needs more optimization.
8 688 0.689071159432 Henry Cohn, 2024, needs more optimization.
8 689 0.689517659381 Henry Cohn, 2024, needs more optimization.
8 691 0.689531455679 Henry Cohn, 2024, needs more optimization.
8 693 0.689804699875 Henry Cohn, 2024, needs more optimization.
8 697 0.690104243892 Henry Cohn, 2024, needs more optimization.
8 698 0.690366596482 Henry Cohn, 2024, needs more optimization.
8 699 0.690689439707 Henry Cohn, 2024, needs more optimization.
8 700 0.690946967246 Henry Cohn, 2024, needs more optimization.
8 702 0.690954076138 Henry Cohn, 2024, needs more optimization.
8 704 0.691128712663 Henry Cohn, 2024, needs more optimization.
8 705 0.691522116096 Henry Cohn, 2024, needs more optimization.
8 706 0.691662208308 Henry Cohn, 2024, needs more optimization.
8 707 0.691668695195 Henry Cohn, 2024, needs more optimization.
8 708 0.691897818392 Henry Cohn, 2024, needs more optimization.
8 709 0.691980087646 Henry Cohn, 2024, needs more optimization.
8 711 0.692229320227 Henry Cohn, 2024, needs more optimization.
8 712 0.692344643066 Henry Cohn, 2024, needs more optimization.
8 713 0.692404929482 Henry Cohn, 2024, needs more optimization.
8 714 0.692731800565 Henry Cohn, 2024, needs more optimization.
8 716 0.692843644999 Henry Cohn, 2024, needs more optimization.
8 717 0.693108816592 Henry Cohn, 2024, needs more optimization.
8 719 0.693287491254 Henry Cohn, 2024, needs more optimization.
8 720 0.693338855017 Henry Cohn, 2024, needs more optimization.
8 721 0.693414007488 Henry Cohn, 2024, needs more optimization.
8 722 0.693777884309 Henry Cohn, 2024, needs more optimization.
8 723 0.693855855038 Henry Cohn, 2024, needs more optimization.
8 724 0.693948743072 Henry Cohn, 2024, needs more optimization.
8 726 0.693978284685 Henry Cohn, 2024, needs more optimization.
8 727 0.694332674478 Henry Cohn, 2024, needs more optimization.
8 728 0.694468872414 Henry Cohn, 2024, needs more optimization.
8 729 0.694544028736 Henry Cohn, 2024, needs more optimization.
8 731 0.694727064559 Henry Cohn, 2024, needs more optimization.
8 732 0.694829339692 Henry Cohn, 2024, needs more optimization.
8 734 0.694929835698 Henry Cohn, 2024, needs more optimization.
8 735 0.695182554084 Henry Cohn, 2024, needs more optimization.
8 737 0.695567556342 Henry Cohn, 2024, needs more optimization.
8 738 0.695613055090 Henry Cohn, 2024, needs more optimization.
8 739 0.695741117971 Henry Cohn, 2024, needs more optimization.
8 740 0.695983841289 Henry Cohn, 2024, needs more optimization.
8 742 0.696073459732 Henry Cohn, 2024, needs more optimization.
8 743 0.696179001708 Henry Cohn, 2024, needs more optimization.
8 744 0.696417972427 Henry Cohn, 2024, needs more optimization.
8 745 0.696433150143 Henry Cohn, 2024, needs more optimization.
8 746 0.696600460350 Henry Cohn, 2024, needs more optimization.
8 747 0.696677125460 Henry Cohn, 2024, needs more optimization.
8 748 0.696847922106 Henry Cohn, 2024, needs more optimization.
8 749 0.696999300117 Henry Cohn, 2024, needs more optimization.
8 752 0.697244357985 Henry Cohn, 2024, needs more optimization.
8 755 0.697618598375 Henry Cohn, 2024, needs more optimization.
8 757 0.697761358569 Henry Cohn, 2024, needs more optimization.
8 759 0.698026611230 Henry Cohn, 2024, needs more optimization.
8 760 0.698161579155 Henry Cohn, 2024, needs more optimization.
8 761 0.698509890548 Henry Cohn, 2024, needs more optimization.
8 762 0.698527017154 Henry Cohn, 2024, needs more optimization.
8 765 0.698796513894 Henry Cohn, 2024, needs more optimization.
8 766 0.698914540508 Henry Cohn, 2024, needs more optimization.
8 768 0.699041203232 Henry Cohn, 2024, needs more optimization.
8 770 0.699213704487 Henry Cohn, 2024, needs more optimization.
8 772 0.699674212783 Henry Cohn, 2024, needs more optimization.
8 773 0.699760157847 Henry Cohn, 2024, needs more optimization.
8 774 0.699853064581 Henry Cohn, 2024, needs more optimization.
8 775 0.699998749442 Henry Cohn, 2024, needs more optimization.
8 776 0.700231322126 Henry Cohn, 2024, needs more optimization.
8 777 0.700311208521 Henry Cohn, 2024, needs more optimization.
8 778 0.700457548328 Henry Cohn, 2024, needs more optimization.
8 779 0.700541883086 Henry Cohn, 2024, needs more optimization.
8 780 0.700554970411 Henry Cohn, 2024, needs more optimization.
8 782 0.700676780515 Henry Cohn, 2024, needs more optimization.
8 783 0.701092369576 Henry Cohn, 2024, needs more optimization.
8 785 0.701111239119 Henry Cohn, 2024, needs more optimization.
8 787 0.701171385996 Henry Cohn, 2024, needs more optimization.
8 788 0.701633286554 Henry Cohn, 2024, needs more optimization.
8 790 0.701693446647 Henry Cohn, 2024, needs more optimization.
8 792 0.701861169362 Henry Cohn, 2024, needs more optimization.
8 794 0.701981884601 Henry Cohn, 2024, needs more optimization.
8 795 0.702428100484 Henry Cohn, 2024, needs more optimization.
8 797 0.702505570388 Henry Cohn, 2024, needs more optimization.
8 799 0.702672876174 Henry Cohn, 2024, needs more optimization.
8 800 0.702867328037 Henry Cohn, 2024, needs more optimization.
8 801 0.702960665077 Henry Cohn, 2024, needs more optimization.
8 802 0.703014783053 Henry Cohn, 2024, needs more optimization.
8 804 0.703153581757 Henry Cohn, 2024, needs more optimization.
8 805 0.703484482331 Henry Cohn, 2024, needs more optimization.
8 806 0.703614530771 Henry Cohn, 2024, needs more optimization.
8 808 0.703648546764 Henry Cohn, 2024, needs more optimization.
8 809 0.703805831612 Henry Cohn, 2024, needs more optimization.
8 810 0.703878944647 Henry Cohn, 2024, needs more optimization.
8 811 0.703914027805 Henry Cohn, 2024, needs more optimization.
8 813 0.704188859863 Henry Cohn, 2024, needs more optimization.
8 814 0.704421512898 Henry Cohn, 2024, needs more optimization.
8 815 0.704496887596 Henry Cohn, 2024, needs more optimization.
8 817 0.704674301542 Henry Cohn, 2024, needs more optimization.
8 818 0.704860873407 Henry Cohn, 2024, needs more optimization.
8 820 0.705045529502 Henry Cohn, 2024, needs more optimization.
8 821 0.705143543456 Henry Cohn, 2024, needs more optimization.
8 822 0.705147133074 Henry Cohn, 2024, needs more optimization.
8 823 0.705328922582 Henry Cohn, 2024, needs more optimization.
8 824 0.705414140588 Henry Cohn, 2024, needs more optimization.
8 825 0.705457744554 Henry Cohn, 2024, needs more optimization.
8 826 0.705582110043 Henry Cohn, 2024, needs more optimization.
8 827 0.705727615911 Henry Cohn, 2024, needs more optimization.
8 828 0.705745655315 Henry Cohn, 2024, needs more optimization.
8 830 0.705980317644 Henry Cohn, 2024, needs more optimization.
8 832 0.706102758424 Henry Cohn, 2024, needs more optimization.
8 835 0.706572744466 Henry Cohn, 2024, needs more optimization.
8 836 0.706592103308 Henry Cohn, 2024, needs more optimization.
8 837 0.706732340551 Henry Cohn, 2024, needs more optimization.
8 841 0.706930385131 Henry Cohn, 2024, needs more optimization.
8 843 0.707329359656 Henry Cohn, 2024, needs more optimization.
8 844 0.707516274951 Henry Cohn, 2024, needs more optimization.
8 845 0.707524642138 Henry Cohn, 2024, needs more optimization.
8 847 0.707701754192 Henry Cohn, 2024, needs more optimization.
8 848 0.707898195403 Henry Cohn, 2024, needs more optimization.
8 849 0.707993677101 Henry Cohn, 2024, needs more optimization.
8 850 0.708198052877 Henry Cohn, 2024, needs more optimization.
8 851 0.708254238289 Henry Cohn, 2024, needs more optimization.
8 852 0.708298657545 Henry Cohn, 2024, needs more optimization.
8 853 0.708338040835 Henry Cohn, 2024, needs more optimization.
8 855 0.708528400227 Henry Cohn, 2024, needs more optimization.
8 856 0.708644797597 Henry Cohn, 2024, needs more optimization.
8 857 0.708763100635 Henry Cohn, 2024, needs more optimization.
8 858 0.708933326354 Henry Cohn, 2024, needs more optimization.
8 859 0.709107789912 Henry Cohn, 2024, needs more optimization.
8 860 0.709109705541 Henry Cohn, 2024, needs more optimization.
8 862 0.709202082110 Henry Cohn, 2024, needs more optimization.
8 863 0.709340968315 Henry Cohn, 2024, needs more optimization.
8 865 0.709376232512 Henry Cohn, 2024, needs more optimization.
8 866 0.709635331812 Henry Cohn, 2024, needs more optimization.
8 868 0.709793536548 Henry Cohn, 2024, needs more optimization.
8 870 0.709981318088 Henry Cohn, 2024, needs more optimization.
8 873 0.710181415164 Henry Cohn, 2024, needs more optimization.
8 875 0.710459934086 Henry Cohn, 2024, needs more optimization.
8 878 0.710670608535 Henry Cohn, 2024, needs more optimization.
8 880 0.710824448466 Henry Cohn, 2024, needs more optimization.
8 881 0.710934272040 Henry Cohn, 2024, needs more optimization.
8 883 0.711265768983 Henry Cohn, 2024, needs more optimization.
8 884 0.711451017083 Henry Cohn, 2024, needs more optimization.
8 885 0.711470245496 Henry Cohn, 2024, needs more optimization.
8 887 0.711579089927 Henry Cohn, 2024, needs more optimization.
8 888 0.711705514764 Henry Cohn, 2024, needs more optimization.
8 890 0.712005035187 Henry Cohn, 2024, needs more optimization.
8 891 0.712240106263 Henry Cohn, 2024, needs more optimization.
8 892 0.712368646933 Henry Cohn, 2024, needs more optimization.
8 893 0.712451461413 Henry Cohn, 2024, needs more optimization.
8 894 0.712462166522 Henry Cohn, 2024, needs more optimization.
8 895 0.712573129085 Henry Cohn, 2024, needs more optimization.
8 896 0.712602599804 Henry Cohn, 2024, needs more optimization.
8 897 0.712672274671 Henry Cohn, 2024, needs more optimization.
8 898 0.712840946225 Henry Cohn, 2024, needs more optimization.
8 899 0.712848743530 Henry Cohn, 2024, needs more optimization.
8 900 0.712915572089 Henry Cohn, 2024, needs more optimization.
8 901 0.713032848309 Henry Cohn, 2024, needs more optimization.
8 903 0.713245940522 Henry Cohn, 2024, needs more optimization.
8 904 0.713314564922 Henry Cohn, 2024, needs more optimization.
8 906 0.713473718852 Henry Cohn, 2024, needs more optimization.
8 907 0.713700897865 Henry Cohn, 2024, needs more optimization.
8 910 0.713718002647 Henry Cohn, 2024, needs more optimization.
8 912 0.713853250579 Henry Cohn, 2024, needs more optimization.
8 913 0.714192730639 Henry Cohn, 2024, needs more optimization.
8 996 0.714269304535 Henry Cohn, 2024, 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 0.149930200077 H. Cohn, Small spherical and projective codes, data set, updated 2024, 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, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
5⁢x−1
9 37 0.213783378437 Henry Cohn, 2024.
9 38 0.217703240659 Henry Cohn, 2025.
9 39 0.222837046412 Henry Cohn, 2023.
9 40 0.225704407232 Henry Cohn, 2023.
9 41 0.230353619603 Henry Cohn, 2023.
9 42 0.231125263657 Henry Cohn, 2024.
9 43 0.231201190091 Henry Cohn, 2023.
9 44 0.233554527157 Henry Cohn, 2025.
9 47 0.238172399483 Henry Cohn, 2023.
335⁢x2−42⁢x−9
9 48 0.254741941811 Henry Cohn, 2023.
9 49 0.261827927697 Henry Cohn, 2023.
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 55 0.273480785193 Henry Cohn, 2024.
576⁢x4+576⁢x3−768⁢x2−24⁢x+49
9 56 0.287378710663 Henry Cohn, 2023.
9 57 0.290508376519 Henry Cohn, 2024.
9 58 0.294003724264 Henry Cohn, 2024.
9 59 0.294328630820 Henry Cohn, 2024.
9 60 0.297651969467 Henry Cohn, 2023.
9 61 0.297700422270 Henry Cohn, 2023.
9 62 0.299745509903 Henry Cohn, 2025.
9 63 0.302965656950 Henry Cohn, 2025, needs more optimization.
9 64 0.306653313780 Henry Cohn, 2023.
9 65 0.310507879444 Henry Cohn, 2025.
9 66 0.314219501967 Henry Cohn, 2024.
9 67 0.319328524370 Henry Cohn, 2025.
9 68 0.322085809494 Henry Cohn, 2025.
9 69 0.324726490455 Henry Cohn, 2025.
9 70 0.329010071163 Henry Cohn, 2025.
9 71 0.329914915092 Henry Cohn, 2025.
9 72 0.330036102740 Henry Cohn, 2025, needs more optimization.
9 73 0.330041808451 Henry Cohn, 2025, needs more optimization.
9 74 0.330112547842 Henry Cohn, 2025, needs more optimization.
9 75 0.330112965835 Henry Cohn, 2025, needs more optimization.
9 76 0.330113020426 Henry Cohn, 2024.
9 77 0.330113020436 Henry Cohn, 2025.
9 78 0.330908012656 Henry Cohn, 2025.
9 79 0.330918543665 Henry Cohn, 2024.
9 80 0.333107087319 Henry Cohn, 2024, needs more optimization.
9 96 0.333333333334 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.
3⁢x−1
9 97 0.371099110252 Henry Cohn, 2024.
9 98 0.372095119903 Henry Cohn, 2025.
9 99 0.378708142507 Henry Cohn, 2024, needs more optimization.
9 100 0.378761448559 Henry Cohn, 2025.
9 102 0.378797075313 Henry Cohn, 2025.
9 103 0.379146212242 Henry Cohn, 2024, needs more optimization.
9 104 0.379158316136 Henry Cohn, 2024, needs more optimization.
9 105 0.394777357459 Henry Cohn, 2024, needs more optimization.
9 106 0.397079046506 Henry Cohn, 2024, needs more optimization.
9 107 0.398216737591 Henry Cohn, 2024, needs more optimization.
9 108 0.400400283479 Henry Cohn, 2024, needs more optimization.
9 109 0.403205992664 Henry Cohn, 2024, needs more optimization.
9 110 0.405773877046 Henry Cohn, 2024, needs more optimization.
9 111 0.408532717138 Henry Cohn, 2024, needs more optimization.
9 112 0.409132016778 Henry Cohn, 2024, needs more optimization.
9 113 0.413984308954 Henry Cohn, 2024, needs more optimization.
9 114 0.415397732794 Henry Cohn, 2024, needs more optimization.
9 115 0.417527894038 Henry Cohn, 2024, needs more optimization.
9 116 0.418892829013 Henry Cohn, 2024, needs more optimization.
9 117 0.421190743631 Henry Cohn, 2024, needs more optimization.
9 118 0.422836382187 Henry Cohn, 2024, needs more optimization.
9 119 0.424113538650 Henry Cohn, 2024, needs more optimization.
9 120 0.425585733507 Henry Cohn, 2024, needs more optimization.
9 121 0.426630643501 Henry Cohn, 2024, needs more optimization.
9 122 0.427904434100 Henry Cohn, 2024, needs more optimization.
9 146 0.428571428572 M. Ganzhinov and P. R. J. Östergård, Spherical codes with prescribed signed permutation automorphisms inside shells of low-dimensional integer lattices, IEEE Trans. Inform. Theory 70 (2024), 8669–8674, doi:10.1109/tit.2024.3462593, arXiv:2403.04330.
7⁢x−3
9 165 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 0.465458090553 Henry Cohn, 2024, needs more optimization.
9 167 0.473656937172 Henry Cohn, 2024, needs more optimization.
9 168 0.474746985603 Henry Cohn, 2024, needs more optimization.
9 169 0.475497755302 Henry Cohn, 2024, needs more optimization.
9 170 0.476236236143 Henry Cohn, 2024, needs more optimization.
9 171 0.477105132981 Henry Cohn, 2024, needs more optimization.
9 172 0.478086023503 Henry Cohn, 2024, needs more optimization.
9 173 0.478632924432 Henry Cohn, 2024, needs more optimization.
9 174 0.479905787659 Henry Cohn, 2024, needs more optimization.
9 175 0.480287366798 Henry Cohn, 2024, needs more optimization.
9 176 0.481175044974 Henry Cohn, 2024, needs more optimization.
9 177 0.481718144205 Henry Cohn, 2024, needs more optimization.
9 178 0.482619706367 Henry Cohn, 2024, needs more optimization.
9 179 0.483253416194 Henry Cohn, 2024, needs more optimization.
9 180 0.484433051377 Henry Cohn, 2024, needs more optimization.
9 181 0.485124952860 Henry Cohn, 2024, needs more optimization.
9 182 0.485770697551 Henry Cohn, 2024, needs more optimization.
9 183 0.486840018146 Henry Cohn, 2024, needs more optimization.
9 184 0.487357100064 Henry Cohn, 2024, needs more optimization.
9 185 0.488016561449 Henry Cohn, 2024, needs more optimization.
9 186 0.488769295482 Henry Cohn, 2024, needs more optimization.
9 187 0.489235720373 Henry Cohn, 2024, needs more optimization.
9 188 0.490465014229 Henry Cohn, 2024, needs more optimization.
9 189 0.491271065299 Henry Cohn, 2024, needs more optimization.
9 190 0.491717185588 Henry Cohn, 2024, needs more optimization.
9 191 0.492457306975 Henry Cohn, 2024, needs more optimization.
9 192 0.493257491390 Henry Cohn, 2024, needs more optimization.
9 193 0.493800763718 Henry Cohn, 2024, needs more optimization.
9 194 0.494573518575 Henry Cohn, 2024, needs more optimization.
9 195 0.495127968925 Henry Cohn, 2024, needs more optimization.
9 196 0.496760170446 Henry Cohn, 2024, needs more optimization.
9 197 0.497200280137 Henry Cohn, 2024, needs more optimization.
9 198 0.497957752752 Henry Cohn, 2024, needs more optimization.
9 200 0.498311538234 Henry Cohn, 2024, 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.
9 482 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
9 612 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
9 722 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 0.643657274301 Henry Cohn, 2024, needs more optimization.
9 724 0.643939517061 Henry Cohn, 2024, needs more optimization.
9 726 0.643998013038 Henry Cohn, 2024, needs more optimization.
9 728 0.644514303358 Henry Cohn, 2024, needs more optimization.
9 730 0.644695139658 Henry Cohn, 2024, needs more optimization.
9 731 0.644854938092 Henry Cohn, 2024, needs more optimization.
9 732 0.644966583730 Henry Cohn, 2024, needs more optimization.
9 733 0.645054890069 Henry Cohn, 2024, needs more optimization.
9 734 0.645119660256 Henry Cohn, 2024, needs more optimization.
9 737 0.645453329339 Henry Cohn, 2024, needs more optimization.
9 739 0.645703085851 Henry Cohn, 2024, needs more optimization.
9 740 0.645985941381 Henry Cohn, 2024, needs more optimization.
9 741 0.646109257828 Henry Cohn, 2024, needs more optimization.
9 743 0.646357130982 Henry Cohn, 2024, needs more optimization.
9 744 0.646485978527 Henry Cohn, 2024, needs more optimization.
9 745 0.646734337068 Henry Cohn, 2024, needs more optimization.
9 746 0.646993699927 Henry Cohn, 2024, needs more optimization.
9 748 0.646994510396 Henry Cohn, 2024, needs more optimization.
9 749 0.647144041905 Henry Cohn, 2024, needs more optimization.
9 750 0.647283339314 Henry Cohn, 2024, needs more optimization.
9 751 0.647426851530 Henry Cohn, 2024, needs more optimization.
9 753 0.647603819863 Henry Cohn, 2024, needs more optimization.
9 754 0.647893045310 Henry Cohn, 2024, needs more optimization.
9 756 0.647975984210 Henry Cohn, 2024, needs more optimization.
9 758 0.648227714171 Henry Cohn, 2024, needs more optimization.
9 761 0.648376413271 Henry Cohn, 2024, needs more optimization.
9 762 0.648598571925 Henry Cohn, 2024, needs more optimization.
9 763 0.648738012972 Henry Cohn, 2024, needs more optimization.
9 765 0.649056979804 Henry Cohn, 2024, needs more optimization.
9 766 0.649169093609 Henry Cohn, 2024, needs more optimization.
9 768 0.649306283622 Henry Cohn, 2024, needs more optimization.
9 769 0.649488403633 Henry Cohn, 2024, needs more optimization.
9 770 0.649643115842 Henry Cohn, 2024, needs more optimization.
9 771 0.649810705995 Henry Cohn, 2024, needs more optimization.
9 772 0.649977141833 Henry Cohn, 2024, needs more optimization.
9 774 0.650167309814 Henry Cohn, 2024, needs more optimization.
9 775 0.650275985769 Henry Cohn, 2024, needs more optimization.
9 776 0.650411712326 Henry Cohn, 2024, needs more optimization.
9 777 0.650535354536 Henry Cohn, 2024, needs more optimization.
9 778 0.650606981905 Henry Cohn, 2024, needs more optimization.
9 779 0.650813669225 Henry Cohn, 2024, needs more optimization.
9 781 0.650957869498 Henry Cohn, 2024, needs more optimization.
9 782 0.651148504067 Henry Cohn, 2024, needs more optimization.
9 783 0.651202853867 Henry Cohn, 2024, needs more optimization.
9 784 0.651256687190 Henry Cohn, 2024, needs more optimization.
9 785 0.651388942235 Henry Cohn, 2024, needs more optimization.
9 787 0.651486297799 Henry Cohn, 2024, needs more optimization.
9 788 0.651644656966 Henry Cohn, 2024, needs more optimization.
9 791 0.651890794327 Henry Cohn, 2024, needs more optimization.
9 792 0.652094300866 Henry Cohn, 2024, needs more optimization.
9 793 0.652274236266 Henry Cohn, 2024, needs more optimization.
9 794 0.652514536378 Henry Cohn, 2024, needs more optimization.
9 795 0.652723462340 Henry Cohn, 2024, needs more optimization.
9 797 0.652782218116 Henry Cohn, 2024, needs more optimization.
9 798 0.653053687547 Henry Cohn, 2024, needs more optimization.
9 801 0.653172264394 Henry Cohn, 2024, needs more optimization.
9 803 0.653439807670 Henry Cohn, 2024, needs more optimization.
9 805 0.653647374233 Henry Cohn, 2024, needs more optimization.
9 806 0.653720152322 Henry Cohn, 2024, needs more optimization.
9 807 0.653728337065 Henry Cohn, 2024, needs more optimization.
9 808 0.653910967965 Henry Cohn, 2024, needs more optimization.
9 809 0.654125667081 Henry Cohn, 2024, needs more optimization.
9 810 0.654362995301 Henry Cohn, 2024, needs more optimization.
9 811 0.654558907931 Henry Cohn, 2024, needs more optimization.
9 812 0.654623274981 Henry Cohn, 2024, needs more optimization.
9 813 0.654729844039 Henry Cohn, 2024, needs more optimization.
9 814 0.654779734980 Henry Cohn, 2024, needs more optimization.
9 815 0.654815272716 Henry Cohn, 2024, needs more optimization.
9 818 0.655063808020 Henry Cohn, 2024, needs more optimization.
9 820 0.655249079340 Henry Cohn, 2024, needs more optimization.
9 821 0.655494038663 Henry Cohn, 2024, needs more optimization.
9 822 0.655791111715 Henry Cohn, 2024, needs more optimization.
9 824 0.655844528376 Henry Cohn, 2024, needs more optimization.
9 825 0.656062844575 Henry Cohn, 2024, needs more optimization.
9 826 0.656122863151 Henry Cohn, 2024, needs more optimization.
9 828 0.656309541762 Henry Cohn, 2024, needs more optimization.
9 829 0.656402962495 Henry Cohn, 2024, needs more optimization.
9 830 0.656441164225 Henry Cohn, 2024, needs more optimization.
9 832 0.656633197669 Henry Cohn, 2024, needs more optimization.
9 833 0.656835790396 Henry Cohn, 2024, needs more optimization.
9 834 0.656936881409 Henry Cohn, 2024, needs more optimization.
9 835 0.656996805600 Henry Cohn, 2024, needs more optimization.
9 836 0.657092271473 Henry Cohn, 2024, needs more optimization.
9 837 0.657329083801 Henry Cohn, 2024, needs more optimization.
9 840 0.657392657267 Henry Cohn, 2024, needs more optimization.
9 841 0.657743295092 Henry Cohn, 2024, needs more optimization.
9 842 0.657832396156 Henry Cohn, 2024, needs more optimization.
9 843 0.658001773430 Henry Cohn, 2024, needs more optimization.
9 845 0.658115682474 Henry Cohn, 2024, needs more optimization.
9 846 0.658184790215 Henry Cohn, 2024, needs more optimization.
9 848 0.658383758638 Henry Cohn, 2024, needs more optimization.
9 850 0.658462811548 Henry Cohn, 2024, needs more optimization.
9 852 0.658766697216 Henry Cohn, 2024, needs more optimization.
9 853 0.658967102410 Henry Cohn, 2024, needs more optimization.
9 854 0.659190050231 Henry Cohn, 2024, needs more optimization.
9 856 0.659375912475 Henry Cohn, 2024, needs more optimization.
9 857 0.659414774850 Henry Cohn, 2024, needs more optimization.
9 858 0.659484013418 Henry Cohn, 2024, needs more optimization.
9 860 0.659727020220 Henry Cohn, 2024, needs more optimization.
9 861 0.659910043343 Henry Cohn, 2024, needs more optimization.
9 863 0.659924015022 Henry Cohn, 2024, needs more optimization.
9 864 0.660166123542 Henry Cohn, 2024, needs more optimization.
9 865 0.660241024158 Henry Cohn, 2024, needs more optimization.
9 867 0.660258152252 Henry Cohn, 2024, needs more optimization.
9 868 0.660473163175 Henry Cohn, 2024, needs more optimization.
9 869 0.660662372833 Henry Cohn, 2024, needs more optimization.
9 871 0.660696779866 Henry Cohn, 2024, needs more optimization.
9 872 0.661007842716 Henry Cohn, 2024, needs more optimization.
9 874 0.661037441704 Henry Cohn, 2024, needs more optimization.
9 875 0.661305050811 Henry Cohn, 2024, needs more optimization.
9 876 0.661485790243 Henry Cohn, 2024, needs more optimization.
9 879 0.661597030428 Henry Cohn, 2024, needs more optimization.
9 880 0.661788206896 Henry Cohn, 2024, needs more optimization.
9 882 0.661904445425 Henry Cohn, 2024, needs more optimization.
9 883 0.662168494563 Henry Cohn, 2024, needs more optimization.
9 884 0.662187483976 Henry Cohn, 2024, needs more optimization.
9 885 0.662216755170 Henry Cohn, 2024, needs more optimization.
9 887 0.662407495138 Henry Cohn, 2024, needs more optimization.
9 888 0.662622602605 Henry Cohn, 2024, needs more optimization.
9 889 0.662752508741 Henry Cohn, 2024, needs more optimization.
9 891 0.662879436196 Henry Cohn, 2024, needs more optimization.
9 892 0.662881008458 Henry Cohn, 2024, needs more optimization.
9 893 0.663030819107 Henry Cohn, 2024, needs more optimization.
9 896 0.663099556691 Henry Cohn, 2024, needs more optimization.
9 898 0.663455129249 Henry Cohn, 2024, needs more optimization.
9 899 0.663546654413 Henry Cohn, 2024, needs more optimization.
9 901 0.663693603908 Henry Cohn, 2024, needs more optimization.
9 902 0.663876327774 Henry Cohn, 2024, needs more optimization.
9 905 0.664037285450 Henry Cohn, 2024, needs more optimization.
9 907 0.664419510748 Henry Cohn, 2024, needs more optimization.
9 908 0.664445575376 Henry Cohn, 2024, needs more optimization.
9 910 0.664547515745 Henry Cohn, 2024, needs more optimization.
9 911 0.664811277946 Henry Cohn, 2024, needs more optimization.
9 914 0.664910283908 Henry Cohn, 2024, needs more optimization.
9 917 0.665281156110 Henry Cohn, 2024, needs more optimization.
9 918 0.665511427273 Henry Cohn, 2024, needs more optimization.
9 919 0.665568524459 Henry Cohn, 2024, needs more optimization.
9 922 0.665635047740 Henry Cohn, 2024, needs more optimization.
9 923 0.665997191391 Henry Cohn, 2024, needs more optimization.
9 924 0.666122996139 Henry Cohn, 2024, needs more optimization.
9 925 0.666173389356 Henry Cohn, 2024, needs more optimization.
9 927 0.666336436562 Henry Cohn, 2024, needs more optimization.
9 931 0.666565908284 Henry Cohn, 2024, needs more optimization.
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, preprint, 2024, 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 0.150154619557 Henry Cohn, 2025.
10 34 0.150193686833 Henry Cohn, 2025.
10 35 0.157414060724 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 0.196239837717 Henry Cohn, 2024.
10 43 0.205907349245 Henry Cohn, 2023.
10 44 0.210560489799 Henry Cohn, 2023.
10 45 0.210852888442 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 0.216693334107 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 0.256704396577 Henry Cohn, 2023.
10 61 0.258835264721 Henry Cohn, 2025.
10 62 0.264949402851 Henry Cohn, 2025.
10 63 0.265067765440 Henry Cohn, 2025.
10 66 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
10 67 0.271303448847 Henry Cohn, 2024.
25⁢x4−20⁢x3−10⁢x2+1
10 68 0.275524154611 Henry Cohn, 2024.
10 69 0.275982144251 Henry Cohn, 2024.
10 72 0.275987133320 Henry Cohn, 2024.
10 73 0.278813753189 Henry Cohn, 2024.
10 74 0.279838252095 Henry Cohn, 2025.
10 75 0.284852639993 Henry Cohn, 2024, needs more optimization.
10 76 0.286645863733 Henry Cohn, 2025.
10 77 0.288311763482 Henry Cohn, 2024, needs more optimization.
10 78 0.296975535281 Henry Cohn, 2025.
10 79 0.303029412652 Henry Cohn, 2025.
10 80 0.304027945531 Henry Cohn, 2025.
10 81 0.315256103878 Henry Cohn, 2024, needs more optimization.
10 82 0.319445222938 Henry Cohn, 2025.
10 83 0.321363420052 Henry Cohn, 2025.
10 84 0.323652652912 Henry Cohn, 2025.
10 85 0.324564797629 Henry Cohn, 2024, needs more optimization.
10 86 0.324721588331 Henry Cohn, 2024, needs more optimization.
10 87 0.324782149230 Henry Cohn, 2025, needs more optimization.
10 88 0.324854874716 Henry Cohn, 2024, needs more optimization.
10 89 0.325810134210 Henry Cohn, 2025, needs more optimization.
10 90 0.326810640723 Henry Cohn, 2025, needs more optimization.
10 91 0.328978458897 Henry Cohn, 2025, needs more optimization.
10 92 0.329035737309 Henry Cohn, 2025, needs more optimization.
10 93 0.329547406792 Henry Cohn, 2025, needs more optimization.
10 94 0.329809284888 Henry Cohn, 2024, 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 0.330922311527 Henry Cohn, 2025, needs more optimization.
10 98 0.331014101524 Henry Cohn, 2025, needs more optimization.
10 99 0.331202510314 Henry Cohn, 2025, needs more optimization.
10 100 0.331255782342 Henry Cohn, 2024, needs more optimization.
10 101 0.331771958564 Henry Cohn, 2023, needs more optimization.
10 102 0.331785869642 Henry Cohn, 2025.
10 103 0.333259583856 Henry Cohn, 2024, needs more optimization.
10 104 0.333262369272 Henry Cohn, 2024, needs more optimization.
10 105 0.333276592491 Henry Cohn, 2024, 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 0.335318650634 Henry Cohn, 2024, needs more optimization.
10 110 0.340620761632 Henry Cohn, 2023, 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 0.348684613501 Henry Cohn, 2024, needs more optimization.
10 114 0.350518187162 Henry Cohn, 2024, needs more optimization.
10 115 0.352629567807 Henry Cohn, 2023, needs more optimization.
10 116 0.354276308661 Henry Cohn, 2024, needs more optimization.
10 117 0.361131127566 Henry Cohn, 2024, needs more optimization.
10 118 0.362516515684 Henry Cohn, 2023, needs more optimization.
10 119 0.364865633219 Henry Cohn, 2024, needs more optimization.
10 120 0.365053235138 Henry Cohn, 2024, needs more optimization.
10 124 0.365564414471 Henry Cohn, 2024, needs more optimization.
10 125 0.365564415374 Henry Cohn, 2024, needs more optimization.
10 126 0.365564836872 Henry Cohn, 2024, needs more optimization.
10 127 0.366035053027 Henry Cohn, 2024.
10 128 0.367877988603 Henry Cohn, 2024, needs more optimization.
10 129 0.371169747996 Henry Cohn, 2024, needs more optimization.
10 131 0.371536622584 Henry Cohn, 2024, needs more optimization.
10 132 0.372272319936 Henry Cohn, 2024, needs more optimization.
10 133 0.386695719261 Henry Cohn, 2024, needs more optimization.
10 134 0.390551958511 Henry Cohn, 2024, needs more optimization.
10 135 0.393085484605 Henry Cohn, 2024, needs more optimization.
10 136 0.393902739877 Henry Cohn, 2024, needs more optimization.
10 137 0.397227658864 Henry Cohn, 2024, needs more optimization.
10 138 0.398866926321 Henry Cohn, 2024, needs more optimization.
10 139 0.400975278368 Henry Cohn, 2024, needs more optimization.
10 140 0.401956722238 Henry Cohn, 2024, needs more optimization.
10 141 0.403164423671 Henry Cohn, 2024, needs more optimization.
10 142 0.404804248378 Henry Cohn, 2024, 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 0.421657857689 Henry Cohn, 2024, needs more optimization.
10 158 0.422119858021 Henry Cohn, 2024, needs more optimization.
10 159 0.423569999217 Henry Cohn, 2024, needs more optimization.
10 160 0.424121835575 Henry Cohn, 2024, needs more optimization.
10 161 0.425270105804 Henry Cohn, 2024, needs more optimization.
10 162 0.425892474310 Henry Cohn, 2024, needs more optimization.
10 163 0.426082965287 Henry Cohn, 2024, needs more optimization.
10 164 0.427248635857 Henry Cohn, 2024, needs more optimization.
10 165 0.428193811903 Henry Cohn, 2024, 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 0.439297021692 Henry Cohn, 2024, needs more optimization.
10 196 0.451065176210 Henry Cohn, 2024, needs more optimization.
10 197 0.453205961743 Henry Cohn, 2024, needs more optimization.
10 198 0.453792160604 Henry Cohn, 2024, needs more optimization.
10 199 0.454431768034 Henry Cohn, 2024, needs more optimization.
10 200 0.455326073909 Henry Cohn, 2024, needs more optimization.
10 201 0.455769544796 Henry Cohn, 2024, needs more optimization.
10 202 0.456458559991 Henry Cohn, 2024, needs more optimization.
10 203 0.457096995909 Henry Cohn, 2024, needs more optimization.
10 204 0.457644793777 Henry Cohn, 2024, needs more optimization.
10 205 0.458498367127 Henry Cohn, 2024, needs more optimization.
10 206 0.459110298718 Henry Cohn, 2024, needs more optimization.
10 207 0.459807858367 Henry Cohn, 2024, needs more optimization.
10 208 0.460370276832 Henry Cohn, 2024, needs more optimization.
10 209 0.460915143032 Henry Cohn, 2024, needs more optimization.
10 210 0.461853831285 Henry Cohn, 2024, needs more optimization.
10 211 0.462156364202 Henry Cohn, 2024, needs more optimization.
10 212 0.462915560543 Henry Cohn, 2024, needs more optimization.
10 213 0.463718810819 Henry Cohn, 2024, needs more optimization.
10 215 0.464503621175 Henry Cohn, 2024, needs more optimization.
10 216 0.465281691694 Henry Cohn, 2024, needs more optimization.
10 217 0.466108384159 Henry Cohn, 2024, needs more optimization.
10 218 0.466652379663 Henry Cohn, 2024, needs more optimization.
10 219 0.467171354140 Henry Cohn, 2024, needs more optimization.
10 220 0.467847584478 Henry Cohn, 2024, needs more optimization.
10 221 0.467963942281 Henry Cohn, 2024, needs more optimization.
10 222 0.469050156497 Henry Cohn, 2024, needs more optimization.
10 223 0.469392736040 Henry Cohn, 2024, needs more optimization.
10 224 0.470131562598 Henry Cohn, 2024, needs more optimization.
10 225 0.470625213922 Henry Cohn, 2024, needs more optimization.
10 226 0.471200121930 Henry Cohn, 2024, needs more optimization.
10 227 0.471944844533 Henry Cohn, 2024, needs more optimization.
10 228 0.472627361305 Henry Cohn, 2024, needs more optimization.
10 229 0.472656339738 Henry Cohn, 2024, needs more optimization.
10 230 0.473418798125 Henry Cohn, 2024, needs more optimization.
10 231 0.474161399902 Henry Cohn, 2024, needs more optimization.
10 232 0.474771720293 Henry Cohn, 2024, needs more optimization.
10 233 0.475321539491 Henry Cohn, 2024, needs more optimization.
10 234 0.475838563007 Henry Cohn, 2024, needs more optimization.
10 235 0.476273899679 Henry Cohn, 2024, needs more optimization.
10 236 0.476761264100 Henry Cohn, 2024, needs more optimization.
10 237 0.477555176317 Henry Cohn, 2024, needs more optimization.
10 238 0.478012570312 Henry Cohn, 2024, needs more optimization.
10 239 0.478549102190 Henry Cohn, 2024, needs more optimization.
10 240 0.478969110129 Henry Cohn, 2024, needs more optimization.
10 241 0.479589852234 Henry Cohn, 2024, needs more optimization.
10 242 0.479863564037 Henry Cohn, 2024, needs more optimization.
10 243 0.480432122073 Henry Cohn, 2024, needs more optimization.
10 244 0.481135807646 Henry Cohn, 2024, needs more optimization.
10 245 0.481574042016 Henry Cohn, 2024, needs more optimization.
10 246 0.481966087648 Henry Cohn, 2024, needs more optimization.
10 247 0.482638668393 Henry Cohn, 2024, needs more optimization.
10 248 0.483138187292 Henry Cohn, 2024, needs more optimization.
10 249 0.483512915999 Henry Cohn, 2024, needs more optimization.
10 250 0.483864509360 Henry Cohn, 2024, needs more optimization.
10 251 0.484558802701 Henry Cohn, 2024, needs more optimization.
10 252 0.484826225341 Henry Cohn, 2024, needs more optimization.
10 253 0.485532072134 Henry Cohn, 2024, needs more optimization.
10 254 0.486095520144 Henry Cohn, 2024, needs more optimization.
10 255 0.486542838105 Henry Cohn, 2024, needs more optimization.
10 256 0.486834341924 Henry Cohn, 2024, needs more optimization.
10 257 0.487627132488 Henry Cohn, 2024, needs more optimization.
10 258 0.487768815256 Henry Cohn, 2024, needs more optimization.
10 259 0.488451340856 Henry Cohn, 2024, needs more optimization.
10 260 0.488734430404 Henry Cohn, 2024, needs more optimization.
10 261 0.489491384056 Henry Cohn, 2024, needs more optimization.
10 262 0.490045603876 Henry Cohn, 2024, needs more optimization.
10 263 0.490349029549 Henry Cohn, 2024, needs more optimization.
10 264 0.490600756215 Henry Cohn, 2024, needs more optimization.
10 265 0.491248900713 Henry Cohn, 2024, needs more optimization.
10 266 0.491802233527 Henry Cohn, 2024, needs more optimization.
10 267 0.492247325165 Henry Cohn, 2024, needs more optimization.
10 268 0.492620811732 Henry Cohn, 2024, needs more optimization.
10 269 0.493128434823 Henry Cohn, 2024, needs more optimization.
10 270 0.493591621990 Henry Cohn, 2024, needs more optimization.
10 271 0.494020077152 Henry Cohn, 2024, needs more optimization.
10 272 0.494210067496 Henry Cohn, 2024, needs more optimization.
10 273 0.494446372038 Henry Cohn, 2024, needs more optimization.
10 274 0.494918198848 Henry Cohn, 2024, needs more optimization.
10 275 0.495763875921 Henry Cohn, 2024, needs more optimization.
10 276 0.495964713944 Henry Cohn, 2024, needs more optimization.
10 277 0.496252321776 Henry Cohn, 2024, needs more optimization.
10 278 0.497099363961 Henry Cohn, 2024, needs more optimization.
10 279 0.498043755382 Henry Cohn, 2024, needs more optimization.
10 280 0.498313276042 Henry Cohn, 2024, needs more optimization.
10 281 0.498404179661 Henry Cohn, 2024, needs more optimization.
10 282 0.499056506198 Henry Cohn, 2024, needs more optimization.
10 283 0.499330946866 Henry Cohn, 2024, needs more optimization.
10 510 0.5 M. Ganzhinov, Highly symmetric lines, preprint, 2022, arXiv:2207.08266.
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 0.077296880695 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
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 0.108571212221 H. Cohn, Small spherical and projective codes, data set, updated 2024, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
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 0.193277477549 Henry Cohn, 2023.
11 48 0.198581200102 Henry Cohn, 2024.
11 49 0.201349058297 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 0.209837940546 Henry Cohn, 2024.
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 0.253285704081 Henry Cohn, 2025.
11 70 0.261885065789 Henry Cohn, 2025.
11 71 0.264364568340 Henry Cohn, 2025.
11 72 0.266600075434 Henry Cohn, 2025.
11 88 0.267191024627 Henry Cohn, 2023.
71⁢x2−4⁢x−4
11 89 0.271415424968 Henry Cohn, 2025.
11 90 0.282660978222 Henry Cohn, 2025, needs more optimization.
11 91 0.284308921778 Henry Cohn, 2025, needs more optimization.
11 92 0.285049189189 Henry Cohn, 2025, needs more optimization.
11 93 0.286216553275 Henry Cohn, 2025, needs more optimization.
11 94 0.298848795024 Henry Cohn, 2024, needs more optimization.
11 95 0.308606883963 Henry Cohn, 2025.
11 96 0.311040676183 Henry Cohn, 2025, needs more optimization.
11 97 0.313144511241 Henry Cohn, 2025, needs more optimization.
11 98 0.314772583538 Henry Cohn, 2025, needs more optimization.
11 99 0.316332352750 Henry Cohn, 2025, needs more optimization.
11 100 0.317817664322 Henry Cohn, 2025, needs more optimization.
11 101 0.319423628735 Henry Cohn, 2024, needs more optimization.
11 102 0.320912090309 Henry Cohn, 2025, needs more optimization.
11 103 0.321865876941 Henry Cohn, 2024, needs more optimization.
11 104 0.322444709475 Henry Cohn, 2024, needs more optimization.
11 105 0.323347177159 Henry Cohn, 2024, needs more optimization.
11 106 0.324111693563 Henry Cohn, 2024, needs more optimization.
11 107 0.325107906217 Henry Cohn, 2024, needs more optimization.
11 108 0.326088161934 Henry Cohn, 2024, needs more optimization.
11 109 0.326088618973 Henry Cohn, 2024, needs more optimization.
11 111 0.327513996201 Henry Cohn, 2024, needs more optimization.
11 112 0.327752515271 Henry Cohn, 2023, needs more optimization.
11 113 0.329803040552 Henry Cohn, 2023, needs more optimization.
11 114 0.330031659273 Henry Cohn, 2024, needs more optimization.
11 115 0.330406388060 Henry Cohn, 2024, needs more optimization.
11 117 0.330883912264 Henry Cohn, 2024, needs more optimization.
11 118 0.330883912307 Henry Cohn, 2024, needs more optimization.
11 119 0.331116854340 Henry Cohn, 2023, needs more optimization.
11 120 0.331150136199 Henry Cohn, 2023, needs more optimization.
11 121 0.331853558292 Henry Cohn, 2024, needs more optimization.
11 122 0.331861095984 Henry Cohn, 2023, needs more optimization.
11 123 0.332448533773 Henry Cohn, 2024, needs more optimization.
11 124 0.332448566639 Henry Cohn, 2024, needs more optimization.
11 125 0.333212924685 Henry Cohn, 2023, needs more optimization.
11 126 0.333227597876 Henry Cohn, 2024, needs more optimization.
11 127 0.333270861920 Henry Cohn, 2024, needs more optimization.
11 128 0.333273747639 Henry Cohn, 2024, needs more optimization.
11 129 0.333274996083 Henry Cohn, 2024, needs more optimization.
11 130 0.333276029314 Henry Cohn, 2024, needs more optimization.
11 156 0.333333333334 Henry Cohn, 2024.
3⁢x−1
11 157 0.363728530555 Henry Cohn, 2024, 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 0.387722229231 Henry Cohn, 2024, needs more optimization.
11 168 0.389391527379 Henry Cohn, 2024, needs more optimization.
11 169 0.390170475796 Henry Cohn, 2024, needs more optimization.
11 170 0.391490429618 Henry Cohn, 2024, needs more optimization.
11 171 0.392850460696 Henry Cohn, 2024, needs more optimization.
11 172 0.393657569226 Henry Cohn, 2024, needs more optimization.
11 173 0.395033954695 Henry Cohn, 2024, needs more optimization.
11 174 0.395869456955 Henry Cohn, 2024, needs more optimization.
11 175 0.396736838203 Henry Cohn, 2024, needs more optimization.
11 176 0.398352796192 Henry Cohn, 2024, needs more optimization.
11 177 0.399060629924 Henry Cohn, 2024, needs more optimization.
11 178 0.400114944611 Henry Cohn, 2024, needs more optimization.
11 179 0.401212948825 Henry Cohn, 2024, needs more optimization.
11 180 0.402008054713 Henry Cohn, 2024, needs more optimization.
11 181 0.402840226809 Henry Cohn, 2024, needs more optimization.
11 182 0.404028845859 Henry Cohn, 2024, needs more optimization.
11 183 0.404487593290 Henry Cohn, 2024, needs more optimization.
11 184 0.405668684622 Henry Cohn, 2024, needs more optimization.
11 185 0.406634952271 Henry Cohn, 2024, needs more optimization.
11 186 0.407358366607 Henry Cohn, 2024, needs more optimization.
11 187 0.407944918047 Henry Cohn, 2024, needs more optimization.
11 188 0.409296595777 Henry Cohn, 2024, needs more optimization.
11 189 0.410191685023 Henry Cohn, 2024, needs more optimization.
11 190 0.410306850585 Henry Cohn, 2024, needs more optimization.
11 192 0.411485699691 Henry Cohn, 2024, needs more optimization.
11 193 0.413112726346 Henry Cohn, 2024, needs more optimization.
11 194 0.413686703228 Henry Cohn, 2024, needs more optimization.
11 195 0.413896438364 Henry Cohn, 2024, needs more optimization.
11 196 0.414976984303 Henry Cohn, 2024, needs more optimization.
11 197 0.415324616108 Henry Cohn, 2024, needs more optimization.
11 198 0.416238786678 Henry Cohn, 2024, needs more optimization.
11 199 0.417274705380 Henry Cohn, 2024, needs more optimization.
11 200 0.417785770400 Henry Cohn, 2024, needs more optimization.
11 201 0.418400378586 Henry Cohn, 2024, needs more optimization.
11 202 0.418878054921 Henry Cohn, 2024, needs more optimization.
11 203 0.419441442826 Henry Cohn, 2024, needs more optimization.
11 204 0.419982879052 Henry Cohn, 2024, needs more optimization.
11 205 0.420769017640 Henry Cohn, 2024, needs more optimization.
11 206 0.421521115488 Henry Cohn, 2024, needs more optimization.
11 207 0.422102628006 Henry Cohn, 2024, needs more optimization.
11 208 0.422715436488 Henry Cohn, 2024, needs more optimization.
11 209 0.423419399386 Henry Cohn, 2024, needs more optimization.
11 210 0.424062207347 Henry Cohn, 2024, needs more optimization.
11 211 0.424502284272 Henry Cohn, 2024, needs more optimization.
11 212 0.425242699985 Henry Cohn, 2024, needs more optimization.
11 213 0.425835492599 Henry Cohn, 2024, needs more optimization.
11 214 0.426358697600 Henry Cohn, 2024, needs more optimization.
11 215 0.426886357282 Henry Cohn, 2024, needs more optimization.
11 216 0.427442154929 Henry Cohn, 2024, needs more optimization.
11 217 0.428038463918 Henry Cohn, 2024, needs more optimization.
11 224 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
11 225 0.430945568080 Henry Cohn, 2024, needs more optimization.
11 226 0.433028105421 Henry Cohn, 2024, needs more optimization.
11 227 0.433859701409 Henry Cohn, 2024, needs more optimization.
11 228 0.434434763567 Henry Cohn, 2024, needs more optimization.
11 229 0.434830203784 Henry Cohn, 2024, needs more optimization.
11 230 0.435650211709 Henry Cohn, 2024, needs more optimization.
11 231 0.436027521618 Henry Cohn, 2024, needs more optimization.
11 232 0.436712434095 Henry Cohn, 2024, needs more optimization.
11 233 0.437283002042 Henry Cohn, 2024, needs more optimization.
11 234 0.437606412817 Henry Cohn, 2024, needs more optimization.
11 235 0.438119446578 Henry Cohn, 2024, needs more optimization.
11 236 0.438793698212 Henry Cohn, 2024, needs more optimization.
11 237 0.439248677158 Henry Cohn, 2024, needs more optimization.
11 238 0.439665660845 Henry Cohn, 2024, needs more optimization.
11 239 0.440010753003 Henry Cohn, 2024, needs more optimization.
11 240 0.440743834790 Henry Cohn, 2024, needs more optimization.
11 241 0.441502863786 Henry Cohn, 2024, needs more optimization.
11 242 0.441966768156 Henry Cohn, 2024, needs more optimization.
11 243 0.442518469544 Henry Cohn, 2024, needs more optimization.
11 244 0.442690090583 Henry Cohn, 2024, needs more optimization.
11 245 0.443086597505 Henry Cohn, 2024, needs more optimization.
11 246 0.443869392521 Henry Cohn, 2024, needs more optimization.
11 247 0.444277222162 Henry Cohn, 2024, needs more optimization.
11 248 0.445175256924 Henry Cohn, 2024, needs more optimization.
11 249 0.445619004777 Henry Cohn, 2024, needs more optimization.
11 250 0.445987541728 Henry Cohn, 2024, needs more optimization.
11 251 0.446311480044 Henry Cohn, 2024, needs more optimization.
11 252 0.446881171502 Henry Cohn, 2024, needs more optimization.
11 253 0.447297470697 Henry Cohn, 2024, needs more optimization.
11 254 0.447988346809 Henry Cohn, 2024, needs more optimization.
11 255 0.448582681980 Henry Cohn, 2024, needs more optimization.
11 256 0.448904365202 Henry Cohn, 2024, needs more optimization.
11 257 0.449472675151 Henry Cohn, 2024, needs more optimization.
11 258 0.450067939779 Henry Cohn, 2024, needs more optimization.
11 259 0.450477957723 Henry Cohn, 2024, needs more optimization.
11 260 0.450761028154 Henry Cohn, 2024, needs more optimization.
11 261 0.451460296117 Henry Cohn, 2024, needs more optimization.
11 262 0.451773110981 Henry Cohn, 2024, needs more optimization.
11 263 0.452133925068 Henry Cohn, 2024, needs more optimization.
11 264 0.452616253718 Henry Cohn, 2024, needs more optimization.
11 265 0.453229751432 Henry Cohn, 2024, needs more optimization.
11 266 0.453749946828 Henry Cohn, 2024, needs more optimization.
11 267 0.454042290565 Henry Cohn, 2024, needs more optimization.
11 268 0.454518317099 Henry Cohn, 2024, needs more optimization.
11 293 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
11 294 0.465818613274 Henry Cohn, 2024, needs more optimization.
11 295 0.466117440244 Henry Cohn, 2024, needs more optimization.
11 296 0.466877720002 Henry Cohn, 2024, needs more optimization.
11 297 0.467191495262 Henry Cohn, 2024, needs more optimization.
11 298 0.467902801896 Henry Cohn, 2024, needs more optimization.
11 299 0.468008220268 Henry Cohn, 2024, needs more optimization.
11 300 0.468405326037 Henry Cohn, 2024, needs more optimization.
11 301 0.468787015701 Henry Cohn, 2024, needs more optimization.
11 302 0.469273661150 Henry Cohn, 2024, needs more optimization.
11 303 0.469922685620 Henry Cohn, 2024, needs more optimization.
11 304 0.470263000491 Henry Cohn, 2024, needs more optimization.
11 305 0.470617019492 Henry Cohn, 2024, needs more optimization.
11 306 0.470924258001 Henry Cohn, 2024, needs more optimization.
11 307 0.471292800064 Henry Cohn, 2024, needs more optimization.
11 308 0.471550751368 Henry Cohn, 2024, needs more optimization.
11 309 0.471935907073 Henry Cohn, 2024, needs more optimization.
11 310 0.472124415972 Henry Cohn, 2024, needs more optimization.
11 311 0.472809390664 Henry Cohn, 2024, needs more optimization.
11 312 0.472813354765 Henry Cohn, 2024, needs more optimization.
11 314 0.473548108194 Henry Cohn, 2024, needs more optimization.
11 315 0.474265087738 Henry Cohn, 2024, needs more optimization.
11 316 0.474446858538 Henry Cohn, 2024, needs more optimization.
11 317 0.474524010522 Henry Cohn, 2024, needs more optimization.
11 318 0.475233301345 Henry Cohn, 2024, needs more optimization.
11 319 0.475630199047 Henry Cohn, 2024, needs more optimization.
11 320 0.475759312614 Henry Cohn, 2024, needs more optimization.
11 321 0.476493543462 Henry Cohn, 2024, needs more optimization.
11 322 0.476664855522 Henry Cohn, 2024, needs more optimization.
11 323 0.477216954661 Henry Cohn, 2024, needs more optimization.
11 324 0.477381808725 Henry Cohn, 2024, needs more optimization.
11 325 0.477579689044 Henry Cohn, 2024, needs more optimization.
11 326 0.477897461765 Henry Cohn, 2024, needs more optimization.
11 327 0.478442841090 Henry Cohn, 2024, needs more optimization.
11 329 0.479035042709 Henry Cohn, 2024, needs more optimization.
11 330 0.479274998817 Henry Cohn, 2024, needs more optimization.
11 331 0.479788239041 Henry Cohn, 2024, needs more optimization.
11 332 0.480168372448 Henry Cohn, 2024, needs more optimization.
11 333 0.480654965436 Henry Cohn, 2024, needs more optimization.
11 334 0.481473155061 Henry Cohn, 2024, needs more optimization.
11 335 0.481625471944 Henry Cohn, 2024, needs more optimization.
11 337 0.481666489194 Henry Cohn, 2024, needs more optimization.
11 338 0.482107706576 Henry Cohn, 2024, needs more optimization.
11 339 0.482336976927 Henry Cohn, 2024, needs more optimization.
11 340 0.483070879321 Henry Cohn, 2024, needs more optimization.
11 341 0.483497327631 Henry Cohn, 2024, needs more optimization.
11 342 0.483928741182 Henry Cohn, 2024, needs more optimization.
11 344 0.483997443744 Henry Cohn, 2024, needs more optimization.
11 345 0.484429935956 Henry Cohn, 2024, needs more optimization.
11 347 0.485077176155 Henry Cohn, 2024, needs more optimization.
11 348 0.485456240606 Henry Cohn, 2024, needs more optimization.
11 350 0.485981579846 Henry Cohn, 2024, needs more optimization.
11 352 0.486673860686 Henry Cohn, 2024, needs more optimization.
11 353 0.487277809613 Henry Cohn, 2024, needs more optimization.
11 354 0.487474475444 Henry Cohn, 2024, needs more optimization.
11 355 0.487857508121 Henry Cohn, 2024, needs more optimization.
11 356 0.487889373172 Henry Cohn, 2024, needs more optimization.
11 357 0.488620095747 Henry Cohn, 2024, needs more optimization.
11 358 0.489002822541 Henry Cohn, 2024, needs more optimization.
11 359 0.489129367474 Henry Cohn, 2024, needs more optimization.
11 360 0.489157371350 Henry Cohn, 2024, needs more optimization.
11 361 0.489475226163 Henry Cohn, 2024, needs more optimization.
11 362 0.490332158670 Henry Cohn, 2024, needs more optimization.
11 363 0.490489325359 Henry Cohn, 2024, needs more optimization.
11 364 0.490558217258 Henry Cohn, 2024, needs more optimization.
11 365 0.491091615401 Henry Cohn, 2024, needs more optimization.
11 366 0.491118423933 Henry Cohn, 2024, needs more optimization.
11 367 0.491813268979 Henry Cohn, 2024, needs more optimization.
11 368 0.491987764115 Henry Cohn, 2024, needs more optimization.
11 369 0.492213099487 Henry Cohn, 2024, needs more optimization.
11 370 0.492520899573 Henry Cohn, 2024, needs more optimization.
11 371 0.492826927101 Henry Cohn, 2024, needs more optimization.
11 372 0.493137157287 Henry Cohn, 2024, needs more optimization.
11 373 0.493838307322 Henry Cohn, 2024, needs more optimization.
11 375 0.493841932615 Henry Cohn, 2024, needs more optimization.
11 376 0.494177334613 Henry Cohn, 2024, needs more optimization.
11 377 0.494465332401 Henry Cohn, 2024, needs more optimization.
11 378 0.494836548858 Henry Cohn, 2024, needs more optimization.
11 379 0.495078911638 Henry Cohn, 2024, needs more optimization.
11 380 0.495611077764 Henry Cohn, 2024, needs more optimization.
11 381 0.495696132134 Henry Cohn, 2024, needs more optimization.
11 382 0.495846036218 Henry Cohn, 2024, needs more optimization.
11 383 0.496277726235 Henry Cohn, 2024, needs more optimization.
11 384 0.496455231277 Henry Cohn, 2024, needs more optimization.
11 385 0.497050106126 Henry Cohn, 2024, needs more optimization.
11 386 0.497327194854 Henry Cohn, 2024, needs more optimization.
11 387 0.497355937207 Henry Cohn, 2024, needs more optimization.
11 389 0.497509189194 Henry Cohn, 2024, needs more optimization.
11 390 0.498326308217 Henry Cohn, 2024, needs more optimization.
11 391 0.498407975888 Henry Cohn, 2024, needs more optimization.
11 392 0.498932583872 Henry Cohn, 2024, needs more optimization.
11 393 0.499224721628 Henry Cohn, 2024, needs more optimization.
11 394 0.499420673608 Henry Cohn, 2024, needs more optimization.
11 396 0.499797822481 Henry Cohn, 2024, needs more optimization.
11 397 0.499997103646 Henry Cohn, 2024, needs more optimization.
11 592 0.5 M. Ganzhinov, Highly symmetric lines, preprint, 2022, arXiv:2207.08266.
2⁢x−1
11 593 0.542166805849 Henry Cohn, 2024, needs more optimization.
11 594 0.542373072314 Henry Cohn, 2024, needs more optimization.
11 595 0.542636788628 Henry Cohn, 2024, needs more optimization.
11 596 0.542824525965 Henry Cohn, 2024, needs more optimization.
11 597 0.542965137370 Henry Cohn, 2024, needs more optimization.
11 598 0.543089938752 Henry Cohn, 2024, needs more optimization.
11 599 0.543196722572 Henry Cohn, 2024, needs more optimization.
11 601 0.543387157147 Henry Cohn, 2024, needs more optimization.
11 602 0.543837340934 Henry Cohn, 2024, needs more optimization.
11 603 0.543949188905 Henry Cohn, 2024, needs more optimization.
11 604 0.544082398293 Henry Cohn, 2024, needs more optimization.
11 605 0.544262815270 Henry Cohn, 2024, needs more optimization.
11 606 0.544581411516 Henry Cohn, 2024, needs more optimization.
11 607 0.544685372801 Henry Cohn, 2024, needs more optimization.
11 608 0.544908488221 Henry Cohn, 2024, needs more optimization.
11 610 0.544999389667 Henry Cohn, 2024, needs more optimization.
11 611 0.545421576009 Henry Cohn, 2024, needs more optimization.
11 612 0.545479985058 Henry Cohn, 2024, needs more optimization.
11 614 0.545591268670 Henry Cohn, 2024, needs more optimization.
11 616 0.546152892319 Henry Cohn, 2024, needs more optimization.
11 617 0.546166884274 Henry Cohn, 2024, needs more optimization.
11 618 0.546588496875 Henry Cohn, 2024, needs more optimization.
11 619 0.546618554743 Henry Cohn, 2024, needs more optimization.
11 620 0.546806604898 Henry Cohn, 2024, needs more optimization.
11 622 0.547012977072 Henry Cohn, 2024, needs more optimization.
11 625 0.547143874126 Henry Cohn, 2024, needs more optimization.
11 626 0.547597493108 Henry Cohn, 2024, needs more optimization.
11 628 0.547760593053 Henry Cohn, 2024, needs more optimization.
11 630 0.548438032309 Henry Cohn, 2024, needs more optimization.
11 631 0.548569445989 Henry Cohn, 2024, needs more optimization.
11 633 0.548597434778 Henry Cohn, 2024, needs more optimization.
11 636 0.549126999037 Henry Cohn, 2024, needs more optimization.
11 638 0.549517753525 Henry Cohn, 2024, needs more optimization.
11 639 0.549619645465 Henry Cohn, 2024, needs more optimization.
11 640 0.549731596793 Henry Cohn, 2024, needs more optimization.
11 641 0.550139962982 Henry Cohn, 2024, needs more optimization.
11 642 0.550193273782 Henry Cohn, 2024, needs more optimization.
11 643 0.550215282830 Henry Cohn, 2024, needs more optimization.
11 644 0.550681125595 Henry Cohn, 2024, needs more optimization.
11 646 0.550719102068 Henry Cohn, 2024, needs more optimization.
11 647 0.551088089130 Henry Cohn, 2024, needs more optimization.
11 651 0.551407870920 Henry Cohn, 2024, needs more optimization.
11 652 0.551674877670 Henry Cohn, 2024, needs more optimization.
11 653 0.551886885566 Henry Cohn, 2024, needs more optimization.
11 654 0.552054870309 Henry Cohn, 2024, needs more optimization.
11 656 0.552301337830 Henry Cohn, 2024, needs more optimization.
11 658 0.552511984481 Henry Cohn, 2024, needs more optimization.
11 660 0.552935937988 Henry Cohn, 2024, needs more optimization.
11 662 0.553191190730 Henry Cohn, 2024, needs more optimization.
11 664 0.553270476154 Henry Cohn, 2024, needs more optimization.
11 666 0.553689169353 Henry Cohn, 2024, needs more optimization.
11 667 0.553988733664 Henry Cohn, 2024, needs more optimization.
11 668 0.554126456578 Henry Cohn, 2024, needs more optimization.
11 669 0.554265784694 Henry Cohn, 2024, needs more optimization.
11 670 0.554326200853 Henry Cohn, 2024, needs more optimization.
11 671 0.554496857192 Henry Cohn, 2024, needs more optimization.
11 672 0.554742555812 Henry Cohn, 2024, needs more optimization.
11 673 0.555006293329 Henry Cohn, 2024, needs more optimization.
11 675 0.555115562931 Henry Cohn, 2024, needs more optimization.
11 676 0.555375880758 Henry Cohn, 2024, needs more optimization.
11 677 0.555462637644 Henry Cohn, 2024, needs more optimization.
11 679 0.555521427561 Henry Cohn, 2024, 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
11 984 0.590012090363 Henry Cohn, 2024, needs more optimization.
11 985 0.590119691865 Henry Cohn, 2024, needs more optimization.
11 987 0.590187435878 Henry Cohn, 2024, needs more optimization.
11 988 0.590614015574 Henry Cohn, 2024, needs more optimization.
11 990 0.590817460575 Henry Cohn, 2024, needs more optimization.
11 992 0.590818885180 Henry Cohn, 2024, needs more optimization.
11 994 0.590972623258 Henry Cohn, 2024, needs more optimization.
11 996 0.591212333688 Henry Cohn, 2024, needs more optimization.
11 997 0.591232020965 Henry Cohn, 2024, needs more optimization.
11 999 0.591493727317 Henry Cohn, 2024, needs more optimization.
11 1004 0.591588941919 Henry Cohn, 2024, needs more optimization.
11 1005 0.592017801301 Henry Cohn, 2024, needs more optimization.
11 1007 0.592169408952 Henry Cohn, 2024, needs more optimization.
11 1009 0.592308571380 Henry Cohn, 2024, needs more optimization.
11 1010 0.592529109387 Henry Cohn, 2024, needs more optimization.
11 1012 0.592637923831 Henry Cohn, 2024, needs more optimization.
11 1014 0.592655784570 Henry Cohn, 2024, needs more optimization.
11 1016 0.593011586794 Henry Cohn, 2024, needs more optimization.
11 1019 0.593055496623 Henry Cohn, 2024, needs more optimization.
11 1021 0.593528325981 Henry Cohn, 2024, needs more optimization.
11 1023 0.593579862187 Henry Cohn, 2024, needs more optimization.
11 1024 0.593657884661 Henry Cohn, 2024, 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, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
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 0.119914148449 Henry Cohn, 2023.
12 36 0.121737723964 Henry Cohn, 2024.
12 37 0.121971459128 Henry Cohn, 2023.
359⁢x2+30⁢x−9
12 38 0.130788914737 Henry Cohn, 2023.
63002864⁢x4+17841888⁢x3−1199448⁢x2−239112⁢x−6561
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 0.150221894102 Henry Cohn, 2024.
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 0.180095499631 Henry Cohn, 2023.
12 53 0.187411675260 Henry Cohn, 2024.
12 54 0.189746662791 Henry Cohn, 2024.
12 55 0.193425299011 Henry Cohn, 2024.
12 56 0.201062534083 Henry Cohn, 2024.
12 57 0.201958116645 Henry Cohn, 2025.
12 58 0.204393820757 Henry Cohn, 2025.
12 59 0.205166970734 Henry Cohn, 2025.
12 60 0.207656060114 Henry Cohn, 2025.
12 61 0.211404137275 Henry Cohn, 2025.
12 62 0.213865980255 Henry Cohn, 2025.
12 63 0.214216646427 Henry Cohn, 2025.
12 64 0.218883924070 Henry Cohn, 2025.
12 65 0.220878906832 Henry Cohn, 2025.
12 66 0.221524844720 Henry Cohn, 2024, needs more optimization.
12 67 0.223878531613 Henry Cohn, 2025.
12 68 0.227711036968 Henry Cohn, 2025.
12 69 0.229395794726 Henry Cohn, 2024, needs more optimization.
12 70 0.232600795585 Henry Cohn, 2024, needs more optimization.
12 71 0.235449366070 Henry Cohn, 2025.
12 72 0.237810387272 Henry Cohn, 2025.
12 73 0.240583639265 Henry Cohn, 2025.
12 74 0.242782617373 Henry Cohn, 2025.
12 75 0.245156410236 Henry Cohn, 2024, needs more optimization.
12 76 0.247525915196 Henry Cohn, 2025.
12 77 0.249773910919 Henry Cohn, 2024, needs more optimization.
12 78 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.
4⁢x−1
12 79 0.253489783641 Henry Cohn, 2025.
12 80 0.254149331489 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.
96⁢x3+33⁢x2−50⁢x+9
12 81 0.257604744952 Henry Cohn, 2024, needs more optimization.
12 82 0.259221358201 Henry Cohn, 2024, needs more optimization.
12 83 0.261215633290 Henry Cohn, 2024, needs more optimization.
12 84 0.262899344296 Henry Cohn, 2024, needs more optimization.
12 85 0.264690716894 Henry Cohn, 2024, needs more optimization.
12 86 0.266316534374 Henry Cohn, 2024, needs more optimization.
12 87 0.267073532732 Henry Cohn, 2024, needs more optimization.
12 88 0.267144530589 Henry Cohn, 2025, needs more optimization.
12 93 0.267190847653 Henry Cohn, 2025, needs more optimization.
12 94 0.267190848201 Henry Cohn, 2024, needs more optimization.
12 95 0.267190848293 Henry Cohn, 2025, needs more optimization.
12 96 0.272726687648 Henry Cohn, 2024, needs more optimization.
12 97 0.282208649050 Henry Cohn, 2025, needs more optimization.
12 98 0.283388573344 Henry Cohn, 2025, needs more optimization.
12 99 0.284621834575 Henry Cohn, 2025, needs more optimization.
12 100 0.286196851919 Henry Cohn, 2024, needs more optimization.
12 101 0.287403740605 Henry Cohn, 2024, needs more optimization.
12 102 0.289213058850 Henry Cohn, 2024, needs more optimization.
12 103 0.290301057236 Henry Cohn, 2024, needs more optimization.
12 104 0.291679827824 Henry Cohn, 2024, needs more optimization.
12 105 0.293117877420 Henry Cohn, 2024, needs more optimization.
12 106 0.295397421768 Henry Cohn, 2024, needs more optimization.
12 107 0.296856742456 Henry Cohn, 2024, needs more optimization.
12 108 0.297753546117 Henry Cohn, 2024, needs more optimization.
12 109 0.299341729618 Henry Cohn, 2024, needs more optimization.
12 110 0.301543654449 Henry Cohn, 2024, needs more optimization.
12 111 0.302746929192 Henry Cohn, 2024, needs more optimization.
12 112 0.304209400673 Henry Cohn, 2024, needs more optimization.
12 113 0.306272024855 Henry Cohn, 2024, needs more optimization.
12 114 0.307262831341 Henry Cohn, 2024, needs more optimization.
12 115 0.308931288948 Henry Cohn, 2024, needs more optimization.
12 116 0.310010372734 Henry Cohn, 2024, needs more optimization.
12 117 0.311046380385 Henry Cohn, 2024, needs more optimization.
12 118 0.312603711294 Henry Cohn, 2024, needs more optimization.
12 119 0.313831156765 Henry Cohn, 2024, needs more optimization.
12 120 0.314945670523 Henry Cohn, 2024, needs more optimization.
12 121 0.316271867124 Henry Cohn, 2024, needs more optimization.
12 122 0.316824537749 Henry Cohn, 2024, needs more optimization.
12 123 0.318210769837 Henry Cohn, 2024, needs more optimization.
12 124 0.319006331671 Henry Cohn, 2024, needs more optimization.
12 125 0.319203499874 Henry Cohn, 2024, needs more optimization.
12 126 0.319539745481 Henry Cohn, 2024, needs more optimization.
12 127 0.321876910104 Henry Cohn, 2024, needs more optimization.
12 128 0.321897014778 Henry Cohn, 2024, needs more optimization.
12 129 0.322215091285 Henry Cohn, 2024, needs more optimization.
12 130 0.323167983079 Henry Cohn, 2024, needs more optimization.
12 131 0.323807670076 Henry Cohn, 2024, needs more optimization.
12 132 0.323837507315 Henry Cohn, 2024, needs more optimization.
12 134 0.325266128594 Henry Cohn, 2024, needs more optimization.
12 136 0.325662703593 Henry Cohn, 2024, needs more optimization.
12 137 0.326445021034 Henry Cohn, 2024, needs more optimization.
12 138 0.326445475563 Henry Cohn, 2024, needs more optimization.
12 141 0.327356801665 Henry Cohn, 2024, needs more optimization.
12 142 0.327356972064 Henry Cohn, 2024, needs more optimization.
12 144 0.330233863347 Henry Cohn, 2024, needs more optimization.
12 146 0.330572430251 Henry Cohn, 2024, needs more optimization.
12 147 0.330906347225 Henry Cohn, 2024, needs more optimization.
12 148 0.330906347293 Henry Cohn, 2024, needs more optimization.
12 149 0.332832759003 Henry Cohn, 2024, needs more optimization.
12 150 0.332832983013 Henry Cohn, 2024, needs more optimization.
12 151 0.333330342340 Henry Cohn, 2024, needs more optimization.
12 152 0.333330352684 Henry Cohn, 2024, needs more optimization.
12 153 0.333330361343 Henry Cohn, 2024, needs more optimization.
12 154 0.333330367250 Henry Cohn, 2024, needs more optimization.
12 155 0.333330378311 Henry Cohn, 2024, needs more optimization.
12 156 0.333330388687 Henry Cohn, 2024, needs more optimization.
12 157 0.333330393950 Henry Cohn, 2024, needs more optimization.
12 158 0.333330402239 Henry Cohn, 2024, needs more optimization.
12 159 0.333330409036 Henry Cohn, 2024, needs more optimization.
12 160 0.333330418678 Henry Cohn, 2024, needs more optimization.
12 161 0.333330428500 Henry Cohn, 2024, needs more optimization.
12 162 0.333330436804 Henry Cohn, 2024, needs more optimization.
12 163 0.333330447652 Henry Cohn, 2024, needs more optimization.
12 164 0.333330458310 Henry Cohn, 2024, needs more optimization.
12 165 0.333330471544 Henry Cohn, 2024, needs more optimization.
12 166 0.333330485782 Henry Cohn, 2024, needs more optimization.
12 167 0.333330498087 Henry Cohn, 2024, needs more optimization.
12 168 0.333330515215 Henry Cohn, 2024, needs more optimization.
12 169 0.350299733477 Henry Cohn, 2024, needs more optimization.
12 170 0.350682600484 Henry Cohn, 2024, needs more optimization.
12 171 0.351893627839 Henry Cohn, 2024, needs more optimization.
12 172 0.352006576038 Henry Cohn, 2024, needs more optimization.
12 173 0.353496936378 Henry Cohn, 2024, needs more optimization.
12 174 0.353968793093 Henry Cohn, 2024, needs more optimization.
12 176 0.355113812809 Henry Cohn, 2024, needs more optimization.
12 177 0.357329338267 Henry Cohn, 2024, needs more optimization.
12 178 0.357427812261 Henry Cohn, 2024, needs more optimization.
12 179 0.358393335972 Henry Cohn, 2024, needs more optimization.
12 180 0.359212120924 Henry Cohn, 2024, needs more optimization.
12 182 0.360485176813 Henry Cohn, 2024, needs more optimization.
12 183 0.362489681855 Henry Cohn, 2024, needs more optimization.
12 184 0.363101281633 Henry Cohn, 2024, needs more optimization.
12 186 0.364676550537 Henry Cohn, 2024, needs more optimization.
12 187 0.366231387876 Henry Cohn, 2024, needs more optimization.
12 188 0.367440902339 Henry Cohn, 2024, needs more optimization.
12 189 0.368850434550 Henry Cohn, 2024, needs more optimization.
12 190 0.370125489408 Henry Cohn, 2024, needs more optimization.
12 191 0.370846431497 Henry Cohn, 2024, needs more optimization.
12 192 0.373615418047 Henry Cohn, 2024, needs more optimization.
12 193 0.374513723018 Henry Cohn, 2024, needs more optimization.
12 195 0.374732044928 Henry Cohn, 2024, 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 0.388935345471 Henry Cohn, 2024, needs more optimization.
12 212 0.391450462408 Henry Cohn, 2024, needs more optimization.
12 213 0.392340052554 Henry Cohn, 2024, needs more optimization.
12 214 0.393111408921 Henry Cohn, 2024, needs more optimization.
12 215 0.393913723277 Henry Cohn, 2024, needs more optimization.
12 216 0.394302515872 Henry Cohn, 2024, needs more optimization.
12 217 0.395221777776 Henry Cohn, 2024, needs more optimization.
12 218 0.395844057325 Henry Cohn, 2024, needs more optimization.
12 219 0.396549301452 Henry Cohn, 2024, needs more optimization.
12 220 0.397085779594 Henry Cohn, 2024, needs more optimization.
12 221 0.397734927353 Henry Cohn, 2024, needs more optimization.
12 222 0.398415065129 Henry Cohn, 2024, needs more optimization.
12 223 0.399010215046 Henry Cohn, 2024, needs more optimization.
12 224 0.399338755055 Henry Cohn, 2024, 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 0.430891145798 Henry Cohn, 2024, needs more optimization.
12 291 0.431281593111 Henry Cohn, 2024, needs more optimization.
12 292 0.432395009324 Henry Cohn, 2024, needs more optimization.
12 293 0.432580475003 Henry Cohn, 2024, needs more optimization.
12 294 0.432772369006 Henry Cohn, 2024, needs more optimization.
12 295 0.433130415918 Henry Cohn, 2024, needs more optimization.
12 296 0.433791101461 Henry Cohn, 2024, needs more optimization.
12 297 0.434228017698 Henry Cohn, 2024, needs more optimization.
12 298 0.434386557362 Henry Cohn, 2024, needs more optimization.
12 299 0.435240637209 Henry Cohn, 2024, needs more optimization.
12 300 0.435277394193 Henry Cohn, 2024, needs more optimization.
12 301 0.435448798235 Henry Cohn, 2024, needs more optimization.
12 302 0.435739667238 Henry Cohn, 2024, needs more optimization.
12 303 0.436445383700 Henry Cohn, 2024, needs more optimization.
12 304 0.436878509806 Henry Cohn, 2024, needs more optimization.
12 305 0.437173454198 Henry Cohn, 2024, needs more optimization.
12 306 0.437581602736 Henry Cohn, 2024, needs more optimization.
12 309 0.438175512678 Henry Cohn, 2024, needs more optimization.
12 310 0.438987558575 Henry Cohn, 2024, needs more optimization.
12 311 0.439620704345 Henry Cohn, 2024, needs more optimization.
12 312 0.439997670698 Henry Cohn, 2024, needs more optimization.
12 313 0.440344845785 Henry Cohn, 2024, needs more optimization.
12 314 0.440428040487 Henry Cohn, 2024, needs more optimization.
12 316 0.441160873604 Henry Cohn, 2024, needs more optimization.
12 317 0.441522002689 Henry Cohn, 2024, needs more optimization.
12 318 0.442034498452 Henry Cohn, 2024, needs more optimization.
12 320 0.442335638652 Henry Cohn, 2024, needs more optimization.
12 321 0.442718885769 Henry Cohn, 2024, needs more optimization.
12 322 0.443863176798 Henry Cohn, 2024, needs more optimization.
12 323 0.443975086904 Henry Cohn, 2024, needs more optimization.
12 324 0.444086353366 Henry Cohn, 2024, needs more optimization.
12 325 0.444374002110 Henry Cohn, 2024, 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 0.469963565341 Henry Cohn, 2024, needs more optimization.
12 411 0.470639555795 Henry Cohn, 2024, needs more optimization.
12 412 0.470853590706 Henry Cohn, 2024, needs more optimization.
12 413 0.471109171996 Henry Cohn, 2024, needs more optimization.
12 414 0.471734020611 Henry Cohn, 2024, needs more optimization.
12 415 0.471744898271 Henry Cohn, 2024, needs more optimization.
12 416 0.471844221628 Henry Cohn, 2024, needs more optimization.
12 417 0.472304007342 Henry Cohn, 2024, needs more optimization.
12 418 0.472561453758 Henry Cohn, 2024, needs more optimization.
12 419 0.473021372741 Henry Cohn, 2024, needs more optimization.
12 420 0.473138813931 Henry Cohn, 2024, needs more optimization.
12 421 0.473193576067 Henry Cohn, 2024, needs more optimization.
12 422 0.473532904343 Henry Cohn, 2024, needs more optimization.
12 423 0.473618185440 Henry Cohn, 2024, needs more optimization.
12 424 0.474111889418 Henry Cohn, 2024, needs more optimization.
12 425 0.474394433019 Henry Cohn, 2024, needs more optimization.
12 426 0.474502485853 Henry Cohn, 2024, needs more optimization.
12 427 0.474644421417 Henry Cohn, 2024, needs more optimization.
12 428 0.475093494992 Henry Cohn, 2024, needs more optimization.
12 429 0.475189211770 Henry Cohn, 2024, needs more optimization.
12 430 0.475532704632 Henry Cohn, 2024, needs more optimization.
12 431 0.475709143660 Henry Cohn, 2024, needs more optimization.
12 432 0.476056806733 Henry Cohn, 2024, needs more optimization.
12 433 0.476247874685 Henry Cohn, 2024, needs more optimization.
12 434 0.476524310126 Henry Cohn, 2024, needs more optimization.
12 435 0.476876214859 Henry Cohn, 2024, needs more optimization.
12 436 0.476995193746 Henry Cohn, 2024, needs more optimization.
12 437 0.477461770271 Henry Cohn, 2024, needs more optimization.
12 438 0.477616527655 Henry Cohn, 2024, needs more optimization.
12 439 0.477950621101 Henry Cohn, 2024, needs more optimization.
12 441 0.478132543399 Henry Cohn, 2024, needs more optimization.
12 442 0.478384372443 Henry Cohn, 2024, needs more optimization.
12 443 0.478614280458 Henry Cohn, 2024, needs more optimization.
12 444 0.479076998235 Henry Cohn, 2024, needs more optimization.
12 445 0.479133094515 Henry Cohn, 2024, needs more optimization.
12 446 0.479450115806 Henry Cohn, 2024, needs more optimization.
12 448 0.479581777973 Henry Cohn, 2024, needs more optimization.
12 449 0.480203197656 Henry Cohn, 2024, needs more optimization.
12 450 0.480448560384 Henry Cohn, 2024, needs more optimization.
12 451 0.480680593742 Henry Cohn, 2024, needs more optimization.
12 452 0.480839465272 Henry Cohn, 2024, needs more optimization.
12 453 0.481244024103 Henry Cohn, 2024, needs more optimization.
12 455 0.481336804101 Henry Cohn, 2024, needs more optimization.
12 457 0.481957780841 Henry Cohn, 2024, needs more optimization.
12 458 0.482247309520 Henry Cohn, 2024, needs more optimization.
12 459 0.482427342738 Henry Cohn, 2024, needs more optimization.
12 460 0.482699680590 Henry Cohn, 2024, needs more optimization.
12 461 0.483121347486 Henry Cohn, 2024, needs more optimization.
12 462 0.483139561724 Henry Cohn, 2024, needs more optimization.
12 463 0.483224943998 Henry Cohn, 2024, needs more optimization.
12 465 0.483753956340 Henry Cohn, 2024, needs more optimization.
12 466 0.484099039015 Henry Cohn, 2024, needs more optimization.
12 467 0.484314857629 Henry Cohn, 2024, needs more optimization.
12 468 0.484439610659 Henry Cohn, 2024, needs more optimization.
12 469 0.484672462048 Henry Cohn, 2024, needs more optimization.
12 471 0.485017057793 Henry Cohn, 2024, needs more optimization.
12 472 0.485382649785 Henry Cohn, 2024, needs more optimization.
12 473 0.485486305212 Henry Cohn, 2024, needs more optimization.
12 474 0.485897984298 Henry Cohn, 2024, needs more optimization.
12 475 0.485915432152 Henry Cohn, 2024, needs more optimization.
12 476 0.486146182621 Henry Cohn, 2024, needs more optimization.
12 477 0.486274758483 Henry Cohn, 2024, needs more optimization.
12 478 0.486909269630 Henry Cohn, 2024, needs more optimization.
12 479 0.487171320303 Henry Cohn, 2024, needs more optimization.
12 480 0.487224345381 Henry Cohn, 2024, needs more optimization.
12 481 0.487273119890 Henry Cohn, 2024, needs more optimization.
12 482 0.487803552952 Henry Cohn, 2024, needs more optimization.
12 483 0.488093134003 Henry Cohn, 2024, needs more optimization.
12 485 0.488107911292 Henry Cohn, 2024, needs more optimization.
12 486 0.488385975572 Henry Cohn, 2024, needs more optimization.
12 487 0.488634501612 Henry Cohn, 2024, needs more optimization.
12 488 0.488704644890 Henry Cohn, 2024, needs more optimization.
12 489 0.489250801074 Henry Cohn, 2024, needs more optimization.
12 491 0.489253573546 Henry Cohn, 2024, needs more optimization.
12 492 0.489518308411 Henry Cohn, 2024, needs more optimization.
12 494 0.489733128551 Henry Cohn, 2024, needs more optimization.
12 496 0.490624953172 Henry Cohn, 2024, needs more optimization.
12 497 0.490662117365 Henry Cohn, 2024, needs more optimization.
12 498 0.491168383173 Henry Cohn, 2024, needs more optimization.
12 499 0.491191926719 Henry Cohn, 2024, needs more optimization.
12 500 0.491526626815 Henry Cohn, 2024, needs more optimization.
12 501 0.491609069289 Henry Cohn, 2024, needs more optimization.
12 502 0.491740474927 Henry Cohn, 2024, needs more optimization.
12 503 0.492060995100 Henry Cohn, 2024, needs more optimization.
12 505 0.492148706743 Henry Cohn, 2024, needs more optimization.
12 507 0.492889094151 Henry Cohn, 2024, needs more optimization.
12 509 0.493044407420 Henry Cohn, 2024, needs more optimization.
12 510 0.493182056834 Henry Cohn, 2024, needs more optimization.
12 512 0.493527633116 Henry Cohn, 2024, needs more optimization.
12 513 0.493829300943 Henry Cohn, 2024, needs more optimization.
12 514 0.494324478680 Henry Cohn, 2024, needs more optimization.
12 515 0.494497249846 Henry Cohn, 2024, needs more optimization.
12 516 0.494563332060 Henry Cohn, 2024, needs more optimization.
12 517 0.494896795121 Henry Cohn, 2024, needs more optimization.
12 518 0.495025211259 Henry Cohn, 2024, needs more optimization.
12 519 0.495368907383 Henry Cohn, 2024, needs more optimization.
12 520 0.495608740896 Henry Cohn, 2024, needs more optimization.
12 521 0.495690028473 Henry Cohn, 2024, needs more optimization.
12 522 0.495829943158 Henry Cohn, 2024, needs more optimization.
12 524 0.496000033237 Henry Cohn, 2024, needs more optimization.
12 527 0.496473567601 Henry Cohn, 2024, needs more optimization.
12 528 0.497298669743 Henry Cohn, 2024, needs more optimization.
12 531 0.497397791389 Henry Cohn, 2024, needs more optimization.
12 532 0.497976426069 Henry Cohn, 2024, needs more optimization.
12 533 0.498030070615 Henry Cohn, 2024, needs more optimization.
12 534 0.498093443417 Henry Cohn, 2024, needs more optimization.
12 535 0.498236206562 Henry Cohn, 2024, needs more optimization.
12 536 0.498361450244 Henry Cohn, 2024, needs more optimization.
12 538 0.498709656277 Henry Cohn, 2024, needs more optimization.
12 539 0.499005958419 Henry Cohn, 2024, needs more optimization.
12 540 0.499184169956 Henry Cohn, 2024, needs more optimization.
12 541 0.499351474139 Henry Cohn, 2024, needs more optimization.
12 542 0.499479630529 Henry Cohn, 2024, needs more optimization.
12 543 0.499661437239 Henry Cohn, 2024, needs more optimization.
12 544 0.499859718390 Henry Cohn, 2024, needs more optimization.
12 756 0.499999999946 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, needs more 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
12 843 0.542283402313 Henry Cohn, 2024, needs more optimization.
12 845 0.542750138365 Henry Cohn, 2024, needs more optimization.
12 847 0.542950805710 Henry Cohn, 2024, needs more optimization.
12 849 0.543030894719 Henry Cohn, 2024, needs more optimization.
12 850 0.543044768814 Henry Cohn, 2024, needs more optimization.
12 853 0.543361858883 Henry Cohn, 2024, needs more optimization.
12 854 0.543581316065 Henry Cohn, 2024, needs more optimization.
12 856 0.543774630376 Henry Cohn, 2024, needs more optimization.
12 857 0.543806709015 Henry Cohn, 2024, needs more optimization.
12 859 0.544106068443 Henry Cohn, 2024, needs more optimization.
12 861 0.544286157524 Henry Cohn, 2024, needs more optimization.
12 864 0.544510458679 Henry Cohn, 2024, needs more optimization.
12 865 0.544827027625 Henry Cohn, 2024, needs more optimization.
12 870 0.545056255118 Henry Cohn, 2024, needs more optimization.
12 871 0.545304277618 Henry Cohn, 2024, needs more optimization.
12 873 0.545640199670 Henry Cohn, 2024, needs more optimization.
12 874 0.545789444019 Henry Cohn, 2024, needs more optimization.
12 877 0.546055933264 Henry Cohn, 2024, needs more optimization.
12 878 0.546302551624 Henry Cohn, 2024, needs more optimization.
12 879 0.546385316552 Henry Cohn, 2024, needs more optimization.
12 883 0.546674626517 Henry Cohn, 2024, needs more optimization.
12 884 0.546858150696 Henry Cohn, 2024, needs more optimization.
12 885 0.546989217963 Henry Cohn, 2024, needs more optimization.
12 887 0.547092786098 Henry Cohn, 2024, needs more optimization.
12 889 0.547158576851 Henry Cohn, 2024, needs more optimization.
12 890 0.547423561612 Henry Cohn, 2024, needs more optimization.
12 891 0.547636244755 Henry Cohn, 2024, needs more optimization.
12 892 0.547648908375 Henry Cohn, 2024, needs more optimization.
12 893 0.547715113467 Henry Cohn, 2024, needs more optimization.
12 894 0.547943895596 Henry Cohn, 2024, needs more optimization.
12 896 0.547965819808 Henry Cohn, 2024, needs more optimization.
12 898 0.548169304310 Henry Cohn, 2024, needs more optimization.
12 901 0.548429200065 Henry Cohn, 2024, needs more optimization.
12 902 0.548521588728 Henry Cohn, 2024, needs more optimization.
12 904 0.548699008412 Henry Cohn, 2024, needs more optimization.
12 905 0.548970359197 Henry Cohn, 2024, needs more optimization.
12 907 0.549026255238 Henry Cohn, 2024, needs more optimization.
12 908 0.549084037435 Henry Cohn, 2024, needs more optimization.
12 909 0.549284044819 Henry Cohn, 2024, needs more optimization.
12 912 0.549452689108 Henry Cohn, 2024, needs more optimization.
12 913 0.549701400512 Henry Cohn, 2024, needs more optimization.
12 915 0.549822424241 Henry Cohn, 2024, needs more optimization.
12 917 0.550088218942 Henry Cohn, 2024, needs more optimization.
12 918 0.550172692884 Henry Cohn, 2024, needs more optimization.
12 919 0.550314520626 Henry Cohn, 2024, needs more optimization.
12 920 0.550335705427 Henry Cohn, 2024, needs more optimization.
12 921 0.550661529916 Henry Cohn, 2024, needs more optimization.
12 922 0.550707086940 Henry Cohn, 2024, needs more optimization.
12 923 0.550747610669 Henry Cohn, 2024, needs more optimization.
12 925 0.550818889096 Henry Cohn, 2024, needs more optimization.
12 927 0.551084681936 Henry Cohn, 2024, needs more optimization.
12 928 0.551213071913 Henry Cohn, 2024, needs more optimization.
12 929 0.551405417285 Henry Cohn, 2024, needs more optimization.
12 931 0.551424049531 Henry Cohn, 2024, needs more optimization.
12 933 0.551626696412 Henry Cohn, 2024, needs more optimization.
12 935 0.551763635894 Henry Cohn, 2024, needs more optimization.
12 936 0.552037381879 Henry Cohn, 2024, needs more optimization.
12 937 0.552109303436 Henry Cohn, 2024, needs more optimization.
12 939 0.552236034908 Henry Cohn, 2024, needs more optimization.
12 940 0.552429819856 Henry Cohn, 2024, needs more optimization.
12 941 0.552438818228 Henry Cohn, 2024, needs more optimization.
12 943 0.552574202964 Henry Cohn, 2024, needs more optimization.
12 944 0.552790512955 Henry Cohn, 2024, needs more optimization.
12 945 0.552888930173 Henry Cohn, 2024, needs more optimization.
12 946 0.553059851518 Henry Cohn, 2024, needs more optimization.
12 950 0.553187398772 Henry Cohn, 2024, needs more optimization.
12 952 0.553486504900 Henry Cohn, 2024, needs more optimization.
12 954 0.553511296656 Henry Cohn, 2024, needs more optimization.
12 956 0.553737052720 Henry Cohn, 2024, needs more optimization.
12 957 0.553907411229 Henry Cohn, 2024, needs more optimization.
12 960 0.554095747124 Henry Cohn, 2024, needs more optimization.
12 961 0.554209118962 Henry Cohn, 2024, needs more optimization.
12 963 0.554457625979 Henry Cohn, 2024, needs more optimization.
12 965 0.554594577365 Henry Cohn, 2024, needs more optimization.
12 966 0.554979404250 Henry Cohn, 2024, needs more optimization.
12 967 0.555032181157 Henry Cohn, 2024, needs more optimization.
12 968 0.555077441044 Henry Cohn, 2024, needs more optimization.
12 971 0.555109663664 Henry Cohn, 2024, needs more optimization.
12 972 0.555261088872 Henry Cohn, 2024, 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, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
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 0.089954457132 Henry Cohn, 2023.
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 0.121482933605 Henry Cohn, 2024.
13 42 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
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 0.141255994068 Henry Cohn, 2023.
486⁢x4+174⁢x3+30⁢x2−2⁢x−1
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 0.148576024646 Henry Cohn, 2024.
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 0.180544628313 Henry Cohn, 2024.
13 60 0.184767952433 Henry Cohn, 2025.
13 61 0.189841485448 Henry Cohn, 2025.
13 62 0.194878828880 Henry Cohn, 2025.
13 63 0.197580132791 Henry Cohn, 2025.
13 64 0.199614249272 Henry Cohn, 2025.
13 65 0.201075522702 Henry Cohn, 2025.
13 66 0.201510624363 Henry Cohn, 2025.
13 67 0.204213133601 Henry Cohn, 2025.
13 68 0.207271264670 Henry Cohn, 2025.
13 69 0.208427075365 Henry Cohn, 2025.
13 70 0.210856849944 Henry Cohn, 2024, needs more optimization.
13 71 0.212574330623 Henry Cohn, 2025.
13 72 0.214183844238 Henry Cohn, 2025.
13 73 0.216197132251 Henry Cohn, 2024, needs more optimization.
13 74 0.218079724343 Henry Cohn, 2024, needs more optimization.
13 75 0.220028143013 Henry Cohn, 2024, needs more optimization.
13 76 0.222163463432 Henry Cohn, 2024, needs more optimization.
13 77 0.224156052963 Henry Cohn, 2024, needs more optimization.
13 78 0.226443489512 Henry Cohn, 2024, needs more optimization.
13 79 0.228147399376 Henry Cohn, 2024, needs more optimization.
13 80 0.230724709658 Henry Cohn, 2025.
13 81 0.232720216127 Henry Cohn, 2024, needs more optimization.
13 82 0.234641306845 Henry Cohn, 2024, needs more optimization.
13 83 0.236607352860 Henry Cohn, 2025.
13 84 0.238395349363 Henry Cohn, 2024, needs more optimization.
13 85 0.240485031594 Henry Cohn, 2024, needs more optimization.
13 86 0.242169853327 Henry Cohn, 2024, needs more optimization.
13 87 0.243805085803 Henry Cohn, 2024, needs more optimization.
13 88 0.245533239384 Henry Cohn, 2025, needs more optimization.
13 89 0.247269701019 Henry Cohn, 2025, needs more optimization.
13 90 0.248816314606 Henry Cohn, 2025, 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 0.265757903695 Henry Cohn, 2024.
13 107 0.270978248549 Henry Cohn, 2024, needs more optimization.
13 108 0.272504317353 Henry Cohn, 2024, needs more optimization.
13 112 0.272724561398 Henry Cohn, 2024, needs more optimization.
13 113 0.278242701166 Henry Cohn, 2024, needs more optimization.
13 114 0.279313821323 Henry Cohn, 2024, needs more optimization.
13 115 0.280231349612 Henry Cohn, 2024, needs more optimization.
13 116 0.281727556932 Henry Cohn, 2024, needs more optimization.
13 117 0.282253105434 Henry Cohn, 2024, needs more optimization.
13 118 0.283872989791 Henry Cohn, 2024, needs more optimization.
13 119 0.285356793043 Henry Cohn, 2024, needs more optimization.
13 120 0.286161105417 Henry Cohn, 2024, needs more optimization.
13 121 0.287756172309 Henry Cohn, 2024, needs more optimization.
13 122 0.288742202136 Henry Cohn, 2024, needs more optimization.
13 123 0.290001071561 Henry Cohn, 2024, needs more optimization.
13 124 0.291989183230 Henry Cohn, 2024, needs more optimization.
13 125 0.293140528823 Henry Cohn, 2024, needs more optimization.
13 126 0.294165135084 Henry Cohn, 2024, needs more optimization.
13 127 0.295362948602 Henry Cohn, 2024, needs more optimization.
13 128 0.296563827278 Henry Cohn, 2024, needs more optimization.
13 129 0.298122159345 Henry Cohn, 2024, needs more optimization.
13 130 0.299105657017 Henry Cohn, 2024, needs more optimization.
13 131 0.300760170042 Henry Cohn, 2024, needs more optimization.
13 132 0.301826826063 Henry Cohn, 2024, needs more optimization.
13 133 0.302043942244 Henry Cohn, 2024, needs more optimization.
13 134 0.303901796528 Henry Cohn, 2024, needs more optimization.
13 135 0.304159948150 Henry Cohn, 2024, needs more optimization.
13 136 0.305846338818 Henry Cohn, 2024, needs more optimization.
13 137 0.307092216487 Henry Cohn, 2024, needs more optimization.
13 138 0.308414689795 Henry Cohn, 2024, needs more optimization.
13 139 0.308705043059 Henry Cohn, 2024, needs more optimization.
13 140 0.309112687439 Henry Cohn, 2024, needs more optimization.
13 141 0.310509825682 Henry Cohn, 2024, needs more optimization.
13 142 0.311625994989 Henry Cohn, 2024, needs more optimization.
13 143 0.312019579575 Henry Cohn, 2024, needs more optimization.
13 144 0.313387658799 Henry Cohn, 2024, needs more optimization.
13 145 0.313629006895 Henry Cohn, 2024, needs more optimization.
13 146 0.314710548608 Henry Cohn, 2024, needs more optimization.
13 147 0.314912107220 Henry Cohn, 2024, needs more optimization.
13 148 0.316115796939 Henry Cohn, 2024, needs more optimization.
13 150 0.316535464116 Henry Cohn, 2024, needs more optimization.
13 153 0.318817759714 Henry Cohn, 2024, needs more optimization.
13 154 0.319541669317 Henry Cohn, 2024, needs more optimization.
13 155 0.320516414170 Henry Cohn, 2024, needs more optimization.
13 156 0.320835724126 Henry Cohn, 2024, needs more optimization.
13 157 0.320859593240 Henry Cohn, 2024, needs more optimization.
13 159 0.321479537381 Henry Cohn, 2024, needs more optimization.
13 160 0.323206058218 Henry Cohn, 2024, needs more optimization.
13 161 0.323570816829 Henry Cohn, 2024, needs more optimization.
13 163 0.323769041275 Henry Cohn, 2024, needs more optimization.
13 164 0.323829442033 Henry Cohn, 2024, needs more optimization.
13 166 0.325219252867 Henry Cohn, 2024, needs more optimization.
13 169 0.325719753978 Henry Cohn, 2024, needs more optimization.
13 170 0.327187161008 Henry Cohn, 2024, needs more optimization.
13 171 0.327747227298 Henry Cohn, 2024, needs more optimization.
13 172 0.327804980780 Henry Cohn, 2024, needs more optimization.
13 173 0.327937112293 Henry Cohn, 2024, needs more optimization.
13 174 0.328212205737 Henry Cohn, 2024, needs more optimization.
13 176 0.328700350021 Henry Cohn, 2024, needs more optimization.
13 178 0.328710103653 Henry Cohn, 2024, needs more optimization.
13 179 0.329568963625 Henry Cohn, 2024, needs more optimization.
13 180 0.330116076191 Henry Cohn, 2024, needs more optimization.
13 182 0.330456254659 Henry Cohn, 2024, needs more optimization.
13 183 0.331714214552 Henry Cohn, 2024, needs more optimization.
13 184 0.332048647677 Henry Cohn, 2024, 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 0.350487248631 Henry Cohn, 2024, needs more optimization.
13 210 0.353503109482 Henry Cohn, 2024, needs more optimization.
13 211 0.354143409301 Henry Cohn, 2024, needs more optimization.
13 212 0.354689770969 Henry Cohn, 2024, needs more optimization.
13 213 0.355265837684 Henry Cohn, 2024, needs more optimization.
13 215 0.356130560914 Henry Cohn, 2024, needs more optimization.
13 216 0.357593553778 Henry Cohn, 2024, needs more optimization.
13 217 0.358615217099 Henry Cohn, 2024, needs more optimization.
13 218 0.359730178627 Henry Cohn, 2024, needs more optimization.
13 219 0.360010983260 Henry Cohn, 2024, needs more optimization.
13 220 0.361001270769 Henry Cohn, 2024, needs more optimization.
13 221 0.362103847615 Henry Cohn, 2024, needs more optimization.
13 222 0.363107716172 Henry Cohn, 2024, needs more optimization.
13 223 0.363906700495 Henry Cohn, 2024, needs more optimization.
13 224 0.364100100297 Henry Cohn, 2024, needs more optimization.
13 225 0.365748615110 Henry Cohn, 2024, needs more optimization.
13 226 0.366392828435 Henry Cohn, 2024, needs more optimization.
13 227 0.366849621098 Henry Cohn, 2024, needs more optimization.
13 228 0.367648058238 Henry Cohn, 2024, needs more optimization.
13 229 0.368290747083 Henry Cohn, 2024, needs more optimization.
13 230 0.369559102967 Henry Cohn, 2024, needs more optimization.
13 231 0.370940738047 Henry Cohn, 2024, needs more optimization.
13 232 0.371021492018 Henry Cohn, 2024, needs more optimization.
13 233 0.371603030811 Henry Cohn, 2024, needs more optimization.
13 234 0.372485887610 Henry Cohn, 2024, needs more optimization.
13 235 0.373595265624 Henry Cohn, 2024, needs more optimization.
13 236 0.374410338985 Henry Cohn, 2024, needs more optimization.
13 237 0.375028761537 Henry Cohn, 2024, needs more optimization.
13 238 0.375629689519 Henry Cohn, 2024, needs more optimization.
13 239 0.376413869780 Henry Cohn, 2024, needs more optimization.
13 240 0.376865228352 Henry Cohn, 2024, needs more optimization.
13 241 0.377477110743 Henry Cohn, 2024, needs more optimization.
13 242 0.377990664582 Henry Cohn, 2024, needs more optimization.
13 243 0.379091340937 Henry Cohn, 2024, needs more optimization.
13 244 0.379725202509 Henry Cohn, 2024, needs more optimization.
13 245 0.380070976849 Henry Cohn, 2024, needs more optimization.
13 246 0.381226012336 Henry Cohn, 2024, needs more optimization.
13 247 0.381958419890 Henry Cohn, 2024, needs more optimization.
13 252 0.381963272515 Henry Cohn, 2024, needs more optimization.
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 0.419198184248 Henry Cohn, 2024, needs more optimization.
13 338 0.419661495032 Henry Cohn, 2024, needs more optimization.
13 339 0.420269807569 Henry Cohn, 2024, needs more optimization.
13 340 0.420284324419 Henry Cohn, 2024, needs more optimization.
13 341 0.420942638905 Henry Cohn, 2024, needs more optimization.
13 342 0.421127627528 Henry Cohn, 2024, needs more optimization.
13 343 0.421409021737 Henry Cohn, 2024, needs more optimization.
13 345 0.421943128023 Henry Cohn, 2024, needs more optimization.
13 346 0.422297394239 Henry Cohn, 2024, needs more optimization.
13 348 0.422669162551 Henry Cohn, 2024, needs more optimization.
13 349 0.423585792495 Henry Cohn, 2024, needs more optimization.
13 350 0.423677261958 Henry Cohn, 2024, needs more optimization.
13 351 0.423859992869 Henry Cohn, 2024, needs more optimization.
13 352 0.424142346906 Henry Cohn, 2024, needs more optimization.
13 353 0.424584775938 Henry Cohn, 2024, needs more optimization.
13 354 0.424992507291 Henry Cohn, 2024, needs more optimization.
13 355 0.425143427372 Henry Cohn, 2024, needs more optimization.
13 356 0.425531079149 Henry Cohn, 2024, needs more optimization.
13 358 0.425838695833 Henry Cohn, 2024, needs more optimization.
13 359 0.426644169196 Henry Cohn, 2024, needs more optimization.
13 360 0.426692687580 Henry Cohn, 2024, needs more optimization.
13 361 0.427154845644 Henry Cohn, 2024, needs more optimization.
13 362 0.427303694897 Henry Cohn, 2024, needs more optimization.
13 363 0.427650971221 Henry Cohn, 2024, needs more optimization.
13 364 0.427847966966 Henry Cohn, 2024, needs more optimization.
13 365 0.428282391274 Henry Cohn, 2024, needs more optimization.
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
13 601 0.473684210527 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.
19⁢x−9
13 602 0.480491758394 Henry Cohn, 2024, needs more optimization.
13 603 0.480715933600 Henry Cohn, 2024, needs more optimization.
13 606 0.480821480611 Henry Cohn, 2024, needs more optimization.
13 607 0.481276586680 Henry Cohn, 2024, needs more optimization.
13 608 0.481366890226 Henry Cohn, 2024, needs more optimization.
13 612 0.481845831226 Henry Cohn, 2024, needs more optimization.
13 614 0.482252008488 Henry Cohn, 2024, needs more optimization.
13 616 0.482582973880 Henry Cohn, 2024, needs more optimization.
13 617 0.482660838508 Henry Cohn, 2024, needs more optimization.
13 618 0.482879856445 Henry Cohn, 2024, needs more optimization.
13 620 0.483144075971 Henry Cohn, 2024, needs more optimization.
13 621 0.483646996501 Henry Cohn, 2024, needs more optimization.
13 622 0.483722713476 Henry Cohn, 2024, needs more optimization.
13 623 0.483892491992 Henry Cohn, 2024, needs more optimization.
13 624 0.484024244069 Henry Cohn, 2024, needs more optimization.
13 627 0.484101949259 Henry Cohn, 2024, needs more optimization.
13 629 0.484608205254 Henry Cohn, 2024, needs more optimization.
13 632 0.484904518595 Henry Cohn, 2024, needs more optimization.
13 633 0.485332577461 Henry Cohn, 2024, needs more optimization.
13 635 0.485581032178 Henry Cohn, 2024, needs more optimization.
13 636 0.485903516255 Henry Cohn, 2024, needs more optimization.
13 637 0.486086094852 Henry Cohn, 2024, needs more optimization.
13 638 0.486190832543 Henry Cohn, 2024, needs more optimization.
13 640 0.486206313250 Henry Cohn, 2024, needs more optimization.
13 641 0.486584860487 Henry Cohn, 2024, needs more optimization.
13 642 0.486794908843 Henry Cohn, 2024, needs more optimization.
13 645 0.486980901765 Henry Cohn, 2024, needs more optimization.
13 646 0.487340023215 Henry Cohn, 2024, needs more optimization.
13 648 0.487484723529 Henry Cohn, 2024, needs more optimization.
13 649 0.487717466390 Henry Cohn, 2024, needs more optimization.
13 650 0.487729518316 Henry Cohn, 2024, needs more optimization.
13 651 0.488224369901 Henry Cohn, 2024, needs more optimization.
13 652 0.488236254675 Henry Cohn, 2024, needs more optimization.
13 654 0.488576427441 Henry Cohn, 2024, needs more optimization.
13 655 0.488598039501 Henry Cohn, 2024, needs more optimization.
13 657 0.488739096398 Henry Cohn, 2024, needs more optimization.
13 658 0.489057555640 Henry Cohn, 2024, needs more optimization.
13 659 0.489261991786 Henry Cohn, 2024, needs more optimization.
13 661 0.489495235526 Henry Cohn, 2024, needs more optimization.
13 662 0.489562883666 Henry Cohn, 2024, needs more optimization.
13 663 0.489676122054 Henry Cohn, 2024, needs more optimization.
13 664 0.489945322790 Henry Cohn, 2024, needs more optimization.
13 665 0.490250272500 Henry Cohn, 2024, needs more optimization.
13 666 0.490343003462 Henry Cohn, 2024, needs more optimization.
13 668 0.490352294168 Henry Cohn, 2024, needs more optimization.
13 669 0.490850911016 Henry Cohn, 2024, needs more optimization.
13 671 0.490855539067 Henry Cohn, 2024, needs more optimization.
13 672 0.490953365212 Henry Cohn, 2024, needs more optimization.
13 673 0.491274570295 Henry Cohn, 2024, needs more optimization.
13 674 0.491293616723 Henry Cohn, 2024, needs more optimization.
13 675 0.491589317059 Henry Cohn, 2024, needs more optimization.
13 676 0.491708212130 Henry Cohn, 2024, needs more optimization.
13 677 0.491780855325 Henry Cohn, 2024, needs more optimization.
13 678 0.491973278752 Henry Cohn, 2024, needs more optimization.
13 679 0.492164378840 Henry Cohn, 2024, needs more optimization.
13 680 0.492250864508 Henry Cohn, 2024, needs more optimization.
13 682 0.492318409784 Henry Cohn, 2024, needs more optimization.
13 683 0.492679577894 Henry Cohn, 2024, needs more optimization.
13 686 0.492898089314 Henry Cohn, 2024, needs more optimization.
13 688 0.493155771578 Henry Cohn, 2024, needs more optimization.
13 689 0.493503888162 Henry Cohn, 2024, needs more optimization.
13 691 0.493692735433 Henry Cohn, 2024, needs more optimization.
13 692 0.493986499296 Henry Cohn, 2024, needs more optimization.
13 693 0.494097841480 Henry Cohn, 2024, needs more optimization.
13 694 0.494205463781 Henry Cohn, 2024, needs more optimization.
13 695 0.494356303394 Henry Cohn, 2024, needs more optimization.
13 696 0.494601380802 Henry Cohn, 2024, needs more optimization.
13 698 0.494764061515 Henry Cohn, 2024, needs more optimization.
13 699 0.494856862075 Henry Cohn, 2024, needs more optimization.
13 702 0.495157123458 Henry Cohn, 2024, needs more optimization.
13 704 0.495281841050 Henry Cohn, 2024, needs more optimization.
13 705 0.495537338518 Henry Cohn, 2024, needs more optimization.
13 707 0.495967251418 Henry Cohn, 2024, needs more optimization.
13 710 0.496026544130 Henry Cohn, 2024, needs more optimization.
13 711 0.496419178248 Henry Cohn, 2024, needs more optimization.
13 714 0.496477441918 Henry Cohn, 2024, needs more optimization.
13 715 0.497019137501 Henry Cohn, 2024, needs more optimization.
13 717 0.497162954387 Henry Cohn, 2024, needs more optimization.
13 718 0.497351465017 Henry Cohn, 2024, needs more optimization.
13 719 0.497548788586 Henry Cohn, 2024, needs more optimization.
13 722 0.497748402096 Henry Cohn, 2024, needs more optimization.
13 723 0.497903196747 Henry Cohn, 2024, needs more optimization.
13 725 0.498287578559 Henry Cohn, 2024, needs more optimization.
13 726 0.498567214765 Henry Cohn, 2024, needs more optimization.
13 727 0.498773157804 Henry Cohn, 2024, needs more optimization.
13 728 0.498855109405 Henry Cohn, 2024, needs more optimization.
13 729 0.498966772647 Henry Cohn, 2024, needs more optimization.
13 731 0.499015511101 Henry Cohn, 2024, needs more optimization.
13 732 0.499176355011 Henry Cohn, 2024, needs more optimization.
13 733 0.499273214457 Henry Cohn, 2024, needs more optimization.
13 734 0.499569716907 Henry Cohn, 2024, needs more optimization.
13 738 0.499804761120 Henry Cohn, 2024, needs more optimization.
13 758 0.499999999946 Orthogonal union of 756 points in 12 dimensions and 2 points in 1 dimension.
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 0.067586771091 H. Cohn, Small spherical and projective codes, data set, 2022, 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 0.071707200618 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 0.092605661196 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, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
10⁢x−1
14 45 0.112912613537 Henry Cohn, 2023.
167⁢x2−10⁢x−1
14 46 0.114212424977 Henry Cohn, 2024.
14 47 0.114784812793 Henry Cohn, 2025.
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 0.125097652359 Henry Cohn, 2023.
14 50 0.126131714982 Henry Cohn, 2025, needs more optimization.
14 52 0.126131983623 Henry Cohn, 2023.
47⁢x2+2⁢x−1
14 53 0.127207031161 Henry Cohn, 2024.
14 54 0.135105967369 Henry Cohn, 2024.
14 55 0.136745922263 Henry Cohn, 2023.
14 56 0.139995758129 Henry Cohn, 2024.
14 57 0.142195254755 Henry Cohn, 2024.
14 64 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
14 65 0.165287555076 Henry Cohn, 2024.
25600⁢x4−5616⁢x3−2736⁢x2+81
14 70 0.166666666667 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
6⁢x−1
14 71 0.177427267176 Henry Cohn, 2024.
196⁢x4−56⁢x3−28⁢x2+1
14 72 0.196842641099 Henry Cohn, 2024, needs more optimization.
14 73 0.197993677840 Henry Cohn, 2025.
14 74 0.200061223182 Henry Cohn, 2025.
14 75 0.201692164161 Henry Cohn, 2024, needs more optimization.
14 76 0.202887111912 Henry Cohn, 2024, needs more optimization.
14 77 0.204740376815 Henry Cohn, 2024, needs more optimization.
14 78 0.205486893676 Henry Cohn, 2024, needs more optimization.
14 79 0.205976955880 Henry Cohn, 2024, needs more optimization.
14 80 0.205984987511 Henry Cohn, 2024, needs more optimization.
14 81 0.206996416972 Henry Cohn, 2024, needs more optimization.
14 82 0.207104975455 Henry Cohn, 2024, needs more optimization.
14 85 0.208849195936 Henry Cohn, 2023.
Minimal polynomial listed in plain text data
14 86 0.209466685806 Henry Cohn, 2024, needs more optimization.
14 87 0.221779341058 Henry Cohn, 2025, needs more optimization.
14 88 0.223533253889 Henry Cohn, 2024, needs more optimization.
14 89 0.225178544196 Henry Cohn, 2025, needs more optimization.
14 90 0.226734071863 Henry Cohn, 2025, needs more optimization.
14 93 0.228030715344 Henry Cohn, 2025, needs more optimization.
14 94 0.228245143126 Henry Cohn, 2025.
14 95 0.228316405283 Henry Cohn, 2025, needs more optimization.
14 96 0.228339459423 Henry Cohn, 2025, needs more optimization.
14 97 0.228381387662 Henry Cohn, 2025, needs more optimization.
14 98 0.228539370088 Henry Cohn, 2025, needs more optimization.
14 99 0.228539370933 Henry Cohn, 2024, needs more optimization.
14 100 0.242081377623 Henry Cohn, 2025, needs more optimization.
14 101 0.243306523991 Henry Cohn, 2024, needs more optimization.
14 102 0.244582938634 Henry Cohn, 2024, needs more optimization.
14 103 0.245689191660 Henry Cohn, 2024, needs more optimization.
14 104 0.247054317020 Henry Cohn, 2024, needs more optimization.
14 105 0.248136602794 Henry Cohn, 2024, needs more optimization.
14 106 0.249655037382 Henry Cohn, 2024, needs more optimization.
14 112 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
14 113 0.257228921190 Henry Cohn, 2024, needs more optimization.
14 114 0.257993546061 Henry Cohn, 2024, needs more optimization.
14 115 0.259423670383 Henry Cohn, 2024, needs more optimization.
14 116 0.260322604691 Henry Cohn, 2024, needs more optimization.
14 117 0.261199699980 Henry Cohn, 2024, needs more optimization.
14 118 0.262837235233 Henry Cohn, 2024, needs more optimization.
14 119 0.263442594742 Henry Cohn, 2024, needs more optimization.
14 120 0.263830091064 Henry Cohn, 2024, needs more optimization.
14 121 0.265322322651 Henry Cohn, 2024, needs more optimization.
14 122 0.266857896982 Henry Cohn, 2024, needs more optimization.
14 123 0.267348315966 Henry Cohn, 2024, needs more optimization.
14 124 0.268482102462 Henry Cohn, 2024, needs more optimization.
14 125 0.269686334654 Henry Cohn, 2024, needs more optimization.
14 126 0.270275646233 Henry Cohn, 2024, needs more optimization.
14 127 0.271232692873 Henry Cohn, 2024, needs more optimization.
14 128 0.272034762575 Henry Cohn, 2024, needs more optimization.
14 136 0.272722029282 Henry Cohn, 2024, needs more optimization.
14 137 0.281505820782 Henry Cohn, 2024, needs more optimization.
14 138 0.282461524447 Henry Cohn, 2024, needs more optimization.
14 156 0.283473354757 Henry Cohn, 2024.
112⁢x2−9
14 157 0.293297670293 Henry Cohn, 2024, needs more optimization.
14 158 0.302077993406 Henry Cohn, 2024, needs more optimization.
14 159 0.303042328761 Henry Cohn, 2024, needs more optimization.
14 160 0.303731941278 Henry Cohn, 2024, needs more optimization.
14 161 0.303919967431 Henry Cohn, 2024, needs more optimization.
14 162 0.305085794061 Henry Cohn, 2024, needs more optimization.
14 163 0.306023718487 Henry Cohn, 2024, needs more optimization.
14 164 0.306239710602 Henry Cohn, 2024, needs more optimization.
14 165 0.307047647609 Henry Cohn, 2024, needs more optimization.
14 166 0.307574205768 Henry Cohn, 2024, needs more optimization.
14 167 0.308748255041 Henry Cohn, 2024, needs more optimization.
14 168 0.309336020316 Henry Cohn, 2024, needs more optimization.
14 169 0.310081676521 Henry Cohn, 2024, needs more optimization.
14 171 0.310946311771 Henry Cohn, 2024, needs more optimization.
14 172 0.311587088871 Henry Cohn, 2024, needs more optimization.
14 173 0.312099492151 Henry Cohn, 2024, needs more optimization.
14 174 0.312627906099 Henry Cohn, 2024, needs more optimization.
14 175 0.313215586197 Henry Cohn, 2024, needs more optimization.
14 176 0.313897890950 Henry Cohn, 2024, needs more optimization.
14 177 0.314281429396 Henry Cohn, 2024, needs more optimization.
14 178 0.315095398589 Henry Cohn, 2024, needs more optimization.
14 179 0.315945235655 Henry Cohn, 2024, needs more optimization.
14 181 0.316273177661 Henry Cohn, 2024, needs more optimization.
14 182 0.316659552907 Henry Cohn, 2024, needs more optimization.
14 183 0.316826620465 Henry Cohn, 2024, needs more optimization.
14 184 0.317728029634 Henry Cohn, 2024, 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 0.325880013489 Henry Cohn, 2024, needs more optimization.
14 212 0.329840956316 Henry Cohn, 2024, needs more optimization.
14 213 0.330347347632 Henry Cohn, 2024, needs more optimization.
14 214 0.331080975846 Henry Cohn, 2024, needs more optimization.
14 215 0.331619350429 Henry Cohn, 2024, needs more optimization.
14 217 0.332026083485 Henry Cohn, 2024, needs more optimization.
14 218 0.332433644311 Henry Cohn, 2024, needs more optimization.
14 219 0.333027229468 Henry Cohn, 2024, needs more optimization.
14 220 0.333080971623 Henry Cohn, 2024, needs more optimization.
14 224 0.333213878014 Henry Cohn, 2024, 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
14 241 0.345135786580 Henry Cohn, 2024, needs more optimization.
14 242 0.345693897708 Henry Cohn, 2024, needs more optimization.
14 243 0.346568770040 Henry Cohn, 2024, needs more optimization.
14 244 0.347367095897 Henry Cohn, 2024, needs more optimization.
14 245 0.347866400375 Henry Cohn, 2024, needs more optimization.
14 246 0.348143587809 Henry Cohn, 2024, needs more optimization.
14 247 0.349558447695 Henry Cohn, 2024, needs more optimization.
14 248 0.350173044336 Henry Cohn, 2024, needs more optimization.
14 249 0.350561544032 Henry Cohn, 2024, needs more optimization.
14 250 0.351175399431 Henry Cohn, 2024, needs more optimization.
14 251 0.351793428166 Henry Cohn, 2024, needs more optimization.
14 253 0.352875430641 Henry Cohn, 2024, needs more optimization.
14 254 0.354600002457 Henry Cohn, 2024, needs more optimization.
14 255 0.354613178708 Henry Cohn, 2024, needs more optimization.
14 256 0.355280791172 Henry Cohn, 2024, needs more optimization.
14 257 0.356442389426 Henry Cohn, 2024, needs more optimization.
14 259 0.357305049062 Henry Cohn, 2024, needs more optimization.
14 260 0.358483678892 Henry Cohn, 2024, needs more optimization.
14 261 0.358770770115 Henry Cohn, 2024, needs more optimization.
14 262 0.359544275012 Henry Cohn, 2024, needs more optimization.
14 263 0.359845210853 Henry Cohn, 2024, needs more optimization.
14 265 0.360535450936 Henry Cohn, 2024, needs more optimization.
14 267 0.362037141858 Henry Cohn, 2024, needs more optimization.
14 268 0.362804370525 Henry Cohn, 2024, needs more optimization.
14 269 0.363971374341 Henry Cohn, 2024, needs more optimization.
14 270 0.364351458897 Henry Cohn, 2024, needs more optimization.
14 272 0.365091629540 Henry Cohn, 2024, needs more optimization.
14 273 0.366806628324 Henry Cohn, 2024, needs more optimization.
14 274 0.367249173767 Henry Cohn, 2024, needs more optimization.
14 275 0.367660701754 Henry Cohn, 2024, needs more optimization.
14 276 0.368316478600 Henry Cohn, 2024, needs more optimization.
14 277 0.369165312896 Henry Cohn, 2024, needs more optimization.
14 278 0.369976264361 Henry Cohn, 2024, needs more optimization.
14 279 0.370125184926 Henry Cohn, 2024, needs more optimization.
14 280 0.371128637686 Henry Cohn, 2024, needs more optimization.
14 281 0.371404854828 Henry Cohn, 2024, needs more optimization.
14 282 0.371951171452 Henry Cohn, 2024, needs more optimization.
14 283 0.372009582880 Henry Cohn, 2024, needs more optimization.
14 285 0.372810402149 Henry Cohn, 2024, needs more optimization.
14 286 0.373648891729 Henry Cohn, 2024, needs more optimization.
14 287 0.374391191036 Henry Cohn, 2024, needs more optimization.
14 288 0.374857607337 Henry Cohn, 2024, needs more optimization.
14 290 0.375570618529 Henry Cohn, 2024, needs more optimization.
14 291 0.376227229803 Henry Cohn, 2024, needs more optimization.
14 292 0.376361629712 Henry Cohn, 2024, needs more optimization.
14 293 0.376859145855 Henry Cohn, 2024, needs more optimization.
14 294 0.377180729783 Henry Cohn, 2024, needs more optimization.
14 295 0.377886083886 Henry Cohn, 2024, needs more optimization.
14 296 0.378249283988 Henry Cohn, 2024, needs more optimization.
14 297 0.378903920683 Henry Cohn, 2024, needs more optimization.
14 298 0.379499351200 Henry Cohn, 2024, needs more optimization.
14 299 0.379575098546 Henry Cohn, 2024, needs more optimization.
14 300 0.380007008973 Henry Cohn, 2024, needs more optimization.
14 301 0.380357917918 Henry Cohn, 2024, needs more optimization.
14 302 0.380698426354 Henry Cohn, 2024, needs more optimization.
14 364 0.380952380953 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.
21⁢x−8
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 0.453760527789 Henry Cohn, 2024, needs more optimization.
14 604 0.454121667254 Henry Cohn, 2024, needs more optimization.
14 605 0.454464378613 Henry Cohn, 2024, needs more optimization.
14 607 0.454530893440 Henry Cohn, 2024, 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 0.490974033191 Henry Cohn, 2024, needs more optimization.
14 898 0.491205691685 Henry Cohn, 2024, needs more optimization.
14 900 0.491315042274 Henry Cohn, 2024, needs more optimization.
14 902 0.491645994465 Henry Cohn, 2024, needs more optimization.
14 903 0.491772522257 Henry Cohn, 2024, needs more optimization.
14 904 0.491966580477 Henry Cohn, 2024, needs more optimization.
14 905 0.492086418073 Henry Cohn, 2024, needs more optimization.
14 906 0.492200466398 Henry Cohn, 2024, needs more optimization.
14 908 0.492371330580 Henry Cohn, 2024, needs more optimization.
14 909 0.492488677816 Henry Cohn, 2024, needs more optimization.
14 911 0.492673148890 Henry Cohn, 2024, needs more optimization.
14 912 0.492707821799 Henry Cohn, 2024, needs more optimization.
14 914 0.492784687777 Henry Cohn, 2024, needs more optimization.
14 916 0.493128138471 Henry Cohn, 2024, needs more optimization.
14 917 0.493156112855 Henry Cohn, 2024, needs more optimization.
14 918 0.493187287588 Henry Cohn, 2024, needs more optimization.
14 919 0.493336256596 Henry Cohn, 2024, needs more optimization.
14 921 0.493384438894 Henry Cohn, 2024, needs more optimization.
14 922 0.493752124991 Henry Cohn, 2024, needs more optimization.
14 925 0.493771733330 Henry Cohn, 2024, needs more optimization.
14 926 0.494105777311 Henry Cohn, 2024, needs more optimization.
14 928 0.494239247769 Henry Cohn, 2024, needs more optimization.
14 931 0.494414879203 Henry Cohn, 2024, needs more optimization.
14 932 0.494449383209 Henry Cohn, 2024, needs more optimization.
14 934 0.494833803582 Henry Cohn, 2024, needs more optimization.
14 937 0.494937770185 Henry Cohn, 2024, needs more optimization.
14 938 0.495241523164 Henry Cohn, 2024, needs more optimization.
14 941 0.495412186367 Henry Cohn, 2024, needs more optimization.
14 942 0.495725331740 Henry Cohn, 2024, needs more optimization.
14 943 0.495738808765 Henry Cohn, 2024, needs more optimization.
14 945 0.495740000302 Henry Cohn, 2024, needs more optimization.
14 946 0.495905607098 Henry Cohn, 2024, needs more optimization.
14 947 0.496242320328 Henry Cohn, 2024, needs more optimization.
14 949 0.496245183802 Henry Cohn, 2024, needs more optimization.
14 951 0.496248210365 Henry Cohn, 2024, needs more optimization.
14 955 0.496711256713 Henry Cohn, 2024, needs more optimization.
14 956 0.497005768317 Henry Cohn, 2024, needs more optimization.
14 960 0.497033902814 Henry Cohn, 2024, needs more optimization.
14 962 0.497353281598 Henry Cohn, 2024, needs more optimization.
14 964 0.497571000577 Henry Cohn, 2024, needs more optimization.
14 967 0.497611323846 Henry Cohn, 2024, needs more optimization.
14 968 0.497761620745 Henry Cohn, 2024, needs more optimization.
14 970 0.498204722717 Henry Cohn, 2024, needs more optimization.
14 971 0.498284021016 Henry Cohn, 2024, needs more optimization.
14 973 0.498325899934 Henry Cohn, 2024, needs more optimization.
14 975 0.498454846899 Henry Cohn, 2024, needs more optimization.
14 976 0.498752089499 Henry Cohn, 2024, needs more optimization.
14 978 0.498956427267 Henry Cohn, 2024, needs more optimization.
14 981 0.498978704663 Henry Cohn, 2024, needs more optimization.
14 985 0.499154217680 Henry Cohn, 2024, needs more optimization.
14 986 0.499614863687 Henry Cohn, 2024, needs more optimization.
14 988 0.499742623240 Henry Cohn, 2024, needs more optimization.
14 989 0.499854605664 Henry Cohn, 2024, needs more optimization.
14 990 0.499918603174 Henry Cohn, 2024, 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 0.067169650200 Henry Cohn, 2023.
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 0.078799310669 Henry Cohn, 2023.
15 38 0.079985446142 Henry Cohn, 2025.
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 0.093096832161 Henry Cohn, 2024.
15 42 0.096809796022 Henry Cohn, 2023.
15 43 0.099946852848 Henry Cohn, 2024.
15 44 0.099976638106 Henry Cohn, 2025.
15 45 0.105767188891 Henry Cohn, 2023.
15 46 0.111296992199 Henry Cohn, 2025.
15 47 0.111399554996 Henry Cohn, 2025.
15 48 0.112658502183 Henry Cohn, 2025.
15 52 0.112912613537 Henry Cohn, 2025.
167⁢x2−10⁢x−1
15 57 0.115470053838 Henry Cohn, 2024.
75⁢x2−1
15 58 0.119569915565 Henry Cohn, 2025.
15 59 0.128965242731 Henry Cohn, 2025.
15 60 0.129260671861 Henry Cohn, 2024.
15 61 0.129429372250 Henry Cohn, 2025, needs more optimization.
15 62 0.129619231940 Henry Cohn, 2024.
15 63 0.129676179739 Henry Cohn, 2024.
15 64 0.129676245978 Henry Cohn, 2025, needs more optimization.
15 65 0.129676247112 Henry Cohn, 2024.
15 66 0.142857038845 Henry Cohn, 2024, needs more optimization.
15 67 0.144353409494 Henry Cohn, 2023.
15 68 0.147909051068 Henry Cohn, 2024.
15 69 0.160033734974 Henry Cohn, 2024.
15 70 0.160964563056 Henry Cohn, 2024.
15 71 0.166657746131 Henry Cohn, 2024, needs more optimization.
15 72 0.166658039776 Henry Cohn, 2024, 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, needs more optimization.
15 128 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
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 0.254610729363 Henry Cohn, 2024.
15 158 0.256564571531 Henry Cohn, 2024, needs more optimization.
15 159 0.280130356486 Henry Cohn, 2024, needs more optimization.
15 160 0.281059975646 Henry Cohn, 2024, needs more optimization.
15 161 0.282057112781 Henry Cohn, 2024, needs more optimization.
15 162 0.282678298991 Henry Cohn, 2024, needs more optimization.
15 163 0.283661509569 Henry Cohn, 2024, needs more optimization.
15 164 0.284237123105 Henry Cohn, 2024, needs more optimization.
15 165 0.285363473503 Henry Cohn, 2024, needs more optimization.
15 166 0.286375522970 Henry Cohn, 2024, needs more optimization.
15 167 0.287313194945 Henry Cohn, 2024, needs more optimization.
15 168 0.287768033516 Henry Cohn, 2024, needs more optimization.
15 169 0.288895182602 Henry Cohn, 2024, needs more optimization.
15 170 0.289702568949 Henry Cohn, 2024, needs more optimization.
15 171 0.290201101460 Henry Cohn, 2024, needs more optimization.
15 172 0.290805256504 Henry Cohn, 2024, needs more optimization.
15 173 0.291858658701 Henry Cohn, 2024, needs more optimization.
15 174 0.292811879031 Henry Cohn, 2024, needs more optimization.
15 175 0.293440262179 Henry Cohn, 2024, needs more optimization.
15 176 0.294255499703 Henry Cohn, 2024, needs more optimization.
15 177 0.294658898290 Henry Cohn, 2024, needs more optimization.
15 178 0.295689181025 Henry Cohn, 2024, needs more optimization.
15 179 0.295985066779 Henry Cohn, 2024, needs more optimization.
15 180 0.296793433274 Henry Cohn, 2024, needs more optimization.
15 181 0.297683682621 Henry Cohn, 2024, needs more optimization.
15 182 0.298449814451 Henry Cohn, 2024, needs more optimization.
15 183 0.299600647808 Henry Cohn, 2024, needs more optimization.
15 184 0.299629266163 Henry Cohn, 2024, needs more optimization.
15 185 0.300400493106 Henry Cohn, 2024, needs more optimization.
15 187 0.301216376819 Henry Cohn, 2024, needs more optimization.
15 188 0.302312803378 Henry Cohn, 2024, needs more optimization.
15 189 0.302652823645 Henry Cohn, 2024, needs more optimization.
15 190 0.303690296475 Henry Cohn, 2024, needs more optimization.
15 192 0.303954671461 Henry Cohn, 2024, needs more optimization.
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 0.317412198799 Henry Cohn, 2024, needs more optimization.
15 259 0.332040958510 Henry Cohn, 2024, needs more optimization.
15 260 0.333072887348 Henry Cohn, 2024, 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 0.363358749296 Henry Cohn, 2024, needs more optimization.
15 322 0.364066327210 Henry Cohn, 2024, needs more optimization.
15 323 0.364514553812 Henry Cohn, 2024, needs more optimization.
15 324 0.364891697764 Henry Cohn, 2024, needs more optimization.
15 325 0.365279586273 Henry Cohn, 2024, needs more optimization.
15 326 0.365719358712 Henry Cohn, 2024, needs more optimization.
15 327 0.366018821119 Henry Cohn, 2024, needs more optimization.
15 328 0.366211580822 Henry Cohn, 2024, needs more optimization.
15 329 0.366749332176 Henry Cohn, 2024, needs more optimization.
15 330 0.367006324190 Henry Cohn, 2024, needs more optimization.
15 331 0.367562454063 Henry Cohn, 2024, needs more optimization.
15 332 0.367794759394 Henry Cohn, 2024, needs more optimization.
15 333 0.368497236315 Henry Cohn, 2024, needs more optimization.
15 334 0.368868207318 Henry Cohn, 2024, needs more optimization.
15 335 0.368870101739 Henry Cohn, 2024, needs more optimization.
15 336 0.369365089162 Henry Cohn, 2024, needs more optimization.
15 337 0.369481586574 Henry Cohn, 2024, needs more optimization.
15 339 0.370203946791 Henry Cohn, 2024, needs more optimization.
15 341 0.371025269164 Henry Cohn, 2024, needs more optimization.
15 342 0.371408497184 Henry Cohn, 2024, needs more optimization.
15 344 0.372262377941 Henry Cohn, 2024, needs more optimization.
15 346 0.372625663487 Henry Cohn, 2024, needs more optimization.
15 347 0.373470696872 Henry Cohn, 2024, needs more optimization.
15 348 0.373653854755 Henry Cohn, 2024, needs more optimization.
15 349 0.374034580267 Henry Cohn, 2024, needs more optimization.
15 351 0.374606248244 Henry Cohn, 2024, needs more optimization.
15 352 0.374783706513 Henry Cohn, 2024, needs more optimization.
15 353 0.375206716505 Henry Cohn, 2024, needs more optimization.
15 354 0.375958902948 Henry Cohn, 2024, needs more optimization.
15 355 0.376082597764 Henry Cohn, 2024, needs more optimization.
15 356 0.376341762584 Henry Cohn, 2024, needs more optimization.
15 357 0.376602161741 Henry Cohn, 2024, needs more optimization.
15 358 0.376875240185 Henry Cohn, 2024, needs more optimization.
15 359 0.377331907227 Henry Cohn, 2024, needs more optimization.
15 360 0.377643215480 Henry Cohn, 2024, needs more optimization.
15 361 0.377921744658 Henry Cohn, 2024, needs more optimization.
15 362 0.377956622728 Henry Cohn, 2024, needs more optimization.
15 363 0.378553914750 Henry Cohn, 2024, needs more optimization.
15 365 0.378996472936 Henry Cohn, 2024, needs more optimization.
15 366 0.379214686472 Henry Cohn, 2024, needs more optimization.
15 367 0.379820318743 Henry Cohn, 2024, needs more optimization.
15 368 0.379929918400 Henry Cohn, 2024, needs more optimization.
15 369 0.380017259066 Henry Cohn, 2024, needs more optimization.
15 370 0.380584306699 Henry Cohn, 2024, needs more optimization.
15 371 0.381012202942 Henry Cohn, 2024, needs more optimization.
15 373 0.381423239403 Henry Cohn, 2024, needs more optimization.
15 374 0.381584774615 Henry Cohn, 2024, needs more optimization.
15 375 0.382216711808 Henry Cohn, 2024, needs more optimization.
15 376 0.382724177193 Henry Cohn, 2024, needs more optimization.
15 378 0.382997224506 Henry Cohn, 2024, needs more optimization.
15 379 0.383061076778 Henry Cohn, 2024, needs more optimization.
15 381 0.383521361620 Henry Cohn, 2024, needs more optimization.
15 382 0.383936650366 Henry Cohn, 2024, needs more optimization.
15 383 0.384412946374 Henry Cohn, 2024, needs more optimization.
15 384 0.384426437317 Henry Cohn, 2024, needs more optimization.
15 385 0.384835093532 Henry Cohn, 2024, needs more optimization.
15 386 0.385298311394 Henry Cohn, 2024, needs more optimization.
15 388 0.385424149333 Henry Cohn, 2024, needs more optimization.
15 390 0.386050309191 Henry Cohn, 2024, needs more optimization.
15 391 0.386462532837 Henry Cohn, 2024, needs more optimization.
15 392 0.386854182489 Henry Cohn, 2024, needs more optimization.
15 394 0.387178553284 Henry Cohn, 2024, needs more optimization.
15 395 0.387622857814 Henry Cohn, 2024, needs more optimization.
15 396 0.387766177478 Henry Cohn, 2024, needs more optimization.
15 397 0.388001815248 Henry Cohn, 2024, needs more optimization.
15 398 0.388764204036 Henry Cohn, 2024, needs more optimization.
15 399 0.388772988900 Henry Cohn, 2024, needs more optimization.
15 400 0.389233333538 Henry Cohn, 2024, needs more optimization.
15 401 0.389363352958 Henry Cohn, 2024, needs more optimization.
15 403 0.389811622267 Henry Cohn, 2024, needs more optimization.
15 404 0.390088691342 Henry Cohn, 2024, needs more optimization.
15 405 0.390474544837 Henry Cohn, 2024, needs more optimization.
15 407 0.390792428871 Henry Cohn, 2024, needs more optimization.
15 408 0.390953831609 Henry Cohn, 2024, needs more optimization.
15 409 0.391435799702 Henry Cohn, 2024, needs more optimization.
15 410 0.391622243477 Henry Cohn, 2024, needs more optimization.
15 411 0.392134136287 Henry Cohn, 2024, needs more optimization.
15 412 0.392150775547 Henry Cohn, 2024, needs more optimization.
15 413 0.392473918736 Henry Cohn, 2024, needs more optimization.
15 414 0.392634002250 Henry Cohn, 2024, needs more optimization.
15 415 0.393089153382 Henry Cohn, 2024, needs more optimization.
15 416 0.393214150379 Henry Cohn, 2024, needs more optimization.
15 417 0.393798385071 Henry Cohn, 2024, needs more optimization.
15 418 0.393838118421 Henry Cohn, 2024, needs more optimization.
15 419 0.393992820073 Henry Cohn, 2024, needs more optimization.
15 420 0.394035394834 Henry Cohn, 2024, needs more optimization.
15 421 0.394444799206 Henry Cohn, 2024, needs more optimization.
15 423 0.394891507967 Henry Cohn, 2024, needs more optimization.
15 425 0.395203876879 Henry Cohn, 2024, needs more optimization.
15 426 0.395368178533 Henry Cohn, 2024, needs more optimization.
15 427 0.395800728402 Henry Cohn, 2024, needs more optimization.
15 429 0.395961824860 Henry Cohn, 2024, needs more optimization.
15 430 0.396788819410 Henry Cohn, 2024, needs more optimization.
15 431 0.396811937522 Henry Cohn, 2024, needs more optimization.
15 432 0.397101620278 Henry Cohn, 2024, needs more optimization.
15 433 0.397408711488 Henry Cohn, 2024, needs more optimization.
15 434 0.397432015881 Henry Cohn, 2024, needs more optimization.
15 435 0.397657230326 Henry Cohn, 2024, needs more optimization.
15 437 0.398153377805 Henry Cohn, 2024, needs more optimization.
15 438 0.398468752288 Henry Cohn, 2024, needs more optimization.
15 439 0.398837640103 Henry Cohn, 2024, needs more optimization.
15 440 0.398960616606 Henry Cohn, 2024, needs more optimization.
15 442 0.399038250230 Henry Cohn, 2024, needs more optimization.
15 443 0.399712039104 Henry Cohn, 2024, 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, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
7⁢x−3
15 1024 0.459410961393 Henry Cohn, 2023, 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, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
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 0.074362231516 Henry Cohn, 2023.
16 40 0.077433436468 Henry Cohn, 2024.
16 41 0.078328485376 Henry Cohn, 2023.
16 42 0.085144928730 Henry Cohn, 2023.
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 0.095441675774 Henry Cohn, 2023.
16 47 0.097487241368 Henry Cohn, 2024.
16 48 0.098771717854 Henry Cohn, 2023.
143⁢x2−4⁢x−1
16 49 0.105637615804 Henry Cohn, 2024.
16 50 0.110920705171 Henry Cohn, 2024.
16 51 0.111318830650 Henry Cohn, 2025.
16 52 0.112399717045 Henry Cohn, 2025.
16 54 0.112912613537 Orthogonal union of 52 points in 15 dimensions and 2 points in 1 dimension.
167⁢x2−10⁢x−1
16 55 0.115467707901 Henry Cohn, 2023, needs more optimization.
16 56 0.115468483561 Henry Cohn, 2023, needs more optimization.
16 57 0.115468611697 Henry Cohn, 2025.
16 58 0.115469159083 Henry Cohn, 2023, needs more optimization.
16 59 0.115469803431 Henry Cohn, 2023, needs more optimization.
16 60 0.115472406484 Henry Cohn, 2024, 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 0.142488765484 Henry Cohn, 2024, needs more optimization.
16 76 0.157616857308 Henry Cohn, 2025.
16 77 0.162143681909 Henry Cohn, 2024, needs more optimization.
16 94 0.168685175113 Code with 92 points in 15 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.
47⁢x2−2⁢x−1
16 95 0.169357805023 Henry Cohn, 2025, needs more optimization.
16 130 0.2 Code with 128 points in 15 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
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
16 288* 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
16 291 0.328090702838 Henry Cohn, 2024, needs more optimization.
16 294 0.329008178201 Henry Cohn, 2024, needs more optimization.
16 296 0.330316708584 Henry Cohn, 2024, needs more optimization.
16 298 0.330397905967 Henry Cohn, 2024, needs more optimization.
16 302 0.331404082068 Henry Cohn, 2024, needs more optimization.
16 303 0.332457088318 Henry Cohn, 2024, needs more optimization.
16 512 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
16 513 0.393228380521 Henry Cohn, 2024, needs more optimization.
16 514 0.393500503267 Henry Cohn, 2024, needs more optimization.
16 516 0.393716342162 Henry Cohn, 2024, needs more optimization.
16 517 0.394006961285 Henry Cohn, 2024, needs more optimization.
16 519 0.394434600527 Henry Cohn, 2024, needs more optimization.
16 520 0.394738497756 Henry Cohn, 2024, needs more optimization.
16 521 0.394810720864 Henry Cohn, 2024, needs more optimization.
16 522 0.395437433696 Henry Cohn, 2024, needs more optimization.
16 524 0.395447268160 Henry Cohn, 2024, needs more optimization.
16 526 0.395603847248 Henry Cohn, 2024, needs more optimization.
16 528 0.396030290007 Henry Cohn, 2024, needs more optimization.
16 531 0.396448065610 Henry Cohn, 2024, needs more optimization.
16 532 0.396818769177 Henry Cohn, 2024, needs more optimization.
16 533 0.397007959106 Henry Cohn, 2024, needs more optimization.
16 534 0.397408488565 Henry Cohn, 2024, needs more optimization.
16 535 0.397429031141 Henry Cohn, 2024, needs more optimization.
16 536 0.397687774658 Henry Cohn, 2024, needs more optimization.
16 537 0.397892047946 Henry Cohn, 2024, needs more optimization.
16 538 0.397990773710 Henry Cohn, 2024, needs more optimization.
16 539 0.398385997032 Henry Cohn, 2024, needs more optimization.
16 540 0.398551708720 Henry Cohn, 2024, needs more optimization.
16 541 0.398555132284 Henry Cohn, 2024, needs more optimization.
16 542 0.398765122447 Henry Cohn, 2024, needs more optimization.
16 543 0.398798812184 Henry Cohn, 2024, needs more optimization.
16 544 0.398930643797 Henry Cohn, 2024, needs more optimization.
16 545 0.399277513322 Henry Cohn, 2024, needs more optimization.
16 546 0.399504879076 Henry Cohn, 2024, needs more optimization.
16 547 0.399738786490 Henry Cohn, 2024, needs more optimization.
16 548 0.399878896846 Henry Cohn, 2024, 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
16 992 0.428571428572 Orthogonal union of 990 points in 15 dimensions and 2 points in 1 dimension.
7⁢x−3
16 993 0.454299678053 Henry Cohn, 2024, needs more optimization.
16 995 0.454412891126 Henry Cohn, 2024, needs more optimization.
16 997 0.454490455504 Henry Cohn, 2024, needs more optimization.
16 1000 0.454759937508 Henry Cohn, 2024, needs more optimization.
16 1001 0.454962343308 Henry Cohn, 2024, needs more optimization.
16 1002 0.455108465884 Henry Cohn, 2024, needs more optimization.
16 1004 0.455191087759 Henry Cohn, 2024, needs more optimization.
16 1005 0.455380287216 Henry Cohn, 2024, needs more optimization.
16 1006 0.455413622409 Henry Cohn, 2024, needs more optimization.
16 1008 0.455542791687 Henry Cohn, 2024, needs more optimization.
16 1009 0.455563264403 Henry Cohn, 2024, needs more optimization.
16 1011 0.455685972460 Henry Cohn, 2024, needs more optimization.
16 1013 0.455843607042 Henry Cohn, 2024, needs more optimization.
16 1014 0.456133892602 Henry Cohn, 2024, needs more optimization.
16 1016 0.456200075029 Henry Cohn, 2024, needs more optimization.
16 1019 0.456455020559 Henry Cohn, 2024, needs more optimization.
16 1020 0.456469307412 Henry Cohn, 2024, needs more optimization.
16 1021 0.456588933387 Henry Cohn, 2024, needs more optimization.
16 1024 0.456714420511 Henry Cohn, 2024, needs more optimization.
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 0.052701900034 Henry Cohn, 2023.
17 37 0.055980759337 Henry Cohn, 2025.
17 38 0.056000774985 Henry Cohn, 2025.
17 39 0.062879614874 Henry Cohn, 2024.
17 40 0.064972486881 Henry Cohn, 2024.
17 41 0.070153891671 Henry Cohn, 2023.
17 42 0.073342095231 Henry Cohn, 2023.
17 45 0.073591871415 Henry Cohn, 2023.
239⁢x2−4⁢x−1
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 54 0.107200465762 Henry Cohn, 2025.
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 0.126993878853 Henry Cohn, 2024, needs more optimization.
17 76 0.127284656799 Orthogonal union of 74 points in 16 dimensions and 2 points in 1 dimension.
156⁢x2−12⁢x−1
17 77 0.127344939238 Henry Cohn, 2024, needs more optimization.
17 78 0.135261813761 Henry Cohn, 2024, needs more optimization.
17 79 0.143915449445 Henry Cohn, 2024, needs more optimization.
17 80 0.148099364596 Henry Cohn, 2024, needs more optimization.
17 81 0.152547937502 Henry Cohn, 2024, needs more optimization.
17 82 0.158890501235 Henry Cohn, 2024, needs more optimization.
17 83 0.160388172055 Henry Cohn, 2024, needs more optimization.
17 84 0.166655179307 Henry Cohn, 2024, needs more optimization.
17 85 0.167793291954 Henry Cohn, 2024, needs more optimization.
17 86 0.168430857330 Henry Cohn, 2024, needs more optimization.
17 87 0.168432208406 Henry Cohn, 2025, needs more optimization.
17 88 0.168444897778 Henry Cohn, 2025, needs more optimization.
17 90 0.168462143022 Henry Cohn, 2025, needs more optimization.
17 91 0.168472569442 Henry Cohn, 2025, needs more optimization.
17 92 0.168490830009 Henry Cohn, 2025, needs more optimization.
17 93 0.168492240135 Henry Cohn, 2025, needs more optimization.
17 94 0.168493573378 Henry Cohn, 2025, needs more optimization.
17 95 0.168495669781 Henry Cohn, 2024, needs more optimization.
17 96 0.168496565189 Henry Cohn, 2025, needs more optimization.
17 97 0.169354686250 Henry Cohn, 2025, needs more optimization.
17 98 0.188439868949 Henry Cohn, 2025, needs more optimization.
17 99 0.190219270741 Henry Cohn, 2025, needs more optimization.
17 100 0.191220639197 Henry Cohn, 2024, needs more optimization.
17 101 0.192331242362 Henry Cohn, 2024, needs more optimization.
17 102 0.193702524346 Henry Cohn, 2024, needs more optimization.
17 103 0.194559855113 Henry Cohn, 2024, needs more optimization.
17 104 0.195582793636 Henry Cohn, 2024, needs more optimization.
17 105 0.197387527149 Henry Cohn, 2024, needs more optimization.
17 106 0.197781706802 Henry Cohn, 2024, needs more optimization.
17 107 0.199326561219 Henry Cohn, 2024, needs more optimization.
17 132 0.199979258638 Henry Cohn, 2024, 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 0.203540421439 Henry Cohn, 2024, needs more optimization.
17 163 0.248485495761 Henry Cohn, 2024, needs more optimization.
17 164 0.248856984641 Henry Cohn, 2024, needs more optimization.
17 165 0.249504870049 Henry Cohn, 2024, needs more optimization.
17 290 0.25 Code with 288 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.
4⁢x−1
17 315 0.307692307693 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
13⁢x−4
17 336 0.307692307693 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−4
17 338 0.327635219930 Henry Cohn, 2024, needs more optimization.
17 339 0.328610221248 Henry Cohn, 2024, needs more optimization.
17 342 0.328912294447 Henry Cohn, 2024, needs more optimization.
17 344 0.329425171377 Henry Cohn, 2024, needs more optimization.
17 346 0.330121249666 Henry Cohn, 2024, needs more optimization.
17 347 0.331101749479 Henry Cohn, 2024, needs more optimization.
17 350 0.331668494605 Henry Cohn, 2024, needs more optimization.
17 351 0.332190092078 Henry Cohn, 2024, needs more optimization.
17 355 0.332784799655 Henry Cohn, 2024, 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
17 553 0.347369928900 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
639⁢x2−150⁢x−25
17 554 0.381727073898 Henry Cohn, 2024, needs more optimization.
17 555 0.381861501497 Henry Cohn, 2024, needs more optimization.
17 556 0.382000484934 Henry Cohn, 2024, needs more optimization.
17 557 0.382002686683 Henry Cohn, 2024, needs more optimization.
17 558 0.382288923623 Henry Cohn, 2024, needs more optimization.
17 560 0.382499504868 Henry Cohn, 2024, needs more optimization.
17 561 0.382644473446 Henry Cohn, 2024, needs more optimization.
17 562 0.383044918209 Henry Cohn, 2024, needs more optimization.
17 564 0.383162672435 Henry Cohn, 2024, needs more optimization.
17 565 0.383444224570 Henry Cohn, 2024, needs more optimization.
17 566 0.383556319021 Henry Cohn, 2024, needs more optimization.
17 567 0.383592037395 Henry Cohn, 2024, needs more optimization.
17 568 0.383702281498 Henry Cohn, 2024, needs more optimization.
17 570 0.384236071913 Henry Cohn, 2024, needs more optimization.
17 571 0.384284966995 Henry Cohn, 2024, needs more optimization.
17 572 0.384536976472 Henry Cohn, 2024, needs more optimization.
17 573 0.384709424365 Henry Cohn, 2024, needs more optimization.
17 574 0.384775343916 Henry Cohn, 2024, needs more optimization.
17 576 0.385058753724 Henry Cohn, 2024, needs more optimization.
17 577 0.385449337039 Henry Cohn, 2024, needs more optimization.
17 579 0.385550501401 Henry Cohn, 2024, needs more optimization.
17 580 0.385912598987 Henry Cohn, 2024, needs more optimization.
17 581 0.385968810537 Henry Cohn, 2024, needs more optimization.
17 582 0.386167868652 Henry Cohn, 2024, needs more optimization.
17 583 0.386292432900 Henry Cohn, 2024, needs more optimization.
17 584 0.386532590433 Henry Cohn, 2024, needs more optimization.
17 586 0.386711834374 Henry Cohn, 2024, needs more optimization.
17 587 0.386876558958 Henry Cohn, 2024, needs more optimization.
17 590 0.387347950724 Henry Cohn, 2024, needs more optimization.
17 591 0.387881924724 Henry Cohn, 2024, needs more optimization.
17 592 0.387986472300 Henry Cohn, 2024, needs more optimization.
17 593 0.388135815343 Henry Cohn, 2024, needs more optimization.
17 594 0.388165959006 Henry Cohn, 2024, needs more optimization.
17 595 0.388271614376 Henry Cohn, 2024, needs more optimization.
17 596 0.388342828073 Henry Cohn, 2024, needs more optimization.
17 597 0.388620722855 Henry Cohn, 2024, needs more optimization.
17 599 0.388880064728 Henry Cohn, 2024, needs more optimization.
17 600 0.388967003949 Henry Cohn, 2024, needs more optimization.
17 601 0.389412163346 Henry Cohn, 2024, needs more optimization.
17 602 0.389535039073 Henry Cohn, 2024, needs more optimization.
17 603 0.389659133516 Henry Cohn, 2024, needs more optimization.
17 606 0.389806149544 Henry Cohn, 2024, needs more optimization.
17 607 0.390276482038 Henry Cohn, 2024, needs more optimization.
17 608 0.390428600491 Henry Cohn, 2024, needs more optimization.
17 609 0.390624418242 Henry Cohn, 2024, needs more optimization.
17 610 0.390641377010 Henry Cohn, 2024, needs more optimization.
17 611 0.390785496745 Henry Cohn, 2024, needs more optimization.
17 612 0.391043020144 Henry Cohn, 2024, needs more optimization.
17 613 0.391060649978 Henry Cohn, 2024, needs more optimization.
17 614 0.391381850635 Henry Cohn, 2024, needs more optimization.
17 615 0.391398609995 Henry Cohn, 2024, needs more optimization.
17 616 0.391444475324 Henry Cohn, 2024, needs more optimization.
17 618 0.391847833642 Henry Cohn, 2024, needs more optimization.
17 620 0.392016507215 Henry Cohn, 2024, needs more optimization.
17 622 0.392158626156 Henry Cohn, 2024, needs more optimization.
17 624 0.392764714860 Henry Cohn, 2024, needs more optimization.
17 625 0.392894098373 Henry Cohn, 2024, needs more optimization.
17 627 0.393127648017 Henry Cohn, 2024, needs more optimization.
17 629 0.393474000133 Henry Cohn, 2024, needs more optimization.
17 630 0.393598471895 Henry Cohn, 2024, needs more optimization.
17 632 0.393883309237 Henry Cohn, 2024, needs more optimization.
17 633 0.394088440557 Henry Cohn, 2024, needs more optimization.
17 634 0.394298803689 Henry Cohn, 2024, needs more optimization.
17 636 0.394530300728 Henry Cohn, 2024, needs more optimization.
17 637 0.394711856817 Henry Cohn, 2024, needs more optimization.
17 638 0.394795724159 Henry Cohn, 2024, needs more optimization.
17 640 0.394947484369 Henry Cohn, 2024, needs more optimization.
17 641 0.395045476729 Henry Cohn, 2024, needs more optimization.
17 642 0.395366972272 Henry Cohn, 2024, needs more optimization.
17 644 0.395579259925 Henry Cohn, 2024, needs more optimization.
17 646 0.395819202397 Henry Cohn, 2024, needs more optimization.
17 647 0.396054451855 Henry Cohn, 2024, needs more optimization.
17 649 0.396395441677 Henry Cohn, 2024, needs more optimization.
17 650 0.396658569624 Henry Cohn, 2024, needs more optimization.
17 651 0.396755111838 Henry Cohn, 2024, needs more optimization.
17 652 0.396867555241 Henry Cohn, 2024, needs more optimization.
17 653 0.396911934158 Henry Cohn, 2024, needs more optimization.
17 654 0.397207399317 Henry Cohn, 2024, needs more optimization.
17 656 0.397536254008 Henry Cohn, 2024, needs more optimization.
17 657 0.397539415110 Henry Cohn, 2024, needs more optimization.
17 658 0.397577064076 Henry Cohn, 2024, needs more optimization.
17 659 0.397891587335 Henry Cohn, 2024, needs more optimization.
17 660 0.398098453350 Henry Cohn, 2024, needs more optimization.
17 661 0.398196725294 Henry Cohn, 2024, needs more optimization.
17 662 0.398440147278 Henry Cohn, 2024, needs more optimization.
17 664 0.398515636774 Henry Cohn, 2024, needs more optimization.
17 666 0.398636654558 Henry Cohn, 2024, needs more optimization.
17 667 0.399121132122 Henry Cohn, 2024, needs more optimization.
17 668 0.399122450982 Henry Cohn, 2024, needs more optimization.
17 669 0.399333421300 Henry Cohn, 2024, needs more optimization.
17 670 0.399475526431 Henry Cohn, 2024, needs more optimization.
17 673 0.399720355371 Henry Cohn, 2024, needs more optimization.
17 674 0.399939210113 Henry Cohn, 2024, 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 0.412201245094 Henry Cohn, 2024, needs more optimization.
17 773 0.412412250768 Henry Cohn, 2024, needs more optimization.
17 775 0.412563243620 Henry Cohn, 2024, needs more optimization.
17 776 0.412773329255 Henry Cohn, 2024, needs more optimization.
17 777 0.412915364237 Henry Cohn, 2024, needs more optimization.
17 780 0.413041886749 Henry Cohn, 2024, needs more optimization.
17 781 0.413166278309 Henry Cohn, 2024, needs more optimization.
17 782 0.413394140590 Henry Cohn, 2024, needs more optimization.
17 784 0.413652144766 Henry Cohn, 2024, needs more optimization.
17 786 0.413875685257 Henry Cohn, 2024, needs more optimization.
17 788 0.413974726560 Henry Cohn, 2024, needs more optimization.
17 790 0.414222362312 Henry Cohn, 2024, needs more optimization.
17 791 0.414508295245 Henry Cohn, 2024, needs more optimization.
17 794 0.414560656821 Henry Cohn, 2024, needs more optimization.
17 796 0.414821708020 Henry Cohn, 2024, needs more optimization.
17 797 0.415091223390 Henry Cohn, 2024, needs more optimization.
17 798 0.415303745841 Henry Cohn, 2024, needs more optimization.
17 799 0.415400891575 Henry Cohn, 2024, needs more optimization.
17 801 0.415644357058 Henry Cohn, 2024, needs more optimization.
17 802 0.415807920272 Henry Cohn, 2024, needs more optimization.
17 803 0.415865959479 Henry Cohn, 2024, needs more optimization.
17 806 0.415916150645 Henry Cohn, 2024, needs more optimization.
17 807 0.416066402184 Henry Cohn, 2024, needs more optimization.
17 808 0.416194586493 Henry Cohn, 2024, needs more optimization.
17 809 0.416427420558 Henry Cohn, 2024, needs more optimization.
17 812 0.416531942153 Henry Cohn, 2024, needs more optimization.
17 814 0.416889754319 Henry Cohn, 2024, needs more optimization.
17 815 0.416922369402 Henry Cohn, 2024, needs more optimization.
17 817 0.417100697734 Henry Cohn, 2024, needs more optimization.
17 820 0.417453232457 Henry Cohn, 2024, needs more optimization.
17 823 0.417820359472 Henry Cohn, 2024, needs more optimization.
17 824 0.418020370985 Henry Cohn, 2024, needs more optimization.
17 826 0.418340971011 Henry Cohn, 2024, needs more optimization.
17 827 0.418442058142 Henry Cohn, 2024, needs more optimization.
17 830 0.418586961080 Henry Cohn, 2024, needs more optimization.
17 831 0.418898165425 Henry Cohn, 2024, needs more optimization.
17 832 0.418900253527 Henry Cohn, 2024, needs more optimization.
17 833 0.418988012649 Henry Cohn, 2024, needs more optimization.
17 834 0.419203301502 Henry Cohn, 2024, needs more optimization.
17 835 0.419227933572 Henry Cohn, 2024, needs more optimization.
17 837 0.419416022360 Henry Cohn, 2024, needs more optimization.
17 839 0.419558230408 Henry Cohn, 2024, needs more optimization.
17 840 0.419834504503 Henry Cohn, 2024, needs more optimization.
17 842 0.420043780538 Henry Cohn, 2024, needs more optimization.
17 843 0.420143067929 Henry Cohn, 2024, needs more optimization.
17 844 0.420251730229 Henry Cohn, 2024, needs more optimization.
17 847 0.420343238623 Henry Cohn, 2024, needs more optimization.
17 849 0.420631677158 Henry Cohn, 2024, needs more optimization.
17 853 0.421016579593 Henry Cohn, 2024, needs more optimization.
17 856 0.421391518726 Henry Cohn, 2024, needs more optimization.
17 857 0.421638523160 Henry Cohn, 2024, needs more optimization.
17 858 0.421678872814 Henry Cohn, 2024, needs more optimization.
17 860 0.421799814025 Henry Cohn, 2024, needs more optimization.
17 861 0.421859022979 Henry Cohn, 2024, needs more optimization.
17 863 0.422047065076 Henry Cohn, 2024, needs more optimization.
17 866 0.422147126988 Henry Cohn, 2024, needs more optimization.
17 867 0.422789533342 Henry Cohn, 2024, needs more optimization.
17 868 0.422864176547 Henry Cohn, 2024, needs more optimization.
17 869 0.422892398576 Henry Cohn, 2024, needs more optimization.
17 870 0.422964028639 Henry Cohn, 2024, needs more optimization.
17 874 0.423139038216 Henry Cohn, 2024, needs more optimization.
17 875 0.423328022035 Henry Cohn, 2024, needs more optimization.
17 876 0.423527630742 Henry Cohn, 2024, needs more optimization.
17 877 0.423649450255 Henry Cohn, 2024, needs more optimization.
17 878 0.423718602829 Henry Cohn, 2024, needs more optimization.
17 879 0.423848421122 Henry Cohn, 2024, needs more optimization.
17 882 0.423868693915 Henry Cohn, 2024, needs more optimization.
17 884 0.424179817042 Henry Cohn, 2024, needs more optimization.
17 885 0.424248093578 Henry Cohn, 2024, needs more optimization.
17 889 0.424554174299 Henry Cohn, 2024, needs more optimization.
17 892 0.424897098733 Henry Cohn, 2024, needs more optimization.
17 893 0.425271479382 Henry Cohn, 2024, needs more optimization.
17 895 0.425298690170 Henry Cohn, 2024, needs more optimization.
17 896 0.425324698239 Henry Cohn, 2024, needs more optimization.
17 898 0.425578226680 Henry Cohn, 2024, needs more optimization.
17 901 0.425827645960 Henry Cohn, 2024, needs more optimization.
17 902 0.426029742896 Henry Cohn, 2024, needs more optimization.
17 904 0.426097585182 Henry Cohn, 2024, needs more optimization.
17 905 0.426407023999 Henry Cohn, 2024, needs more optimization.
17 908 0.426544393903 Henry Cohn, 2024, needs more optimization.
17 909 0.426666714038 Henry Cohn, 2024, needs more optimization.
17 910 0.426884012644 Henry Cohn, 2024, needs more optimization.
17 912 0.426938655283 Henry Cohn, 2024, needs more optimization.
17 913 0.426990171392 Henry Cohn, 2024, needs more optimization.
17 915 0.427225334694 Henry Cohn, 2024, needs more optimization.
17 916 0.427337510493 Henry Cohn, 2024, needs more optimization.
17 917 0.427341392678 Henry Cohn, 2024, needs more optimization.
17 918 0.427386584058 Henry Cohn, 2024, needs more optimization.
17 921 0.427640025110 Henry Cohn, 2024, needs more optimization.
17 922 0.428018687187 Henry Cohn, 2024, needs more optimization.
17 925 0.428149216891 Henry Cohn, 2024, needs more optimization.
17 926 0.428311763697 Henry Cohn, 2024, needs more optimization.
17 929 0.428330726377 Henry Cohn, 2024, needs more optimization.
17 995 0.428571428572 Orthogonal union of 990 points in 15 dimensions and 5 points in 2 dimensions.
7⁢x−3
17 996 0.434428480299 Henry Cohn, 2024, needs more optimization.
17 997 0.434709684307 Henry Cohn, 2024, needs more optimization.
17 998 0.434717902543 Henry Cohn, 2024, needs more optimization.
17 999 0.434856387661 Henry Cohn, 2024, needs more optimization.
17 1000 0.435064547019 Henry Cohn, 2024, needs more optimization.
17 1001 0.435140127073 Henry Cohn, 2024, needs more optimization.
17 1003 0.435302531066 Henry Cohn, 2024, needs more optimization.
17 1007 0.435319232478 Henry Cohn, 2024, needs more optimization.
17 1011 0.435678884176 Henry Cohn, 2024, needs more optimization.
17 1012 0.435804281607 Henry Cohn, 2024, needs more optimization.
17 1013 0.436127514640 Henry Cohn, 2024, needs more optimization.
17 1015 0.436156201525 Henry Cohn, 2024, needs more optimization.
17 1016 0.436229353818 Henry Cohn, 2024, needs more optimization.
17 1020 0.436432321833 Henry Cohn, 2024, needs more optimization.
17 1021 0.436609414377 Henry Cohn, 2024, needs more optimization.
17 1022 0.436781203799 Henry Cohn, 2024, needs more optimization.
17 1024 0.436902662142 Henry Cohn, 2024, needs more optimization.
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 0.050097355285 Henry Cohn, 2024.
18 39 0.055496642883 Henry Cohn, 2023.
18 40 0.055679405296 Henry Cohn, 2023.
18 41 0.060967744952 Henry Cohn, 2023.
18 42 0.063513513654 Henry Cohn, 2023.
18 43 0.066629786536 Henry Cohn, 2024.
18 44 0.066804066179 Henry Cohn, 2023.
18 45 0.071480326622 Henry Cohn, 2023.
18 47 0.073591871415 Orthogonal union of 45 points in 17 dimensions and 2 points in 1 dimension.
239⁢x2−4⁢x−1
18 48 0.074706792917 Henry Cohn, 2024.
18 49 0.082857935323 Henry Cohn, 2024.
18 50 0.084341789890 Henry Cohn, 2025.
18 51 0.084342055354 Henry Cohn, 2025.
18 52 0.084342513820 Henry Cohn, 2025, needs more optimization.
18 53 0.084342571240 Henry Cohn, 2025, needs more optimization.
18 54 0.084342580848 Henry Cohn, 2025, needs more optimization.
18 55 0.091780747508 Henry Cohn, 2024.
18 56 0.100706557396 Henry Cohn, 2024, needs more optimization.
18 69 0.101456854890 Henry Cohn, 2024.
176⁢x2−8⁢x−1
18 70 0.124365606167 Henry Cohn, 2024, needs more optimization.
18 71 0.126287326819 Henry Cohn, 2024, needs more optimization.
18 72 0.126734461106 Henry Cohn, 2024, needs more optimization.
18 73 0.127231029811 Henry Cohn, 2024, needs more optimization.
18 74 0.127231034165 Henry Cohn, 2024, needs more optimization.
18 75 0.127231547545 Henry Cohn, 2024, needs more optimization.
18 76 0.127231696530 Henry Cohn, 2024, needs more optimization.
18 77 0.127231993391 Henry Cohn, 2024, needs more optimization.
18 78 0.127232067990 Henry Cohn, 2024, needs more optimization.
18 79 0.127337132836 Henry Cohn, 2024, needs more optimization.
18 80 0.131978166860 Henry Cohn, 2024, needs more optimization.
18 81 0.132691626241 Henry Cohn, 2024, needs more optimization.
18 82 0.132705940144 Henry Cohn, 2024, needs more optimization.
18 83 0.132712957021 Henry Cohn, 2024, needs more optimization.
18 84 0.132840170112 Henry Cohn, 2024, needs more optimization.
18 85 0.134332983545 Henry Cohn, 2024, needs more optimization.
18 88 0.134690494495 Henry Cohn, 2023.
18⁢x2+5⁢x−1
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 98 0.166666666667 Kissing configuration of 192 points in 19 dimensions from T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
6⁢x−1
18 99 0.169352083166 Henry Cohn, 2025, needs more optimization.
18 100 0.178659412307 Henry Cohn, 2024, needs more optimization.
18 101 0.179730319617 Henry Cohn, 2024, needs more optimization.
18 102 0.180547043804 Henry Cohn, 2024, needs more optimization.
18 103 0.181782384802 Henry Cohn, 2024, needs more optimization.
18 104 0.183095085970 Henry Cohn, 2024, needs more optimization.
18 105 0.183761500612 Henry Cohn, 2024, needs more optimization.
18 106 0.185516217075 Henry Cohn, 2024, needs more optimization.
18 107 0.186064748882 Henry Cohn, 2024, needs more optimization.
18 108 0.186999015538 Henry Cohn, 2024, needs more optimization.
18 109 0.188289490261 Henry Cohn, 2024, needs more optimization.
18 110 0.189408874495 Henry Cohn, 2024, needs more optimization.
18 111 0.189985126187 Henry Cohn, 2024, needs more optimization.
18 112 0.191473371837 Henry Cohn, 2024, needs more optimization.
18 120 0.191489361703 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
47⁢x−9
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
18 134 0.199974655603 Henry Cohn, 2024, needs more optimization.
18 144 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
18 163 0.202913709779 Orthogonal union of 159 points in 16 dimensions and 4 points in 2 dimensions.
44⁢x2−4⁢x−1
18 164 0.203540421439 Orthogonal union of 162 points in 17 dimensions and 2 points in 1 dimension.
18 168 0.224489795919 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
49⁢x−11
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
18 292 0.25 Code with 290 points in 17 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.
4⁢x−1
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
18 428 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
18 672 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
18 673 0.381882238347 Henry Cohn, 2024, needs more optimization.
18 674 0.382072236083 Henry Cohn, 2024, needs more optimization.
18 675 0.382142923873 Henry Cohn, 2024, needs more optimization.
18 676 0.382202149475 Henry Cohn, 2024, needs more optimization.
18 677 0.382386802944 Henry Cohn, 2024, needs more optimization.
18 680 0.382715938698 Henry Cohn, 2024, needs more optimization.
18 681 0.383193806956 Henry Cohn, 2024, needs more optimization.
18 682 0.383230994509 Henry Cohn, 2024, needs more optimization.
18 683 0.383352867938 Henry Cohn, 2024, needs more optimization.
18 684 0.383490345654 Henry Cohn, 2024, needs more optimization.
18 685 0.383579516271 Henry Cohn, 2024, needs more optimization.
18 686 0.383800508465 Henry Cohn, 2024, needs more optimization.
18 687 0.383886911322 Henry Cohn, 2024, needs more optimization.
18 688 0.384028417611 Henry Cohn, 2024, needs more optimization.
18 689 0.384281436595 Henry Cohn, 2024, needs more optimization.
18 693 0.384351229812 Henry Cohn, 2024, needs more optimization.
18 694 0.384692581058 Henry Cohn, 2024, needs more optimization.
18 695 0.384985783497 Henry Cohn, 2024, needs more optimization.
18 696 0.385038388725 Henry Cohn, 2024, needs more optimization.
18 698 0.385380469940 Henry Cohn, 2024, needs more optimization.
18 699 0.385628509541 Henry Cohn, 2024, needs more optimization.
18 701 0.385757723183 Henry Cohn, 2024, needs more optimization.
18 702 0.385829167163 Henry Cohn, 2024, needs more optimization.
18 704 0.385892784616 Henry Cohn, 2024, needs more optimization.
18 705 0.386361736598 Henry Cohn, 2024, needs more optimization.
18 706 0.386436422811 Henry Cohn, 2024, needs more optimization.
18 708 0.386585561570 Henry Cohn, 2024, needs more optimization.
18 709 0.386739365227 Henry Cohn, 2024, needs more optimization.
18 710 0.386792807185 Henry Cohn, 2024, needs more optimization.
18 712 0.387156159024 Henry Cohn, 2024, needs more optimization.
18 714 0.387228673982 Henry Cohn, 2024, needs more optimization.
18 716 0.387586823112 Henry Cohn, 2024, needs more optimization.
18 717 0.387658082674 Henry Cohn, 2024, needs more optimization.
18 718 0.387755799152 Henry Cohn, 2024, needs more optimization.
18 719 0.387805752128 Henry Cohn, 2024, needs more optimization.
18 721 0.388079274832 Henry Cohn, 2024, needs more optimization.
18 722 0.388299981075 Henry Cohn, 2024, needs more optimization.
18 723 0.388616828770 Henry Cohn, 2024, needs more optimization.
18 724 0.388665435219 Henry Cohn, 2024, needs more optimization.
18 725 0.388764924235 Henry Cohn, 2024, needs more optimization.
18 726 0.388873634544 Henry Cohn, 2024, needs more optimization.
18 727 0.389114978861 Henry Cohn, 2024, needs more optimization.
18 728 0.389170586020 Henry Cohn, 2024, needs more optimization.
18 730 0.389228720435 Henry Cohn, 2024, needs more optimization.
18 731 0.389554745895 Henry Cohn, 2024, needs more optimization.
18 733 0.389725507021 Henry Cohn, 2024, needs more optimization.
18 734 0.389856823949 Henry Cohn, 2024, needs more optimization.
18 735 0.390176037015 Henry Cohn, 2024, needs more optimization.
18 736 0.390243560927 Henry Cohn, 2024, needs more optimization.
18 738 0.390313861573 Henry Cohn, 2024, needs more optimization.
18 739 0.390335790413 Henry Cohn, 2024, needs more optimization.
18 740 0.390359413753 Henry Cohn, 2024, needs more optimization.
18 741 0.390826521166 Henry Cohn, 2024, needs more optimization.
18 745 0.390943879933 Henry Cohn, 2024, needs more optimization.
18 746 0.391353437884 Henry Cohn, 2024, needs more optimization.
18 747 0.391491200463 Henry Cohn, 2024, needs more optimization.
18 749 0.391648250562 Henry Cohn, 2024, needs more optimization.
18 751 0.391810974203 Henry Cohn, 2024, needs more optimization.
18 752 0.392021063393 Henry Cohn, 2024, needs more optimization.
18 754 0.392188204511 Henry Cohn, 2024, needs more optimization.
18 757 0.392353130681 Henry Cohn, 2024, needs more optimization.
18 758 0.392755353780 Henry Cohn, 2024, needs more optimization.
18 760 0.392930830851 Henry Cohn, 2024, needs more optimization.
18 761 0.392941975224 Henry Cohn, 2024, needs more optimization.
18 762 0.393006281878 Henry Cohn, 2024, needs more optimization.
18 763 0.393112427394 Henry Cohn, 2024, needs more optimization.
18 764 0.393436174790 Henry Cohn, 2024, needs more optimization.
18 767 0.393456759677 Henry Cohn, 2024, needs more optimization.
18 768 0.393728570183 Henry Cohn, 2024, needs more optimization.
18 770 0.394097609975 Henry Cohn, 2024, needs more optimization.
18 771 0.394222665696 Henry Cohn, 2024, needs more optimization.
18 772 0.394296677389 Henry Cohn, 2024, needs more optimization.
18 773 0.394330431277 Henry Cohn, 2024, needs more optimization.
18 774 0.394505713966 Henry Cohn, 2024, needs more optimization.
18 775 0.394528536564 Henry Cohn, 2024, needs more optimization.
18 776 0.394789403081 Henry Cohn, 2024, needs more optimization.
18 779 0.394914404855 Henry Cohn, 2024, needs more optimization.
18 780 0.395066580522 Henry Cohn, 2024, needs more optimization.
18 781 0.395281132651 Henry Cohn, 2024, needs more optimization.
18 784 0.395493176436 Henry Cohn, 2024, needs more optimization.
18 785 0.395536981061 Henry Cohn, 2024, needs more optimization.
18 786 0.395779548425 Henry Cohn, 2024, needs more optimization.
18 787 0.395947021758 Henry Cohn, 2024, needs more optimization.
18 788 0.396163586513 Henry Cohn, 2024, needs more optimization.
18 791 0.396370476254 Henry Cohn, 2024, needs more optimization.
18 792 0.396677515004 Henry Cohn, 2024, needs more optimization.
18 794 0.396773232630 Henry Cohn, 2024, needs more optimization.
18 796 0.396902458963 Henry Cohn, 2024, needs more optimization.
18 798 0.397164374182 Henry Cohn, 2024, needs more optimization.
18 799 0.397250865082 Henry Cohn, 2024, needs more optimization.
18 800 0.397344960638 Henry Cohn, 2024, needs more optimization.
18 801 0.397521126339 Henry Cohn, 2024, needs more optimization.
18 802 0.397608415948 Henry Cohn, 2024, needs more optimization.
18 803 0.397660514969 Henry Cohn, 2024, needs more optimization.
18 806 0.398055907665 Henry Cohn, 2024, needs more optimization.
18 807 0.398210867691 Henry Cohn, 2024, needs more optimization.
18 808 0.398356778498 Henry Cohn, 2024, needs more optimization.
18 809 0.398479654962 Henry Cohn, 2024, needs more optimization.
18 811 0.398587971656 Henry Cohn, 2024, needs more optimization.
18 812 0.398799205928 Henry Cohn, 2024, needs more optimization.
18 813 0.398861905894 Henry Cohn, 2024, needs more optimization.
18 815 0.399011967958 Henry Cohn, 2024, needs more optimization.
18 816 0.399257989217 Henry Cohn, 2024, needs more optimization.
18 817 0.399399093150 Henry Cohn, 2024, needs more optimization.
18 818 0.399447531159 Henry Cohn, 2024, needs more optimization.
18 819 0.399565047151 Henry Cohn, 2024, needs more optimization.
18 820 0.399782470090 Henry Cohn, 2024, needs more optimization.
18 822 0.399828148764 Henry Cohn, 2024, needs more optimization.
18 823 0.399936640023 Henry Cohn, 2024, needs more optimization.
18 824 0.400100753735 Henry Cohn, 2024, needs more optimization.
18 825 0.400262539454 Henry Cohn, 2024, needs more optimization.
18 826 0.400272052483 Henry Cohn, 2024, needs more optimization.
18 827 0.400349667976 Henry Cohn, 2024, needs more optimization.
18 828 0.400482734888 Henry Cohn, 2024, needs more optimization.
18 829 0.400487915511 Henry Cohn, 2024, needs more optimization.
18 831 0.400770979889 Henry Cohn, 2024, needs more optimization.
18 832 0.400781138026 Henry Cohn, 2024, needs more optimization.
18 833 0.401080042384 Henry Cohn, 2024, needs more optimization.
18 834 0.401159758420 Henry Cohn, 2024, needs more optimization.
18 835 0.401177713973 Henry Cohn, 2024, needs more optimization.
18 836 0.401373159382 Henry Cohn, 2024, needs more optimization.
18 837 0.401448683635 Henry Cohn, 2024, needs more optimization.
18 838 0.401478575234 Henry Cohn, 2024, needs more optimization.
18 839 0.401811430144 Henry Cohn, 2024, needs more optimization.
18 840 0.401890420334 Henry Cohn, 2024, needs more optimization.
18 842 0.401905953249 Henry Cohn, 2024, needs more optimization.
18 844 0.402074410431 Henry Cohn, 2024, needs more optimization.
18 845 0.402291613993 Henry Cohn, 2024, needs more optimization.
18 846 0.402420741155 Henry Cohn, 2024, needs more optimization.
18 847 0.402494843281 Henry Cohn, 2024, needs more optimization.
18 850 0.402544372853 Henry Cohn, 2024, needs more optimization.
18 851 0.402872999392 Henry Cohn, 2024, needs more optimization.
18 853 0.402984706030 Henry Cohn, 2024, needs more optimization.
18 855 0.403069506847 Henry Cohn, 2024, needs more optimization.
18 856 0.403477317038 Henry Cohn, 2024, needs more optimization.
18 858 0.403633348837 Henry Cohn, 2024, needs more optimization.
18 859 0.403813599919 Henry Cohn, 2024, needs more optimization.
18 860 0.403836027434 Henry Cohn, 2024, needs more optimization.
18 861 0.403934970638 Henry Cohn, 2024, needs more optimization.
18 862 0.403994974441 Henry Cohn, 2024, needs more optimization.
18 864 0.404146154357 Henry Cohn, 2024, needs more optimization.
18 866 0.404243120326 Henry Cohn, 2024, needs more optimization.
18 867 0.404434372381 Henry Cohn, 2024, needs more optimization.
18 868 0.404480979810 Henry Cohn, 2024, needs more optimization.
18 870 0.404662731548 Henry Cohn, 2024, needs more optimization.
18 871 0.404806282245 Henry Cohn, 2024, needs more optimization.
18 872 0.404934378238 Henry Cohn, 2024, needs more optimization.
18 874 0.404943335401 Henry Cohn, 2024, needs more optimization.
18 876 0.405323933396 Henry Cohn, 2024, needs more optimization.
18 879 0.405451059230 Henry Cohn, 2024, needs more optimization.
18 882 0.405861383599 Henry Cohn, 2024, needs more optimization.
18 883 0.406202070203 Henry Cohn, 2024, needs more optimization.
18 884 0.406208919820 Henry Cohn, 2024, needs more optimization.
18 886 0.406411852575 Henry Cohn, 2024, needs more optimization.
18 887 0.406496990991 Henry Cohn, 2024, needs more optimization.
18 889 0.406530959547 Henry Cohn, 2024, needs more optimization.
18 890 0.406717872909 Henry Cohn, 2024, needs more optimization.
18 893 0.406768715817 Henry Cohn, 2024, needs more optimization.
18 894 0.407072481723 Henry Cohn, 2024, needs more optimization.
18 896 0.407286205938 Henry Cohn, 2024, needs more optimization.
18 897 0.407345992880 Henry Cohn, 2024, needs more optimization.
18 899 0.407519130680 Henry Cohn, 2024, needs more optimization.
18 900 0.407761704634 Henry Cohn, 2024, needs more optimization.
18 902 0.407867369917 Henry Cohn, 2024, needs more optimization.
18 903 0.407914977119 Henry Cohn, 2024, needs more optimization.
18 904 0.408077380610 Henry Cohn, 2024, needs more optimization.
18 906 0.408079330793 Henry Cohn, 2024, needs more optimization.
18 907 0.408381314672 Henry Cohn, 2024, needs more optimization.
18 909 0.408604614614 Henry Cohn, 2024, needs more optimization.
18 911 0.408735058921 Henry Cohn, 2024, needs more optimization.
18 912 0.408770728698 Henry Cohn, 2024, needs more optimization.
18 913 0.408955611870 Henry Cohn, 2024, needs more optimization.
18 915 0.409101945509 Henry Cohn, 2024, needs more optimization.
18 916 0.409226884664 Henry Cohn, 2024, needs more optimization.
18 917 0.409477036115 Henry Cohn, 2024, needs more optimization.
18 918 0.409569783479 Henry Cohn, 2024, needs more optimization.
18 919 0.409598998905 Henry Cohn, 2024, needs more optimization.
18 921 0.409706986423 Henry Cohn, 2024, needs more optimization.
18 923 0.409855061123 Henry Cohn, 2024, needs more optimization.
18 927 0.410093902076 Henry Cohn, 2024, needs more optimization.
18 928 0.410466394450 Henry Cohn, 2024, needs more optimization.
18 930 0.410492781204 Henry Cohn, 2024, needs more optimization.
18 932 0.410661096232 Henry Cohn, 2024, needs more optimization.
18 935 0.410895638001 Henry Cohn, 2024, needs more optimization.
18 938 0.411114049121 Henry Cohn, 2024, needs more optimization.
18 940 0.411392232466 Henry Cohn, 2024, needs more optimization.
18 942 0.411577192193 Henry Cohn, 2024, needs more optimization.
18 944 0.411741042548 Henry Cohn, 2024, needs more optimization.
18 946 0.411856730126 Henry Cohn, 2024, needs more optimization.
18 947 0.412011170041 Henry Cohn, 2024, needs more optimization.
18 948 0.412040968379 Henry Cohn, 2024, needs more optimization.
18 951 0.412389500138 Henry Cohn, 2024, needs more optimization.
18 952 0.412588389152 Henry Cohn, 2024, needs more optimization.
18 953 0.412673392911 Henry Cohn, 2024, needs more optimization.
18 955 0.412822649056 Henry Cohn, 2024, needs more optimization.
18 959 0.412958817496 Henry Cohn, 2024, needs more optimization.
18 960 0.413049890437 Henry Cohn, 2024, needs more optimization.
18 961 0.413374128398 Henry Cohn, 2024, needs more optimization.
18 962 0.413421222566 Henry Cohn, 2024, needs more optimization.
18 964 0.413486696118 Henry Cohn, 2024, needs more optimization.
18 965 0.413808405479 Henry Cohn, 2024, needs more optimization.
18 966 0.413818088968 Henry Cohn, 2024, needs more optimization.
18 968 0.413891040548 Henry Cohn, 2024, needs more optimization.
18 969 0.414099856215 Henry Cohn, 2024, needs more optimization.
18 970 0.414170270898 Henry Cohn, 2024, needs more optimization.
18 972 0.414334037524 Henry Cohn, 2024, needs more optimization.
18 974 0.414420409458 Henry Cohn, 2024, needs more optimization.
18 975 0.414508069057 Henry Cohn, 2024, needs more optimization.
18 977 0.414886137310 Henry Cohn, 2024, needs more optimization.
18 979 0.414932276509 Henry Cohn, 2024, needs more optimization.
18 981 0.414975637306 Henry Cohn, 2024, needs more optimization.
18 982 0.415125639043 Henry Cohn, 2024, needs more optimization.
18 984 0.415410232025 Henry Cohn, 2024, needs more optimization.
18 988 0.415550952501 Henry Cohn, 2024, needs more optimization.
18 989 0.415870828619 Henry Cohn, 2024, needs more optimization.
18 990 0.415970423379 Henry Cohn, 2024, needs more optimization.
18 991 0.416021202407 Henry Cohn, 2024, needs more optimization.
18 992 0.416070703638 Henry Cohn, 2024, needs more optimization.
18 993 0.416215718016 Henry Cohn, 2024, needs more optimization.
18 994 0.416381065267 Henry Cohn, 2024, needs more optimization.
18 996 0.416414007226 Henry Cohn, 2024, needs more optimization.
18 997 0.416499837145 Henry Cohn, 2024, needs more optimization.
18 1000 0.416535748430 Henry Cohn, 2024, needs more optimization.
18 1003 0.416783580293 Henry Cohn, 2024, needs more optimization.
18 1006 0.417155596180 Henry Cohn, 2024, needs more optimization.
18 1007 0.417343117029 Henry Cohn, 2024, needs more optimization.
18 1008 0.417353930914 Henry Cohn, 2024, needs more optimization.
18 1011 0.417571211515 Henry Cohn, 2024, needs more optimization.
18 1012 0.417868504677 Henry Cohn, 2024, needs more optimization.
18 1014 0.417895527415 Henry Cohn, 2024, needs more optimization.
18 1017 0.417924976976 Henry Cohn, 2024, needs more optimization.
18 1018 0.418152654104 Henry Cohn, 2024, needs more optimization.
18 1020 0.418311431874 Henry Cohn, 2024, needs more optimization.
18 1022 0.418468104840 Henry Cohn, 2024, needs more optimization.
18 1023 0.418536813051 Henry Cohn, 2024, needs more optimization.
18 1024 0.418647742045 Henry Cohn, 2024, needs more optimization.
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, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
21⁢x−1
19 41 0.053165944699 Henry Cohn, 2023.
19 42 0.053978485836 Henry Cohn, 2024.
19 43 0.058595439159 Henry Cohn, 2024.
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 0.077590423532 Henry Cohn, 2025.
19 52 0.081692292171 Henry Cohn, 2024.
19 55 0.082347572441 Henry Cohn, 2024.
19 56 0.083234473074 Henry Cohn, 2024, needs more optimization.
19 57 0.087399418323 Henry Cohn, 2024, needs more optimization.
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 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 71 0.101456854890 Orthogonal union of 69 points in 18 dimensions and 2 points in 1 dimension.
176⁢x2−8⁢x−1
19 72 0.111111111112 Kissing configuration of 105 points in 20 dimensions from T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
9⁢x−1
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
19 100 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
19 132 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
19 161 0.191176470589 Henry Cohn, 2025.
68⁢x−13
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
19 207 0.224489795919 Orthogonal union of 205 points in 18 dimensions and 2 points in 1 dimension.
49⁢x−11
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
19 294 0.25 Code with 292 points in 18 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.
4⁢x−1
19 295 0.25 Orthogonal union of 288 points in 16 dimensions and 7 points in 3 dimensions.
4⁢x−1
19 296 0.261203874964 Orthogonal union of 288 points in 16 dimensions and 8 points in 3 dimensions.
7⁢x2+2⁢x−1
19 297 0.287145797248 Henry Cohn, 2024, needs more optimization.
19 298 0.287650791289 Henry Cohn, 2024, needs more optimization.
19 299 0.287869795969 Henry Cohn, 2024, needs more optimization.
19 300 0.288194637913 Henry Cohn, 2024, needs more optimization.
19 301 0.288677844562 Henry Cohn, 2024, needs more optimization.
19 302 0.288996441769 Henry Cohn, 2024, needs more optimization.
19 303 0.289290540684 Henry Cohn, 2024, needs more optimization.
19 304 0.289998359816 Henry Cohn, 2024, needs more optimization.
19 305 0.290021314680 Henry Cohn, 2024, needs more optimization.
19 306 0.290339955951 Henry Cohn, 2024, needs more optimization.
19 307 0.290837605355 Henry Cohn, 2024, needs more optimization.
19 309 0.291329090639 Henry Cohn, 2024, needs more optimization.
19 310 0.291575526098 Henry Cohn, 2024, needs more optimization.
19 311 0.291881837388 Henry Cohn, 2024, needs more optimization.
19 312 0.292263444969 Henry Cohn, 2024, needs more optimization.
19 314 0.292528278557 Henry Cohn, 2024, needs more optimization.
19 316 0.293309670301 Henry Cohn, 2024, needs more optimization.
19 317 0.293800985760 Henry Cohn, 2024, needs more optimization.
19 318 0.294138131713 Henry Cohn, 2024, needs more optimization.
19 320 0.294554825180 Henry Cohn, 2024, needs more optimization.
19 321 0.295166247077 Henry Cohn, 2024, needs more optimization.
19 322 0.295277376894 Henry Cohn, 2024, needs more optimization.
19 325 0.295816115519 Henry Cohn, 2024, needs more optimization.
19 433 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
19 896 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 0.390834643812 Henry Cohn, 2024, needs more optimization.
19 898 0.390857158396 Henry Cohn, 2024, needs more optimization.
19 899 0.390946592249 Henry Cohn, 2024, needs more optimization.
19 901 0.391030500965 Henry Cohn, 2024, needs more optimization.
19 902 0.391380459985 Henry Cohn, 2024, needs more optimization.
19 903 0.391382187600 Henry Cohn, 2024, needs more optimization.
19 904 0.391400799372 Henry Cohn, 2024, needs more optimization.
19 906 0.391559066154 Henry Cohn, 2024, needs more optimization.
19 907 0.391707435412 Henry Cohn, 2024, needs more optimization.
19 908 0.391921316849 Henry Cohn, 2024, needs more optimization.
19 911 0.392035701674 Henry Cohn, 2024, needs more optimization.
19 912 0.392301156900 Henry Cohn, 2024, needs more optimization.
19 913 0.392445731121 Henry Cohn, 2024, needs more optimization.
19 914 0.392450788785 Henry Cohn, 2024, needs more optimization.
19 915 0.392523966871 Henry Cohn, 2024, needs more optimization.
19 916 0.392613757131 Henry Cohn, 2024, needs more optimization.
19 917 0.392713050951 Henry Cohn, 2024, needs more optimization.
19 918 0.392823363610 Henry Cohn, 2024, needs more optimization.
19 919 0.392954829683 Henry Cohn, 2024, needs more optimization.
19 920 0.392994742253 Henry Cohn, 2024, needs more optimization.
19 922 0.393013851609 Henry Cohn, 2024, needs more optimization.
19 923 0.393324756971 Henry Cohn, 2024, needs more optimization.
19 924 0.393420206358 Henry Cohn, 2024, needs more optimization.
19 925 0.393443142904 Henry Cohn, 2024, needs more optimization.
19 926 0.393605995930 Henry Cohn, 2024, needs more optimization.
19 927 0.393773585459 Henry Cohn, 2024, needs more optimization.
19 928 0.393816574004 Henry Cohn, 2024, needs more optimization.
19 929 0.393872777427 Henry Cohn, 2024, needs more optimization.
19 930 0.394002714050 Henry Cohn, 2024, needs more optimization.
19 932 0.394114863445 Henry Cohn, 2024, needs more optimization.
19 933 0.394158080573 Henry Cohn, 2024, needs more optimization.
19 934 0.394304186478 Henry Cohn, 2024, needs more optimization.
19 935 0.394414717215 Henry Cohn, 2024, needs more optimization.
19 936 0.394447512882 Henry Cohn, 2024, needs more optimization.
19 938 0.394585875542 Henry Cohn, 2024, needs more optimization.
19 939 0.394726940459 Henry Cohn, 2024, needs more optimization.
19 940 0.394769435486 Henry Cohn, 2024, needs more optimization.
19 941 0.394950341427 Henry Cohn, 2024, needs more optimization.
19 943 0.395046159683 Henry Cohn, 2024, needs more optimization.
19 945 0.395247203086 Henry Cohn, 2024, needs more optimization.
19 946 0.395248752867 Henry Cohn, 2024, needs more optimization.
19 948 0.395500530653 Henry Cohn, 2024, needs more optimization.
19 950 0.395671720856 Henry Cohn, 2024, needs more optimization.
19 951 0.395710396579 Henry Cohn, 2024, needs more optimization.
19 952 0.395795312276 Henry Cohn, 2024, needs more optimization.
19 953 0.396062339948 Henry Cohn, 2024, needs more optimization.
19 954 0.396194153258 Henry Cohn, 2024, needs more optimization.
19 955 0.396248060742 Henry Cohn, 2024, needs more optimization.
19 957 0.396300490649 Henry Cohn, 2024, needs more optimization.
19 959 0.396462785919 Henry Cohn, 2024, needs more optimization.
19 960 0.396477079690 Henry Cohn, 2024, needs more optimization.
19 961 0.396697759959 Henry Cohn, 2024, needs more optimization.
19 962 0.396759263616 Henry Cohn, 2024, needs more optimization.
19 963 0.396819306358 Henry Cohn, 2024, needs more optimization.
19 965 0.397013816148 Henry Cohn, 2024, needs more optimization.
19 968 0.397160938691 Henry Cohn, 2024, needs more optimization.
19 969 0.397431807941 Henry Cohn, 2024, needs more optimization.
19 970 0.397502671018 Henry Cohn, 2024, needs more optimization.
19 971 0.397555405911 Henry Cohn, 2024, needs more optimization.
19 972 0.397779247360 Henry Cohn, 2024, needs more optimization.
19 974 0.397779552473 Henry Cohn, 2024, needs more optimization.
19 975 0.397911818010 Henry Cohn, 2024, needs more optimization.
19 976 0.397979801663 Henry Cohn, 2024, needs more optimization.
19 978 0.398205880714 Henry Cohn, 2024, needs more optimization.
19 979 0.398237622934 Henry Cohn, 2024, needs more optimization.
19 981 0.398461075292 Henry Cohn, 2024, needs more optimization.
19 982 0.398630724417 Henry Cohn, 2024, needs more optimization.
19 983 0.398733171399 Henry Cohn, 2024, needs more optimization.
19 984 0.398785592717 Henry Cohn, 2024, needs more optimization.
19 985 0.398809349988 Henry Cohn, 2024, needs more optimization.
19 987 0.398932392475 Henry Cohn, 2024, needs more optimization.
19 989 0.399056393246 Henry Cohn, 2024, needs more optimization.
19 990 0.399291901661 Henry Cohn, 2024, needs more optimization.
19 991 0.399362751981 Henry Cohn, 2024, needs more optimization.
19 994 0.399421456974 Henry Cohn, 2024, needs more optimization.
19 995 0.399581128586 Henry Cohn, 2024, needs more optimization.
19 998 0.399765495260 Henry Cohn, 2024, needs more optimization.
19 1000 0.399970596369 Henry Cohn, 2024, needs more optimization.
19 1001 0.400271078297 Henry Cohn, 2024, needs more optimization.
19 1002 0.400279351183 Henry Cohn, 2024, needs more optimization.
19 1004 0.400355773281 Henry Cohn, 2024, needs more optimization.
19 1005 0.400424827962 Henry Cohn, 2024, needs more optimization.
19 1006 0.400571462524 Henry Cohn, 2024, needs more optimization.
19 1008 0.400634859202 Henry Cohn, 2024, needs more optimization.
19 1009 0.400933800860 Henry Cohn, 2024, needs more optimization.
19 1013 0.401002062744 Henry Cohn, 2024, needs more optimization.
19 1015 0.401263641385 Henry Cohn, 2024, needs more optimization.
19 1016 0.401346431047 Henry Cohn, 2024, needs more optimization.
19 1017 0.401497776525 Henry Cohn, 2024, needs more optimization.
19 1020 0.401602079866 Henry Cohn, 2024, needs more optimization.
19 1021 0.401681432165 Henry Cohn, 2024, needs more optimization.
19 1023 0.401879787697 Henry Cohn, 2024, needs more optimization.
19 1024 0.401890927906 Henry Cohn, 2024, needs more optimization.
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.
20 44 0.051781487230 Henry Cohn, 2023.
20 45 0.053400898990 Henry Cohn, 2023.
Minimal polynomial listed in plain text data
20 46 0.053974615052 Henry Cohn, 2024.
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 0.063705147384 Henry Cohn, 2024, needs more optimization.
20 56* 0.066666666667 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.
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 68 0.097744360903 Code with 66 points in 19 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.
133⁢x−13
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 91 0.112912613537 Orthogonal union of 89 points in 19 dimensions and 2 points in 1 dimension.
167⁢x2−10⁢x−1
20 92 0.121296351927 Henry Cohn, 2024, 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
20 120 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
20 141 0.157693167973 Henry Cohn, 2024, 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
20 178 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, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
5⁢x−1
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
20 473 0.266666666667 Henry Cohn, 2025.
15⁢x−4
20 484 0.285773803325 Henry Cohn, 2025.
600⁢x2−49
20 495 0.3 Henry Cohn, 2025.
10⁢x−3
20 562 0.304347826087 Orthogonal union of 560 points in 19 dimensions and 2 points in 1 dimension.
23⁢x−7
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 1024 0.333333333334 Subcode of a code of size 1280 from T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
3⁢x−1
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 58 0.066666666667 Code with 56 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.
15⁢x−1
21 62 0.076923076924 Orthogonal union of 60 points in 20 dimensions and 2 points in 1 dimension.
13⁢x−1
21 65 0.081967213115 Code with 63 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.
61⁢x−5
21 77* 0.083333333334 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.
12⁢x−1
21 83 0.1 Orthogonal union of 81 points in 20 dimensions and 2 points in 1 dimension.
10⁢x−1
21 84 0.108590652447 Henry Cohn, 2024, needs more optimization.
21 85 0.108625960832 Henry Cohn, 2024, needs more optimization.
21 86 0.108684328078 Henry Cohn, 2025, needs more optimization.
21 87 0.108696266790 Henry Cohn, 2024, needs more optimization.
21 88 0.110904311873 Henry Cohn, 2025, needs more optimization.
21 89 0.110914474416 Henry Cohn, 2025, 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
21 119 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
21 162* 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
21 198 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
21 380 0.236363636364 Orthogonal union of 378 points in 20 dimensions and 2 points in 1 dimension.
55⁢x−13
21 554 0.238095238096 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
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 0.041709069258 Henry Cohn, 2024.
22 47 0.047589349078 Henry Cohn, 2024, needs more optimization.
22 48 0.047607868430 Henry Cohn, 2025.
22 52 0.047619047620 Code with 50 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.
21⁢x−1
22 53 0.057560345703 Henry Cohn, 2024.
22 54 0.060109536347 Henry Cohn, 2024.
22 55 0.064389502899 Henry Cohn, 2024.
22 56 0.066665131058 Henry Cohn, 2024, needs more optimization.
22 57 0.066665224778 Henry Cohn, 2024, needs more optimization.
22 58 0.066665292935 Henry Cohn, 2024, needs more optimization.
22 59 0.066665386858 Henry Cohn, 2024, needs more optimization.
22 60 0.066665425579 Henry Cohn, 2024, needs more optimization.
22 61 0.076913304860 Henry Cohn, 2024, needs more optimization.
22 62 0.076920313939 Henry Cohn, 2024, needs more optimization.
22 63 0.076920526653 Henry Cohn, 2023, needs more optimization.
22 64 0.076921636641 Henry Cohn, 2024, needs more optimization.
22 65 0.081899203124 Henry Cohn, 2024, needs more optimization.
22 66 0.081899399455 Henry Cohn, 2024, needs more optimization.
22 67 0.081899643727 Henry Cohn, 2024, 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
22 100* 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
22 114 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
22 121 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
22 136 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
22 164 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
22 200 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
22 506 0.232142857143 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
56⁢x−13
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 Subcode of a code of size 1068 from T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
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 0.040044426627 Henry Cohn, 2024.
23 49 0.047348527906 Henry Cohn, 2025.
23 50 0.047356448114 Henry Cohn, 2024.
23 51 0.047573587723 Henry Cohn, 2024, needs more optimization.
23 52 0.047591637534 Henry Cohn, 2024, 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 0.058003088304 Henry Cohn, 2024.
23 57 0.061699263995 Henry Cohn, 2025.
23 58 0.064754385740 Henry Cohn, 2025.
23 59 0.066599568077 Henry Cohn, 2024, needs more optimization.
23 60 0.066599747021 Henry Cohn, 2024, needs more optimization.
23 61 0.066599790838 Henry Cohn, 2024, needs more optimization.
23 62 0.066599803571 Henry Cohn, 2024, needs more optimization.
23 63 0.076569485107 Henry Cohn, 2024, needs more optimization.
23 64 0.076843203970 Henry Cohn, 2024, needs more optimization.
23 65 0.076920526653 Orthogonal union of 63 points in 22 dimensions and 2 points in 1 dimension.
23 66 0.076921399534 Henry Cohn, 2024, needs more optimization.
23 67 0.081511410731 Henry Cohn, 2024, needs more optimization.
23 68 0.081515224996 Henry Cohn, 2024, needs more optimization.
23 69 0.081515424425 Henry Cohn, 2024, needs more optimization.
23 81 0.083333333334 Code with 79 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.
12⁢x−1
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
23 116 0.111111111112 Code with 114 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.
9⁢x−1
23 123 0.131782945737 Code with 121 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.
129⁢x−17
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
23 166 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
23 202 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
23 277 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
23 552* 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
23 893 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, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
26⁢x−1
24 51 0.046482394273 Henry Cohn, 2024.
24 52 0.046700054105 Henry Cohn, 2023.
24 53 0.046732253170 Henry Cohn, 2025.
24 54 0.047334654597 Henry Cohn, 2024.
24 55 0.047381601960 Henry Cohn, 2024.
24 56 0.047563043071 Henry Cohn, 2024, needs more optimization.
24 57 0.053585918417 Henry Cohn, 2024.
24 58 0.057420015167 Henry Cohn, 2024.
24 59 0.061115728362 Henry Cohn, 2024.
24 60 0.062898409960 Henry Cohn, 2024.
24 61 0.064988080059 Henry Cohn, 2024, needs more optimization.
24 62 0.066038108888 Henry Cohn, 2024, needs more optimization.
24 63 0.066050514760 Henry Cohn, 2024, needs more optimization.
24 64 0.066069169133 Henry Cohn, 2024, needs more optimization.
24 65 0.073711806050 Henry Cohn, 2024, needs more optimization.
24 66 0.075407294712 Henry Cohn, 2024, needs more optimization.
24 67 0.076920526653 Orthogonal union of 63 points in 22 dimensions and 4 points in 2 dimensions.
24 68 0.076921397044 Henry Cohn, 2024, needs more optimization.
24 69 0.079925619899 Henry Cohn, 2024, needs more optimization.
24 70 0.079928623926 Henry Cohn, 2024, needs more optimization.
24 71 0.079932994450 Henry Cohn, 2024, needs more optimization.
24 72 0.083315867754 Henry Cohn, 2024, needs more optimization.
24 73 0.083316457730 Henry Cohn, 2024, needs more optimization.
24 74 0.083318929144 Henry Cohn, 2024, needs more optimization.
24 75 0.083319496015 Henry Cohn, 2024, needs more optimization.
24 76 0.083320095951 Henry Cohn, 2024, needs more optimization.
24 79 0.083320127741 Henry Cohn, 2024, needs more optimization.
24 81 0.083320171859 Henry Cohn, 2024, needs more optimization.
24 82 0.083320227319 Henry Cohn, 2024, needs more optimization.
24 83 0.083320245711 Henry Cohn, 2024, needs more optimization.
24 104 0.090909090910 Code with 102 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.
11⁢x−1
24 118 0.111111111112 Code with 116 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.
9⁢x−1
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
24 140 0.135135135136 Code with 138 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.
37⁢x−5
24 150 0.137931034483 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
29⁢x−4
24 168 0.142857142858 Code with 166 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.
7⁢x−1
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
24 279 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
24 297 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
24 895 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 0.037068470388 Henry Cohn, 2024.
25 53 0.045305381447 Henry Cohn, 2025, needs more optimization.
25 54 0.045671054769 Henry Cohn, 2025.
25 55 0.046293915744 Henry Cohn, 2025.
25 56 0.046433703861 Henry Cohn, 2025, needs more optimization.
25 57 0.046863896410 Henry Cohn, 2024.
25 58 0.046863921001 Henry Cohn, 2024.
25 59 0.051394584232 Henry Cohn, 2024.
25 60 0.054819497939 Henry Cohn, 2024, needs more optimization.
25 61 0.057834742840 Henry Cohn, 2024, needs more optimization.
25 62 0.060834800804 Henry Cohn, 2024.
25 63 0.062539270718 Henry Cohn, 2024, needs more optimization.
25 64 0.064572924929 Henry Cohn, 2025, 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 0.070859254811 Henry Cohn, 2024, needs more optimization.
25 68 0.072552478667 Henry Cohn, 2024, needs more optimization.
25 69 0.074036582255 Henry Cohn, 2024, needs more optimization.
25 70 0.075890900184 Henry Cohn, 2024, needs more optimization.
25 71 0.077667493440 Henry Cohn, 2024, needs more optimization.
25 72 0.079380967244 Henry Cohn, 2024, needs more optimization.
25 73 0.079932994450 Orthogonal union of 71 points in 24 dimensions and 2 points in 1 dimension.
25 74 0.082517199979 Henry Cohn, 2024, needs more optimization.
25 75 0.083272592808 Henry Cohn, 2024, needs more optimization.
25 76 0.083275379208 Henry Cohn, 2024, needs more optimization.
25 77 0.083277285065 Henry Cohn, 2024, needs more optimization.
25 78 0.083277450243 Henry Cohn, 2024, needs more optimization.
25 80 0.083277480936 Henry Cohn, 2024, needs more optimization.
25 82 0.083277588099 Henry Cohn, 2024, needs more optimization.
25 83 0.083277708963 Henry Cohn, 2024, needs more optimization.
25 84 0.083277726862 Henry Cohn, 2024, needs more optimization.
25 85 0.083277816799 Henry Cohn, 2024, needs more optimization.
25 106 0.090909090910 Orthogonal union of 100 points in 22 dimensions and 6 points in 3 dimensions.
11⁢x−1
25 107 0.091077579654 Henry Cohn, 2024, needs more optimization.
25 120 0.111111111112 Orthogonal union of 112 points in 21 dimensions and 8 points in 4 dimensions.
9⁢x−1
25 127 0.122807017544 Orthogonal union of 125 points in 24 dimensions and 2 points in 1 dimension.
57⁢x−7
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
25 170 0.142857142858 Orthogonal union of 162 points in 21 dimensions and 8 points in 4 dimensions.
7⁢x−1
25 206 0.161898726407 Henry Cohn, 2024, needs more optimization.
25 207 0.162015199612 Orthogonal union of 198 points in 21 dimensions and 9 points in 4 dimensions.
16⁢x3−16⁢x2−4⁢x+1
25 281 0.166666666667 Orthogonal union of 275 points in 22 dimensions and 6 points in 3 dimensions.
6⁢x−1
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
25 565 0.238095238096 Orthogonal union of 554 points in 21 dimensions and 11 points in 4 dimensions.
21⁢x−5
25 898 0.25 Orthogonal union of 891 points in 22 dimensions and 7 points in 3 dimensions.
4⁢x−1
25 899 0.261203874964 Orthogonal union of 891 points in 22 dimensions and 8 points in 3 dimensions.
7⁢x2+2⁢x−1
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 0.044778403793 Henry Cohn, 2025.
26 56 0.045390664046 Henry Cohn, 2025.
26 57 0.045448993142 Henry Cohn, 2024.
26 58 0.045550434603 Henry Cohn, 2024.
26 59 0.046214515003 Henry Cohn, 2025.
26 60 0.046618911314 Henry Cohn, 2023, needs more optimization.
26 61 0.049729285419 Henry Cohn, 2025.
26 62 0.054364580942 Henry Cohn, 2024.
26 63 0.056595940262 Henry Cohn, 2025.
26 64 0.058813887790 Henry Cohn, 2024.
26 65 0.060920226978 Henry Cohn, 2024, needs more optimization.
26 66 0.062409517127 Henry Cohn, 2024, needs more optimization.
26 67 0.064215465511 Henry Cohn, 2024, needs more optimization.
26 68 0.065382255700 Henry Cohn, 2024, needs more optimization.
26 69 0.068055295390 Henry Cohn, 2024, needs more optimization.
26 70 0.069705026847 Henry Cohn, 2024, needs more optimization.
26 71 0.071406776216 Henry Cohn, 2024, needs more optimization.
26 72 0.073162584167 Henry Cohn, 2024, needs more optimization.
26 73 0.074566578138 Henry Cohn, 2024, needs more optimization.
26 74 0.076283300487 Henry Cohn, 2024, needs more optimization.
26 75 0.077693450489 Henry Cohn, 2024, needs more optimization.
26 76 0.079239045280 Henry Cohn, 2024, needs more optimization.
26 77 0.080191732416 Henry Cohn, 2024, needs more optimization.
26 78 0.081889939582 Henry Cohn, 2024, needs more optimization.
26 79 0.083140987186 Henry Cohn, 2024, needs more optimization.
26 81 0.083140988618 Henry Cohn, 2024, needs more optimization.
26 82 0.083141364030 Henry Cohn, 2024, needs more optimization.
26 83 0.083141489579 Henry Cohn, 2024, needs more optimization.
26 84 0.083141948752 Henry Cohn, 2024, needs more optimization.
26 85 0.083142238408 Henry Cohn, 2024, needs more optimization.
26 86 0.083142598753 Henry Cohn, 2024, needs more optimization.
26 87 0.083142622967 Henry Cohn, 2025, needs more optimization.
26 108 0.090909090910 Orthogonal union of 100 points in 22 dimensions and 8 points in 4 dimensions.
11⁢x−1
26 109 0.090919960401 Henry Cohn, 2024, needs more optimization.
26 122 0.111111111112 Orthogonal union of 112 points in 21 dimensions and 10 points in 5 dimensions.
9⁢x−1
26 123 0.122390273743 Henry Cohn, 2024, needs more optimization.
26 129 0.122807017544 Orthogonal union of 125 points in 24 dimensions and 4 points in 2 dimensions.
57⁢x−7
26 130 0.128585872356 Henry Cohn, 2024, needs more optimization.
26 131 0.129621228208 Henry Cohn, 2024, needs more optimization.
26 132 0.130372356879 Henry Cohn, 2024, needs more optimization.
26 133 0.131517845436 Henry Cohn, 2024, needs more optimization.
26 134 0.132673526822 Henry Cohn, 2024, needs more optimization.
26 158 0.133333333334 Orthogonal union of 156 points in 25 dimensions and 2 points in 1 dimension.
15⁢x−2
26 173 0.142857142858 Orthogonal union of 162 points in 21 dimensions and 11 points in 5 dimensions.
7⁢x−1
26 174 0.153931605034 Orthogonal union of 162 points in 21 dimensions and 12 points in 5 dimensions.
25⁢x4+30⁢x3+24⁢x2+2⁢x−1
26 208 0.161738087734 Henry Cohn, 2024, needs more optimization.
26 210 0.161904761905 Orthogonal union of 198 points in 21 dimensions and 12 points in 5 dimensions.
105⁢x−17
26 285 0.166666666667 Orthogonal union of 275 points in 22 dimensions and 10 points in 4 dimensions.
6⁢x−1
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 0.210138312731 Orthogonal union of 552 points in 23 dimensions and 7 points in 3 dimensions.
3⁢x3−9⁢x2−3⁢x+1
26 570 0.238095238096 Orthogonal union of 554 points in 21 dimensions and 16 points in 5 dimensions.
21⁢x−5
26 903 0.25 Orthogonal union of 891 points in 22 dimensions and 12 points in 4 dimensions.
4⁢x−1
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 0.045164767019 Henry Cohn, 2024, needs more optimization.
27 59 0.045448993142 Orthogonal union of 57 points in 26 dimensions and 2 points in 1 dimension.
27 60 0.045477973897 Henry Cohn, 2024, needs more optimization.
27 61 0.045484387668 Henry Cohn, 2024, needs more optimization.
27 62 0.046198040622 Henry Cohn, 2025.
27 63 0.048347310398 Henry Cohn, 2024.
27 64 0.053101886328 Henry Cohn, 2024.
27 65 0.055852334622 Henry Cohn, 2025.
27 66 0.057595208167 Henry Cohn, 2024, needs more optimization.
27 67 0.058925769246 Henry Cohn, 2024, needs more optimization.
27 68 0.060630177601 Henry Cohn, 2024.
27 69 0.062100307600 Henry Cohn, 2024, needs more optimization.
27 70 0.063788626296 Henry Cohn, 2024, needs more optimization.
27 71 0.065669971479 Henry Cohn, 2024, needs more optimization.
27 72 0.067329777604 Henry Cohn, 2024, needs more optimization.
27 73 0.068891549638 Henry Cohn, 2024, needs more optimization.
27 74 0.070466259239 Henry Cohn, 2024, needs more optimization.
27 75 0.072018515155 Henry Cohn, 2024, needs more optimization.
27 76 0.073241051560 Henry Cohn, 2024, needs more optimization.
27 77 0.074846390601 Henry Cohn, 2024, needs more optimization.
27 78 0.076287127570 Henry Cohn, 2024, needs more optimization.
27 79 0.077816591089 Henry Cohn, 2024, needs more optimization.
27 80 0.079130623680 Henry Cohn, 2024, needs more optimization.
27 81 0.080324829620 Henry Cohn, 2024, needs more optimization.
27 82 0.081492203091 Henry Cohn, 2024, needs more optimization.
27 83 0.082067192009 Henry Cohn, 2024, needs more optimization.
27 84 0.082067710679 Henry Cohn, 2024, needs more optimization.
27 85 0.082071695539 Henry Cohn, 2024, needs more optimization.
27 86 0.082072574279 Henry Cohn, 2025, needs more optimization.
27 87 0.082075263739 Henry Cohn, 2024, needs more optimization.
27 88 0.082075884734 Henry Cohn, 2025, needs more optimization.
27 89 0.082076094696 Henry Cohn, 2025, needs more optimization.
27 90 0.090446472303 Henry Cohn, 2025, needs more optimization.
27 91 0.090859358715 Henry Cohn, 2025, needs more optimization.
27 92 0.090859497185 Henry Cohn, 2025, needs more optimization.
27 93 0.090861821499 Henry Cohn, 2024, needs more optimization.
27 94 0.090862219217 Henry Cohn, 2025, needs more optimization.
27 95 0.090865606481 Henry Cohn, 2025, needs more optimization.
27 96 0.090865643951 Henry Cohn, 2025, needs more optimization.
27 97 0.090867007218 Henry Cohn, 2025, needs more optimization.
27 98 0.090869510059 Henry Cohn, 2025, needs more optimization.
27 99 0.090869835110 Henry Cohn, 2024, needs more optimization.
27 103 0.090870551107 Henry Cohn, 2024, needs more optimization.
27 104 0.090870630103 Henry Cohn, 2024, needs more optimization.
27 110 0.090870650464 Henry Cohn, 2024, needs more optimization.
27 111 0.090919960401 Orthogonal union of 109 points in 26 dimensions and 2 points in 1 dimension.
27 112 0.108878495067 Henry Cohn, 2024, needs more optimization.
27 113 0.109720364549 Henry Cohn, 2024, needs more optimization.
27 114 0.110349808592 Henry Cohn, 2024, needs more optimization.
27 115 0.110518388996 Henry Cohn, 2024, needs more optimization.
27 124 0.111111111112 Orthogonal union of 112 points in 21 dimensions and 12 points in 6 dimensions.
9⁢x−1
27 125 0.113079752138 Henry Cohn, 2025.
27 126 0.118655983153 Henry Cohn, 2024, needs more optimization.
27 127 0.119338328577 Henry Cohn, 2024, needs more optimization.
27 128 0.120387403434 Henry Cohn, 2024, needs more optimization.
27 129 0.121086516893 Henry Cohn, 2024, needs more optimization.
27 130 0.121763812095 Henry Cohn, 2024, needs more optimization.
27 131 0.122558272629 Henry Cohn, 2024, needs more optimization.
27 132 0.123356416124 Henry Cohn, 2024, needs more optimization.
27 133 0.124223661681 Henry Cohn, 2024, needs more optimization.
27 134 0.125185178765 Henry Cohn, 2024, needs more optimization.
27 135 0.126000657289 Henry Cohn, 2024, needs more optimization.
27 136 0.126756977493 Henry Cohn, 2024, needs more optimization.
27 137 0.127656378947 Henry Cohn, 2024, needs more optimization.
27 138 0.128386615966 Henry Cohn, 2024, needs more optimization.
27 139 0.129412457879 Henry Cohn, 2024, needs more optimization.
27 140 0.130033331998 Henry Cohn, 2024, needs more optimization.
27 141 0.131239729329 Henry Cohn, 2024, needs more optimization.
27 142 0.132161392127 Henry Cohn, 2024, needs more optimization.
27 143 0.132730104926 Henry Cohn, 2024, needs more optimization.
27 160 0.133282008372 Henry Cohn, 2024, needs more optimization.
27 176 0.142857142858 Orthogonal union of 162 points in 21 dimensions and 14 points in 6 dimensions.
7⁢x−1
27 177 0.144948974279 Orthogonal union of 162 points in 21 dimensions and 15 points in 6 dimensions.
20⁢x2+4⁢x−1
27 178 0.156242051865 Henry Cohn, 2024, needs more optimization.
27 179 0.156835129928 Henry Cohn, 2024, needs more optimization.
27 180 0.157441600379 Henry Cohn, 2024, needs more optimization.
27 181 0.157913122664 Henry Cohn, 2024, needs more optimization.
27 182 0.158503365264 Henry Cohn, 2024, needs more optimization.
27 183 0.158944962985 Henry Cohn, 2024, needs more optimization.
27 184 0.159541261888 Henry Cohn, 2024, needs more optimization.
27 185 0.160048523360 Henry Cohn, 2024, needs more optimization.
27 186 0.160518518303 Henry Cohn, 2024, needs more optimization.
27 187 0.160932133558 Henry Cohn, 2024, needs more optimization.
27 210 0.161180412496 Henry Cohn, 2024, needs more optimization.
27 213 0.161904761905 Orthogonal union of 198 points in 21 dimensions and 15 points in 6 dimensions.
105⁢x−17
27 287 0.166666666667 Orthogonal union of 275 points in 22 dimensions and 12 points in 5 dimensions.
6⁢x−1
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
27 562 0.2 Orthogonal union of 552 points in 23 dimensions and 10 points in 4 dimensions.
5⁢x−1
27 563 0.230405563595 Orthogonal union of 552 points in 23 dimensions and 11 points in 4 dimensions.
8⁢x3−12⁢x2−2⁢x+1
27 574 0.238095238096 Orthogonal union of 554 points in 21 dimensions and 20 points in 6 dimensions.
21⁢x−5
27 575 0.242852848014 Orthogonal union of 554 points in 21 dimensions and 21 points in 6 dimensions.
27 576 0.248865699460 Orthogonal union of 554 points in 21 dimensions and 22 points in 6 dimensions.
27 907 0.25 Orthogonal union of 891 points in 22 dimensions and 16 points in 5 dimensions.
4⁢x−1
27 908 0.270475835269 Orthogonal union of 891 points in 22 dimensions and 17 points in 5 dimensions.
9⁢x4−16⁢x3−10⁢x2+1
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 0.033360604943 Henry Cohn, 2024.
28 59 0.042130667237 Henry Cohn, 2024.
28 60 0.044335083554 Henry Cohn, 2024.
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 0.047212452650 Henry Cohn, 2024, needs more optimization.
28 66 0.051595142120 Henry Cohn, 2024, needs more optimization.
28 67 0.053745231353 Henry Cohn, 2024, needs more optimization.
28 68 0.055390702742 Henry Cohn, 2024, needs more optimization.
28 69 0.057319064203 Henry Cohn, 2024, needs more optimization.
28 70 0.058669312117 Henry Cohn, 2024, needs more optimization.
28 71 0.060192201114 Henry Cohn, 2024, needs more optimization.
28 72 0.061740693910 Henry Cohn, 2024, needs more optimization.
28 73 0.063360229681 Henry Cohn, 2024, needs more optimization.
28 74 0.064985943644 Henry Cohn, 2024, needs more optimization.
28 75 0.066565679359 Henry Cohn, 2024, needs more optimization.
28 76 0.067874887700 Henry Cohn, 2024, needs more optimization.
28 77 0.069292551218 Henry Cohn, 2024, needs more optimization.
28 78 0.070815091100 Henry Cohn, 2024, needs more optimization.
28 79 0.071926142702 Henry Cohn, 2024, needs more optimization.
28 80 0.073502722079 Henry Cohn, 2024, needs more optimization.
28 81 0.074850109644 Henry Cohn, 2024, needs more optimization.
28 82 0.076375494600 Henry Cohn, 2024, needs more optimization.
28 83 0.077468484219 Henry Cohn, 2024, needs more optimization.
28 84 0.078524579372 Henry Cohn, 2024, needs more optimization.
28 85 0.079836008865 Henry Cohn, 2024, needs more optimization.
28 86 0.080985505621 Henry Cohn, 2025, needs more optimization.
28 87 0.080988340134 Henry Cohn, 2025, needs more optimization.
28 88 0.080996399990 Henry Cohn, 2024, needs more optimization.
28 89 0.081000638124 Henry Cohn, 2025, needs more optimization.
28 90 0.081003444701 Henry Cohn, 2025, needs more optimization.
28 91 0.081004846355 Henry Cohn, 2025, needs more optimization.
28 92 0.087317276777 Henry Cohn, 2025, needs more optimization.
28 93 0.088135125366 Henry Cohn, 2025, needs more optimization.
28 94 0.089029160867 Henry Cohn, 2024, needs more optimization.
28 95 0.089990294813 Henry Cohn, 2025, needs more optimization.
28 96 0.090696537808 Henry Cohn, 2025, needs more optimization.
28 97 0.090710429548 Henry Cohn, 2025, needs more optimization.
28 98 0.090716267543 Henry Cohn, 2025, needs more optimization.
28 99 0.090723561662 Henry Cohn, 2025, needs more optimization.
28 100 0.090728961277 Henry Cohn, 2024, needs more optimization.
28 103 0.090729602437 Henry Cohn, 2024, needs more optimization.
28 104 0.090729651234 Henry Cohn, 2024, needs more optimization.
28 112 0.090730194772 Henry Cohn, 2024, needs more optimization.
28 113 0.090919960401 Orthogonal union of 109 points in 26 dimensions and 4 points in 2 dimensions.
28 114 0.105494009421 Henry Cohn, 2024, needs more optimization.
28 115 0.106095088387 Henry Cohn, 2024, needs more optimization.
28 116 0.106849515191 Henry Cohn, 2024, needs more optimization.
28 117 0.107496092108 Henry Cohn, 2024, needs more optimization.
28 118 0.108333682855 Henry Cohn, 2024, needs more optimization.
28 119 0.108549404733 Henry Cohn, 2024, needs more optimization.
28 120 0.109326786849 Henry Cohn, 2024, needs more optimization.
28 121 0.110031676651 Henry Cohn, 2024, needs more optimization.
28 122 0.110559254690 Henry Cohn, 2024, needs more optimization.
28 127 0.111111111112 Orthogonal union of 112 points in 21 dimensions and 15 points in 7 dimensions.
9⁢x−1
28 128 0.113320879596 Henry Cohn, 2025, needs more optimization.
28 129 0.115197945860 Henry Cohn, 2024, needs more optimization.
28 130 0.115732829570 Henry Cohn, 2024, needs more optimization.
28 131 0.116714489119 Henry Cohn, 2024, needs more optimization.
28 132 0.117251267020 Henry Cohn, 2024, needs more optimization.
28 133 0.118049833583 Henry Cohn, 2024, needs more optimization.
28 134 0.118993511351 Henry Cohn, 2024, needs more optimization.
28 135 0.119272591118 Henry Cohn, 2024, needs more optimization.
28 136 0.120401740699 Henry Cohn, 2024, needs more optimization.
28 137 0.121360085779 Henry Cohn, 2024, needs more optimization.
28 138 0.121623408642 Henry Cohn, 2024, needs more optimization.
28 139 0.122401429520 Henry Cohn, 2024, needs more optimization.
28 140 0.123301772544 Henry Cohn, 2024, needs more optimization.
28 141 0.124079629912 Henry Cohn, 2024, needs more optimization.
28 142 0.124830548631 Henry Cohn, 2024, needs more optimization.
28 143 0.125605034265 Henry Cohn, 2024, needs more optimization.
28 144 0.126322902923 Henry Cohn, 2024, needs more optimization.
28 145 0.127396342170 Henry Cohn, 2024, needs more optimization.
28 146 0.127964953350 Henry Cohn, 2024, needs more optimization.
28 147 0.128717364273 Henry Cohn, 2024, needs more optimization.
28 148 0.129665907714 Henry Cohn, 2024, needs more optimization.
28 149 0.130599687500 Henry Cohn, 2024, needs more optimization.
28 150 0.131252205362 Henry Cohn, 2024, needs more optimization.
28 151 0.132190822901 Henry Cohn, 2024, needs more optimization.
28 152 0.132750318628 Henry Cohn, 2024, needs more optimization.
28 162 0.132782322631 Henry Cohn, 2024, needs more optimization.
28 163 0.140583007111 Henry Cohn, 2024, needs more optimization.
28 164 0.141184020484 Henry Cohn, 2024, needs more optimization.
28 165 0.141929463968 Henry Cohn, 2024, needs more optimization.
28 176 0.142046694745 Henry Cohn, 2024, needs more optimization.
28 180 0.142857142858 Orthogonal union of 162 points in 21 dimensions and 18 points in 7 dimensions.
7⁢x−1
28 181 0.151217267618 Henry Cohn, 2024, needs more optimization.
28 182 0.151670323738 Henry Cohn, 2024, needs more optimization.
28 183 0.152268509291 Henry Cohn, 2024, needs more optimization.
28 184 0.152956733161 Henry Cohn, 2024, needs more optimization.
28 185 0.153265485213 Henry Cohn, 2024, needs more optimization.
28 186 0.153798240522 Henry Cohn, 2024, needs more optimization.
28 187 0.154314513905 Henry Cohn, 2024, needs more optimization.
28 188 0.154607956655 Henry Cohn, 2024, needs more optimization.
28 190 0.155893915776 Henry Cohn, 2024, needs more optimization.
28 192 0.156716702404 Henry Cohn, 2024, needs more optimization.
28 194 0.158339236851 Henry Cohn, 2024, needs more optimization.
28 196 0.158518600229 Henry Cohn, 2024, needs more optimization.
28 212 0.159252251498 Henry Cohn, 2024, needs more optimization.
28 217 0.161904761905 Orthogonal union of 198 points in 21 dimensions and 19 points in 7 dimensions.
105⁢x−17
28 290 0.166666666667 Orthogonal union of 275 points in 22 dimensions and 15 points in 6 dimensions.
6⁢x−1
28 291 0.171071421043 Orthogonal union of 275 points in 22 dimensions and 16 points in 6 dimensions.
6400⁢x5+960⁢x4−1024⁢x3−32⁢x2+31⁢x−1
28 307 0.181818181819 Orthogonal union of 297 points in 24 dimensions and 10 points in 4 dimensions.
11⁢x−2
28 340 0.193548387097 Orthogonal union of 330 points in 24 dimensions and 10 points in 4 dimensions.
31⁢x−6
28 568 0.2 Orthogonal union of 552 points in 23 dimensions and 16 points in 5 dimensions.
5⁢x−1
28 580 0.238095238096 Orthogonal union of 554 points in 21 dimensions and 26 points in 7 dimensions.
21⁢x−5
28 581 0.240549382010 Orthogonal union of 554 points in 21 dimensions and 27 points in 7 dimensions.
28 582 0.247356651208 Orthogonal union of 554 points in 21 dimensions and 28 points in 7 dimensions.
28 583 0.248933041753 Orthogonal union of 554 points in 21 dimensions and 29 points in 7 dimensions.
28 584 0.249468282003 Orthogonal union of 554 points in 21 dimensions and 30 points in 7 dimensions.
28 918 0.25 Orthogonal union of 891 points in 22 dimensions and 27 points in 6 dimensions.
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 0.040959648840 Henry Cohn, 2025.
29 62 0.043374719000 Henry Cohn, 2025.
29 63 0.044418323444 Henry Cohn, 2024, needs more optimization.
29 64 0.044625900359 Henry Cohn, 2024, needs more optimization.
29 65 0.045182176447 Orthogonal union of 63 points in 28 dimensions and 2 points in 1 dimension.
29 66 0.045712297400 Henry Cohn, 2024, needs more optimization.
29 67 0.046458234874 Henry Cohn, 2024, needs more optimization.
29 68 0.047745180696 Henry Cohn, 2024, needs more optimization.
29 69 0.051943103594 Henry Cohn, 2024, needs more optimization.
29 70 0.054244258991 Henry Cohn, 2024, needs more optimization.
29 71 0.055454852632 Henry Cohn, 2024, needs more optimization.
29 72 0.057063917253 Henry Cohn, 2024, needs more optimization.
29 73 0.058448382678 Henry Cohn, 2024, needs more optimization.
29 74 0.059675736541 Henry Cohn, 2024, needs more optimization.
29 75 0.061352027582 Henry Cohn, 2024, needs more optimization.
29 76 0.062801628988 Henry Cohn, 2024, needs more optimization.
29 77 0.064294796853 Henry Cohn, 2024, needs more optimization.
29 78 0.065690651531 Henry Cohn, 2024, needs more optimization.
29 79 0.066927542817 Henry Cohn, 2024, needs more optimization.
29 80 0.068512546432 Henry Cohn, 2024, needs more optimization.
29 81 0.069786384649 Henry Cohn, 2024, needs more optimization.
29 82 0.071238959969 Henry Cohn, 2024, needs more optimization.
29 83 0.072372218136 Henry Cohn, 2024, needs more optimization.
29 84 0.073471240382 Henry Cohn, 2024, needs more optimization.
29 85 0.074838961934 Henry Cohn, 2024, needs more optimization.
29 86 0.076011030157 Henry Cohn, 2024, needs more optimization.
29 87 0.077187516756 Henry Cohn, 2025, needs more optimization.
29 88 0.078197558463 Henry Cohn, 2025, needs more optimization.
29 89 0.079364896554 Henry Cohn, 2024, needs more optimization.
29 90 0.079442046459 Henry Cohn, 2025, needs more optimization.
29 91 0.079446660297 Henry Cohn, 2025, needs more optimization.
29 92 0.079447466994 Henry Cohn, 2025, needs more optimization.
29 93 0.079450925290 Henry Cohn, 2025, needs more optimization.
29 94 0.084202334559 Henry Cohn, 2025, needs more optimization.
29 95 0.085181240107 Henry Cohn, 2024, needs more optimization.
29 96 0.086228934687 Henry Cohn, 2025, 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
29 114 0.090597286827 Henry Cohn, 2024, needs more optimization.
29 115 0.090919960401 Orthogonal union of 109 points in 26 dimensions and 6 points in 3 dimensions.
29 116 0.101962562668 Henry Cohn, 2024, needs more optimization.
29 117 0.102748745798 Henry Cohn, 2024, needs more optimization.
29 118 0.103445016065 Henry Cohn, 2024, needs more optimization.
29 119 0.103906667845 Henry Cohn, 2024, needs more optimization.
29 120 0.104680594866 Henry Cohn, 2024, needs more optimization.
29 121 0.105224173440 Henry Cohn, 2024, needs more optimization.
29 122 0.105974322505 Henry Cohn, 2024, needs more optimization.
29 123 0.106641229002 Henry Cohn, 2024, needs more optimization.
29 124 0.107068103287 Henry Cohn, 2024, needs more optimization.
29 125 0.107767906014 Henry Cohn, 2024, needs more optimization.
29 126 0.108518823581 Henry Cohn, 2024, needs more optimization.
29 127 0.109061270466 Henry Cohn, 2024, needs more optimization.
29 128 0.109419532848 Henry Cohn, 2024, needs more optimization.
29 129 0.110176692161 Henry Cohn, 2024, needs more optimization.
29 130 0.110762018930 Henry Cohn, 2024, needs more optimization.
29 131 0.111349700901 Henry Cohn, 2024, needs more optimization.
29 132 0.112111376416 Henry Cohn, 2024, needs more optimization.
29 133 0.112931524032 Henry Cohn, 2024, needs more optimization.
29 134 0.113409671728 Henry Cohn, 2024, needs more optimization.
29 135 0.113782308842 Henry Cohn, 2024, needs more optimization.
29 136 0.114541415969 Henry Cohn, 2024, needs more optimization.
29 137 0.115378135086 Henry Cohn, 2024, needs more optimization.
29 138 0.115958745236 Henry Cohn, 2024, needs more optimization.
29 139 0.116704343430 Henry Cohn, 2024, needs more optimization.
29 140 0.117102540529 Henry Cohn, 2024, needs more optimization.
29 141 0.117944401699 Henry Cohn, 2024, needs more optimization.
29 142 0.118746592958 Henry Cohn, 2024, needs more optimization.
29 143 0.119189091219 Henry Cohn, 2024, needs more optimization.
29 144 0.120034199854 Henry Cohn, 2024, needs more optimization.
29 145 0.120728715866 Henry Cohn, 2024, needs more optimization.
29 146 0.121756773929 Henry Cohn, 2024, needs more optimization.
29 147 0.122197602172 Henry Cohn, 2024, needs more optimization.
29 148 0.123140752142 Henry Cohn, 2024, needs more optimization.
29 149 0.123716670186 Henry Cohn, 2024, needs more optimization.
29 150 0.124097919399 Henry Cohn, 2024, needs more optimization.
29 151 0.125172624884 Henry Cohn, 2024, needs more optimization.
29 152 0.125808429277 Henry Cohn, 2024, needs more optimization.
29 153 0.126429728848 Henry Cohn, 2024, needs more optimization.
29 154 0.127520817384 Henry Cohn, 2024, needs more optimization.
29 155 0.128517917994 Henry Cohn, 2024, needs more optimization.
29 156 0.128902505274 Henry Cohn, 2024, needs more optimization.
29 157 0.129735041974 Henry Cohn, 2024, needs more optimization.
29 164 0.130358843703 Henry Cohn, 2024, needs more optimization.
29 165 0.135349806141 Henry Cohn, 2024, needs more optimization.
29 166 0.135858208338 Henry Cohn, 2024, needs more optimization.
29 167 0.136437725315 Henry Cohn, 2024, needs more optimization.
29 168 0.137329755304 Henry Cohn, 2024, needs more optimization.
29 169 0.137678525764 Henry Cohn, 2024, needs more optimization.
29 170 0.138219591070 Henry Cohn, 2024, needs more optimization.
29 171 0.138945691316 Henry Cohn, 2024, needs more optimization.
29 172 0.139541921445 Henry Cohn, 2024, needs more optimization.
29 173 0.140204807997 Henry Cohn, 2024, needs more optimization.
29 174 0.140762693659 Henry Cohn, 2024, needs more optimization.
29 175 0.141415003435 Henry Cohn, 2024, needs more optimization.
29 176 0.141859287879 Henry Cohn, 2024, needs more optimization.
29 178 0.142046694745 Orthogonal union of 176 points in 28 dimensions and 2 points in 1 dimension.
29 182 0.142854813225 Henry Cohn, 2024, needs more optimization.
29 184 0.142857142858 Orthogonal union of 162 points in 21 dimensions and 22 points in 8 dimensions.
7⁢x−1
29 185 0.146789812392 Henry Cohn, 2024, needs more optimization.
29 186 0.147490841194 Henry Cohn, 2024, needs more optimization.
29 187 0.147805420991 Henry Cohn, 2024, needs more optimization.
29 188 0.148352058193 Henry Cohn, 2024, needs more optimization.
29 189 0.148829383747 Henry Cohn, 2024, needs more optimization.
29 190 0.149294597690 Henry Cohn, 2024, needs more optimization.
29 191 0.149895090566 Henry Cohn, 2024, needs more optimization.
29 192 0.151156183352 Henry Cohn, 2024, needs more optimization.
29 193 0.151851876189 Henry Cohn, 2024, needs more optimization.
29 194 0.152362053705 Henry Cohn, 2024, needs more optimization.
29 195 0.152767476751 Henry Cohn, 2024, needs more optimization.
29 196 0.153277631158 Henry Cohn, 2024, needs more optimization.
29 197 0.153858333990 Henry Cohn, 2024, needs more optimization.
29 198 0.154200756954 Henry Cohn, 2024, needs more optimization.
29 199 0.154806425124 Henry Cohn, 2024, needs more optimization.
29 200 0.155184245847 Henry Cohn, 2024, needs more optimization.
29 201 0.155651294466 Henry Cohn, 2024, needs more optimization.
29 202 0.156064970348 Henry Cohn, 2024, needs more optimization.
29 203 0.156453786328 Henry Cohn, 2024, needs more optimization.
29 218 0.156597700436 Henry Cohn, 2024, needs more optimization.
29 222 0.161904761905 Orthogonal union of 198 points in 21 dimensions and 24 points in 8 dimensions.
105⁢x−17
29 223 0.164334174126 Orthogonal union of 198 points in 21 dimensions and 25 points in 8 dimensions.
Minimal polynomial listed in plain text data
29 224 0.165523581220 Henry Cohn, 2024, needs more optimization.
29 225 0.165785904130 Henry Cohn, 2024, needs more optimization.
29 226 0.166158885386 Henry Cohn, 2024, needs more optimization.
29 227 0.166610018759 Henry Cohn, 2024, needs more optimization.
29 294 0.166666666667 Orthogonal union of 275 points in 22 dimensions and 19 points in 7 dimensions.
6⁢x−1
29 295 0.169520847199 Orthogonal union of 275 points in 22 dimensions and 20 points in 7 dimensions.
23⁢x2+2⁢x−1
29 296 0.181523960801 Orthogonal union of 275 points in 22 dimensions and 21 points in 7 dimensions.
29 309 0.181818181819 Orthogonal union of 297 points in 24 dimensions and 12 points in 5 dimensions.
11⁢x−2
29 310 0.187259851883 Orthogonal union of 297 points in 24 dimensions and 13 points in 5 dimensions.
17⁢x3−5⁢x2−5⁢x+1
29 343 0.193548387097 Orthogonal union of 330 points in 24 dimensions and 13 points in 5 dimensions.
31⁢x−6
29 570 0.2 Orthogonal union of 552 points in 23 dimensions and 18 points in 6 dimensions.
5⁢x−1
29 571 0.200226025892 Orthogonal union of 552 points in 23 dimensions and 19 points in 6 dimensions.
29 572 0.214285714286 Orthogonal union of 552 points in 23 dimensions and 20 points in 6 dimensions.
14⁢x−3
29 589 0.238095238096 Orthogonal union of 554 points in 21 dimensions and 35 points in 8 dimensions.
21⁢x−5
29 592 0.239920745566 Orthogonal union of 554 points in 21 dimensions and 38 points in 8 dimensions.
1088⁢x4−80⁢x2+1
29 593 0.243600150512 Orthogonal union of 554 points in 21 dimensions and 39 points in 8 dimensions.
1183744⁢x8+122880⁢x7−575488⁢x6−138240⁢x5+53632⁢x4+14976⁢x3−1568⁢x2−720⁢x+81
29 594 0.246959912794 Henry Cohn, 2024, needs more optimization.
29 595 0.247038417605 Henry Cohn, 2024, needs more optimization.
29 596 0.247261367455 Henry Cohn, 2024, needs more optimization.
29 597 0.247310935231 Henry Cohn, 2024, needs more optimization.
29 598 0.247453432910 Henry Cohn, 2024, needs more optimization.
29 599 0.247666456630 Henry Cohn, 2024, needs more optimization.
29 600 0.247979203706 Henry Cohn, 2024, needs more optimization.
29 601 0.248006134194 Henry Cohn, 2024, needs more optimization.
29 602 0.248133305051 Henry Cohn, 2024, needs more optimization.
29 603 0.248230461506 Henry Cohn, 2024, needs more optimization.
29 604 0.248335896515 Henry Cohn, 2024, needs more optimization.
29 605 0.248520050165 Henry Cohn, 2024, needs more optimization.
29 606 0.248571307599 Henry Cohn, 2024, needs more optimization.
29 607 0.248582659368 Henry Cohn, 2024, needs more optimization.
29 608 0.248662338600 Henry Cohn, 2024, needs more optimization.
29 609 0.249075055639 Henry Cohn, 2024, needs more optimization.
29 610 0.249123873543 Henry Cohn, 2024, needs more optimization.
29 611 0.249184370908 Henry Cohn, 2024, needs more optimization.
29 612 0.249284568375 Henry Cohn, 2024, needs more optimization.
29 613 0.249421498011 Henry Cohn, 2024, needs more optimization.
29 614 0.249528676345 Henry Cohn, 2024, needs more optimization.
29 615 0.249704358488 Henry Cohn, 2024, needs more optimization.
29 617 0.249869743714 Henry Cohn, 2024, needs more optimization.
29 921 0.25 Orthogonal union of 891 points in 22 dimensions and 30 points in 7 dimensions.
4⁢x−1
29 922 0.254502767515 Orthogonal union of 891 points in 22 dimensions and 31 points in 7 dimensions.
29 923 0.265595699432 Orthogonal union of 891 points in 22 dimensions and 32 points in 7 dimensions.
29 924 0.270023386002 Orthogonal union of 891 points in 22 dimensions and 33 points in 7 dimensions.
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 0.039882314205 Henry Cohn, 2024.
30 64 0.042239451552 Henry Cohn, 2024, 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 0.044636092949 Henry Cohn, 2024, needs more optimization.
30 68 0.045102335021 Henry Cohn, 2024, needs more optimization.
30 69 0.045903208320 Henry Cohn, 2024, needs more optimization.
30 70 0.047745163385 Henry Cohn, 2024, needs more optimization.
30 71 0.051112199071 Henry Cohn, 2024, needs more optimization.
30 72 0.052929292446 Henry Cohn, 2024, needs more optimization.
30 73 0.054094909776 Henry Cohn, 2024, needs more optimization.
30 74 0.055367182963 Henry Cohn, 2024, needs more optimization.
30 75 0.056869974077 Henry Cohn, 2024, needs more optimization.
30 76 0.058114360800 Henry Cohn, 2024, needs more optimization.
30 77 0.059554100050 Henry Cohn, 2024, needs more optimization.
30 78 0.060878894691 Henry Cohn, 2024, needs more optimization.
30 79 0.062197373648 Henry Cohn, 2024, needs more optimization.
30 80 0.063666562117 Henry Cohn, 2024, needs more optimization.
30 81 0.064694563982 Henry Cohn, 2024, needs more optimization.
30 82 0.066307485777 Henry Cohn, 2024, needs more optimization.
30 83 0.067498266536 Henry Cohn, 2024, needs more optimization.
30 84 0.068709256287 Henry Cohn, 2024, needs more optimization.
30 85 0.069753378022 Henry Cohn, 2024, needs more optimization.
30 86 0.071126021632 Henry Cohn, 2024, needs more optimization.
30 87 0.072204338033 Henry Cohn, 2025, needs more optimization.
30 88 0.073445174951 Henry Cohn, 2025, needs more optimization.
30 89 0.074331656829 Henry Cohn, 2025, needs more optimization.
30 90 0.075609508314 Henry Cohn, 2024, needs more optimization.
30 91 0.076738373694 Henry Cohn, 2025, needs more optimization.
30 92 0.077862650393 Henry Cohn, 2025, needs more optimization.
30 93 0.078683804105 Henry Cohn, 2025, needs more optimization.
30 94 0.079445827871 Henry Cohn, 2025, needs more optimization.
30 95 0.079450918200 Henry Cohn, 2025, needs more optimization.
30 96 0.081527851656 Henry Cohn, 2024, needs more optimization.
30 97 0.082380854898 Henry Cohn, 2025, needs more optimization.
30 98 0.083291478653 Henry Cohn, 2025, needs more optimization.
30 99 0.084425268644 Henry Cohn, 2025, needs more optimization.
30 100 0.085216225789 Henry Cohn, 2024, needs more optimization.
30 101 0.085995635252 Henry Cohn, 2024, 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 0.088982380301 Henry Cohn, 2024, needs more optimization.
30 117 0.090909090910 Orthogonal union of 100 points in 22 dimensions and 17 points in 8 dimensions.
11⁢x−1
30 118 0.098909285097 Henry Cohn, 2024, needs more optimization.
30 119 0.099391332684 Henry Cohn, 2024, needs more optimization.
30 120 0.100112965796 Henry Cohn, 2024, needs more optimization.
30 121 0.100689336306 Henry Cohn, 2024, needs more optimization.
30 122 0.101468860958 Henry Cohn, 2024, needs more optimization.
30 123 0.102014577002 Henry Cohn, 2024, needs more optimization.
30 124 0.102756514176 Henry Cohn, 2024, needs more optimization.
30 125 0.103406033654 Henry Cohn, 2024, needs more optimization.
30 126 0.103909210938 Henry Cohn, 2024, needs more optimization.
30 127 0.104468040958 Henry Cohn, 2024, needs more optimization.
30 128 0.105084976994 Henry Cohn, 2024, needs more optimization.
30 129 0.105837217295 Henry Cohn, 2024, needs more optimization.
30 130 0.106298847219 Henry Cohn, 2024, needs more optimization.
30 131 0.106867937200 Henry Cohn, 2024, needs more optimization.
30 132 0.107404606542 Henry Cohn, 2024, needs more optimization.
30 133 0.107767852094 Henry Cohn, 2024, needs more optimization.
30 134 0.108748360403 Henry Cohn, 2024, needs more optimization.
30 135 0.109049767442 Henry Cohn, 2024, needs more optimization.
30 136 0.109716858669 Henry Cohn, 2024, needs more optimization.
30 137 0.110581758627 Henry Cohn, 2024, needs more optimization.
30 138 0.110945899043 Henry Cohn, 2024, needs more optimization.
30 139 0.111629876667 Henry Cohn, 2024, needs more optimization.
30 140 0.112155130945 Henry Cohn, 2024, needs more optimization.
30 141 0.112886822191 Henry Cohn, 2024, needs more optimization.
30 142 0.113583917241 Henry Cohn, 2024, needs more optimization.
30 143 0.113939473978 Henry Cohn, 2024, needs more optimization.
30 144 0.114625000338 Henry Cohn, 2024, needs more optimization.
30 145 0.115319401945 Henry Cohn, 2024, needs more optimization.
30 146 0.116052452160 Henry Cohn, 2024, needs more optimization.
30 147 0.116673276200 Henry Cohn, 2024, needs more optimization.
30 148 0.117108506624 Henry Cohn, 2024, needs more optimization.
30 149 0.117746260016 Henry Cohn, 2024, needs more optimization.
30 150 0.118863953641 Henry Cohn, 2024, needs more optimization.
30 151 0.119158283312 Henry Cohn, 2024, needs more optimization.
30 152 0.119732873041 Henry Cohn, 2024, needs more optimization.
30 153 0.120482343104 Henry Cohn, 2024, needs more optimization.
30 154 0.121202220351 Henry Cohn, 2024, needs more optimization.
30 155 0.121776864450 Henry Cohn, 2024, needs more optimization.
30 156 0.122581307637 Henry Cohn, 2024, needs more optimization.
30 157 0.123528887976 Henry Cohn, 2024, needs more optimization.
30 158 0.124059723596 Henry Cohn, 2024, needs more optimization.
30 159 0.124630970236 Henry Cohn, 2024, needs more optimization.
30 160 0.125270438079 Henry Cohn, 2024, needs more optimization.
30 161 0.126084250726 Henry Cohn, 2024, needs more optimization.
30 162 0.126721230741 Henry Cohn, 2024, needs more optimization.
30 163 0.127434469004 Henry Cohn, 2024, needs more optimization.
30 164 0.127858876268 Henry Cohn, 2024, needs more optimization.
30 165 0.128847680906 Henry Cohn, 2024, needs more optimization.
30 166 0.129314855514 Henry Cohn, 2024, needs more optimization.
30 167 0.129900870161 Henry Cohn, 2024, needs more optimization.
30 168 0.130802530426 Henry Cohn, 2024, needs more optimization.
30 169 0.131498617579 Henry Cohn, 2024, needs more optimization.
30 170 0.132096757734 Henry Cohn, 2024, needs more optimization.
30 171 0.132681923189 Henry Cohn, 2024, needs more optimization.
30 172 0.133240235902 Henry Cohn, 2024, needs more optimization.
30 173 0.133799255754 Henry Cohn, 2024, needs more optimization.
30 174 0.134447182790 Henry Cohn, 2024, needs more optimization.
30 175 0.135197963272 Henry Cohn, 2024, needs more optimization.
30 176 0.135646042909 Henry Cohn, 2024, needs more optimization.
30 177 0.136158868559 Henry Cohn, 2024, needs more optimization.
30 178 0.136717840681 Henry Cohn, 2024, needs more optimization.
30 179 0.137309051759 Henry Cohn, 2024, needs more optimization.
30 180 0.137955802293 Henry Cohn, 2024, needs more optimization.
30 181 0.138535792029 Henry Cohn, 2024, needs more optimization.
30 182 0.139136119913 Henry Cohn, 2024, needs more optimization.
30 183 0.139492713685 Henry Cohn, 2024, needs more optimization.
30 184 0.140166409854 Henry Cohn, 2024, needs more optimization.
30 185 0.140672803960 Henry Cohn, 2024, needs more optimization.
30 186 0.141231989140 Henry Cohn, 2024, needs more optimization.
30 187 0.141850733883 Henry Cohn, 2024, needs more optimization.
30 189 0.142803726104 Henry Cohn, 2024, needs more optimization.
30 190 0.143389113002 Henry Cohn, 2024, needs more optimization.
30 192 0.144101915842 Henry Cohn, 2024, needs more optimization.
30 193 0.144967842395 Henry Cohn, 2024, needs more optimization.
30 195 0.145484696048 Henry Cohn, 2024, needs more optimization.
30 196 0.146164619785 Henry Cohn, 2024, needs more optimization.
30 197 0.147583623976 Henry Cohn, 2024, needs more optimization.
30 198 0.148137866870 Henry Cohn, 2024, needs more optimization.
30 199 0.148632720596 Henry Cohn, 2024, needs more optimization.
30 200 0.149160250740 Henry Cohn, 2024, needs more optimization.
30 201 0.149524153504 Henry Cohn, 2024, needs more optimization.
30 202 0.150035122813 Henry Cohn, 2024, needs more optimization.
30 203 0.150461259689 Henry Cohn, 2024, needs more optimization.
30 204 0.150929784520 Henry Cohn, 2024, needs more optimization.
30 205 0.151332625840 Henry Cohn, 2024, needs more optimization.
30 206 0.151789162827 Henry Cohn, 2024, needs more optimization.
30 207 0.152179274292 Henry Cohn, 2024, needs more optimization.
30 208 0.152634403925 Henry Cohn, 2024, needs more optimization.
30 209 0.153080108585 Henry Cohn, 2024, needs more optimization.
30 210 0.153445775986 Henry Cohn, 2024, needs more optimization.
30 211 0.153921853570 Henry Cohn, 2024, needs more optimization.
30 212 0.154301618212 Henry Cohn, 2024, needs more optimization.
30 213 0.154778078299 Henry Cohn, 2024, needs more optimization.
30 214 0.155183720753 Henry Cohn, 2024, needs more optimization.
30 215 0.155678434150 Henry Cohn, 2024, needs more optimization.
30 216 0.156008113945 Henry Cohn, 2024, needs more optimization.
30 217 0.156346045706 Henry Cohn, 2024, needs more optimization.
30 228 0.156393959963 Henry Cohn, 2024, needs more optimization.
30 229 0.161158962976 Henry Cohn, 2024, needs more optimization.
30 230 0.161605839846 Henry Cohn, 2024, needs more optimization.
30 231 0.162064140086 Henry Cohn, 2024, needs more optimization.
30 232 0.162453672838 Henry Cohn, 2024, needs more optimization.
30 233 0.162769878892 Henry Cohn, 2024, needs more optimization.
30 234 0.163146716880 Henry Cohn, 2024, needs more optimization.
30 235 0.163420877107 Henry Cohn, 2024, needs more optimization.
30 236 0.163884952267 Henry Cohn, 2024, needs more optimization.
30 237 0.164230894994 Henry Cohn, 2024, needs more optimization.
30 238 0.164618948739 Henry Cohn, 2024, needs more optimization.
30 239 0.164983220602 Henry Cohn, 2024, needs more optimization.
30 240 0.165319917459 Henry Cohn, 2024, needs more optimization.
30 241 0.165638272286 Henry Cohn, 2024, needs more optimization.
30 242 0.166067214881 Henry Cohn, 2024, needs more optimization.
30 243 0.166489508980 Henry Cohn, 2024, needs more optimization.
30 300 0.166666666667 Orthogonal union of 275 points in 22 dimensions and 25 points in 8 dimensions.
6⁢x−1
30 301 0.172652095036 Orthogonal union of 275 points in 22 dimensions and 26 points in 8 dimensions.
Minimal polynomial listed in plain text data
30 302 0.179856457059 Orthogonal union of 275 points in 22 dimensions and 27 points in 8 dimensions.
Minimal polynomial listed in plain text data
30 303 0.181158420022 Orthogonal union of 275 points in 22 dimensions and 28 points in 8 dimensions.
36⁢x4+24⁢x3−36⁢x2+1
30 313 0.181818181819 Orthogonal union of 297 points in 24 dimensions and 16 points in 6 dimensions.
11⁢x−2
30 314 0.183274337024 Orthogonal union of 297 points in 24 dimensions and 17 points in 6 dimensions.
400⁢x4+240⁢x3+16⁢x2−8⁢x−1
30 315 0.188839108056 Henry Cohn, 2024, needs more optimization.
30 316 0.188952530908 Henry Cohn, 2024, needs more optimization.
30 317 0.189324446587 Henry Cohn, 2024, needs more optimization.
30 318 0.189600832581 Henry Cohn, 2024, needs more optimization.
30 319 0.189873086550 Henry Cohn, 2024, needs more optimization.
30 320 0.190036335836 Henry Cohn, 2024, needs more optimization.
30 321 0.190430819572 Henry Cohn, 2024, needs more optimization.
30 322 0.190583718314 Henry Cohn, 2024, needs more optimization.
30 323 0.190873723406 Henry Cohn, 2024, needs more optimization.
30 324 0.190954148482 Henry Cohn, 2024, needs more optimization.
30 325 0.191309698182 Henry Cohn, 2024, needs more optimization.
30 326 0.191860275613 Henry Cohn, 2024, needs more optimization.
30 327 0.191879559206 Henry Cohn, 2024, needs more optimization.
30 328 0.192215629997 Henry Cohn, 2024, needs more optimization.
30 329 0.192532507044 Henry Cohn, 2024, needs more optimization.
30 330 0.192881514074 Henry Cohn, 2024, needs more optimization.
30 331 0.192904536076 Henry Cohn, 2024, needs more optimization.
30 332 0.193169457533 Henry Cohn, 2024, needs more optimization.
30 333 0.193533232724 Henry Cohn, 2024, needs more optimization.
30 347 0.193548387097 Orthogonal union of 330 points in 24 dimensions and 17 points in 6 dimensions.
31⁢x−6
30 348 0.196921795460 Henry Cohn, 2024, needs more optimization.
30 349 0.197390129328 Henry Cohn, 2024, needs more optimization.
30 350 0.197422466098 Henry Cohn, 2024, needs more optimization.
30 351 0.197585860300 Henry Cohn, 2024, needs more optimization.
30 352 0.197929298089 Henry Cohn, 2024, needs more optimization.
30 353 0.198200227136 Henry Cohn, 2024, needs more optimization.
30 354 0.198334288318 Henry Cohn, 2024, needs more optimization.
30 355 0.198600562187 Henry Cohn, 2024, needs more optimization.
30 356 0.198903958855 Henry Cohn, 2024, needs more optimization.
30 357 0.199177800047 Henry Cohn, 2024, needs more optimization.
30 358 0.199350765512 Henry Cohn, 2024, needs more optimization.
30 359 0.199467511493 Henry Cohn, 2024, needs more optimization.
30 360 0.199818959501 Henry Cohn, 2024, needs more optimization.
30 361 0.199991079929 Henry Cohn, 2024, 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 0.214737233855 Orthogonal union of 552 points in 23 dimensions and 25 points in 7 dimensions.
31⁢x2−2⁢x−1
30 578 0.231331430372 Orthogonal union of 552 points in 23 dimensions and 26 points in 7 dimensions.
30 579 0.237485479111 Henry Cohn, 2024, needs more optimization.
30 580 0.237713429342 Henry Cohn, 2024, needs more optimization.
30 582 0.238002472550 Henry Cohn, 2024, needs more optimization.
30 598 0.238095238096 Orthogonal union of 554 points in 21 dimensions and 44 points in 9 dimensions.
21⁢x−5
30 601 0.238172399483 Orthogonal union of 554 points in 21 dimensions and 47 points in 9 dimensions.
335⁢x2−42⁢x−9
30 602 0.240666983778 Henry Cohn, 2024, needs more optimization.
30 604 0.240909057055 Henry Cohn, 2024, needs more optimization.
30 605 0.240989801806 Henry Cohn, 2024, needs more optimization.
30 606 0.241236960248 Henry Cohn, 2024, needs more optimization.
30 607 0.241285715941 Henry Cohn, 2024, needs more optimization.
30 608 0.241511849109 Henry Cohn, 2024, needs more optimization.
30 610 0.241537489702 Henry Cohn, 2024, needs more optimization.
30 611 0.241752663444 Henry Cohn, 2024, needs more optimization.
30 613 0.241926154514 Henry Cohn, 2024, needs more optimization.
30 614 0.242188525805 Henry Cohn, 2024, needs more optimization.
30 615 0.242418221392 Henry Cohn, 2024, needs more optimization.
30 616 0.242664783597 Henry Cohn, 2024, needs more optimization.
30 620 0.242763273658 Henry Cohn, 2024, needs more optimization.
30 622 0.243132827944 Henry Cohn, 2024, needs more optimization.
30 623 0.243419937055 Henry Cohn, 2024, needs more optimization.
30 625 0.243638224583 Henry Cohn, 2024, needs more optimization.
30 626 0.243717285581 Henry Cohn, 2024, needs more optimization.
30 627 0.243722755433 Henry Cohn, 2024, needs more optimization.
30 629 0.244112221806 Henry Cohn, 2024, needs more optimization.
30 630 0.244146690471 Henry Cohn, 2024, needs more optimization.
30 633 0.244457224720 Henry Cohn, 2024, needs more optimization.
30 634 0.244633847741 Henry Cohn, 2024, needs more optimization.
30 635 0.244661839377 Henry Cohn, 2024, needs more optimization.
30 636 0.244901700893 Henry Cohn, 2024, needs more optimization.
30 638 0.245169335282 Henry Cohn, 2024, needs more optimization.
30 639 0.245409349224 Henry Cohn, 2024, needs more optimization.
30 640 0.245419862694 Henry Cohn, 2024, needs more optimization.
30 641 0.245532125239 Henry Cohn, 2024, needs more optimization.
30 643 0.245692927388 Henry Cohn, 2024, needs more optimization.
30 645 0.245958133404 Henry Cohn, 2024, needs more optimization.
30 647 0.246189226653 Henry Cohn, 2024, needs more optimization.
30 649 0.246575513921 Henry Cohn, 2024, needs more optimization.
30 651 0.246689810808 Henry Cohn, 2024, needs more optimization.
30 652 0.246909816450 Henry Cohn, 2024, needs more optimization.
30 653 0.247027779868 Henry Cohn, 2024, needs more optimization.
30 654 0.247269000194 Henry Cohn, 2024, needs more optimization.
30 656 0.247462218350 Henry Cohn, 2024, needs more optimization.
30 657 0.247487724503 Henry Cohn, 2024, needs more optimization.
30 658 0.247644310520 Henry Cohn, 2024, needs more optimization.
30 661 0.247817040578 Henry Cohn, 2024, needs more optimization.
30 662 0.248135085749 Henry Cohn, 2024, needs more optimization.
30 663 0.248281412090 Henry Cohn, 2024, needs more optimization.
30 664 0.248378969646 Henry Cohn, 2024, needs more optimization.
30 666 0.248462754395 Henry Cohn, 2024, needs more optimization.
30 669 0.248808037335 Henry Cohn, 2024, needs more optimization.
30 670 0.249040015108 Henry Cohn, 2024, needs more optimization.
30 671 0.249281243219 Henry Cohn, 2024, needs more optimization.
30 672 0.249306322053 Henry Cohn, 2024, needs more optimization.
30 674 0.249364779084 Henry Cohn, 2024, needs more optimization.
30 676 0.249624878330 Henry Cohn, 2024, needs more optimization.
30 677 0.249857148778 Henry Cohn, 2024, needs more optimization.
30 678 0.249973674791 Henry Cohn, 2024, needs more optimization.
30 930 0.25 Orthogonal union of 891 points in 22 dimensions and 39 points in 8 dimensions.
4⁢x−1
30 931 0.265123725370 Orthogonal union of 891 points in 22 dimensions and 40 points in 8 dimensions.
30 932 0.269595854246 Orthogonal union of 891 points in 22 dimensions and 41 points in 8 dimensions.
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 0.038669332262 Henry Cohn, 2024, needs more optimization.
31 66 0.040844253502 Henry Cohn, 2024, needs more optimization.
31 67 0.043552672427 Henry Cohn, 2024, needs more optimization.
31 68 0.043771299231 Henry Cohn, 2024, needs more optimization.
31 69 0.044045329342 Henry Cohn, 2024, needs more optimization.
31 70 0.044243883742 Henry Cohn, 2024, needs more optimization.
31 71 0.045132353747 Henry Cohn, 2024, needs more optimization.
31 72 0.047745153644 Henry Cohn, 2024, needs more optimization.
31 73 0.050119316074 Henry Cohn, 2024, needs more optimization.
31 74 0.051386919945 Henry Cohn, 2024, needs more optimization.
31 75 0.052424769357 Henry Cohn, 2024, needs more optimization.
31 76 0.054086657923 Henry Cohn, 2024, needs more optimization.
31 77 0.055289732585 Henry Cohn, 2024, needs more optimization.
31 78 0.056619831043 Henry Cohn, 2024, needs more optimization.
31 79 0.057794478177 Henry Cohn, 2024, needs more optimization.
31 80 0.059057477139 Henry Cohn, 2024, needs more optimization.
31 81 0.060155060798 Henry Cohn, 2024, needs more optimization.
31 82 0.061699859897 Henry Cohn, 2024, needs more optimization.
31 83 0.063051750870 Henry Cohn, 2024, needs more optimization.
31 84 0.064032535346 Henry Cohn, 2024, needs more optimization.
31 85 0.065365341433 Henry Cohn, 2024, needs more optimization.
31 86 0.066350209613 Henry Cohn, 2025, needs more optimization.
31 87 0.067817875191 Henry Cohn, 2024, needs more optimization.
31 88 0.068598792241 Henry Cohn, 2025, needs more optimization.
31 89 0.069605044975 Henry Cohn, 2025, needs more optimization.
31 90 0.071145383644 Henry Cohn, 2025, needs more optimization.
31 91 0.072118959728 Henry Cohn, 2024, needs more optimization.
31 92 0.073179478118 Henry Cohn, 2025, needs more optimization.
31 93 0.074304491459 Henry Cohn, 2025, needs more optimization.
31 94 0.074964250946 Henry Cohn, 2025, needs more optimization.
31 95 0.076053212263 Henry Cohn, 2025, needs more optimization.
31 96 0.076978365777 Henry Cohn, 2025, needs more optimization.
31 97 0.078019072559 Henry Cohn, 2024, needs more optimization.
31 98 0.079061559860 Henry Cohn, 2025, needs more optimization.
31 99 0.079889697836 Henry Cohn, 2025, needs more optimization.
31 100 0.080572231004 Henry Cohn, 2025, needs more optimization.
31 101 0.081555528236 Henry Cohn, 2024, needs more optimization.
31 102 0.082464015112 Henry Cohn, 2024, needs more optimization.
31 103 0.083340497226 Henry Cohn, 2024, needs more optimization.
31 104 0.084293438310 Henry Cohn, 2024, needs more optimization.
31 105 0.084943811017 Henry Cohn, 2024, needs more optimization.
31 106 0.085957563295 Henry Cohn, 2024, needs more optimization.
31 116 0.086333305850 Henry Cohn, 2024, needs more optimization.
31 119 0.088384604201 Henry Cohn, 2024, needs more optimization.
31 121 0.090909090910 Orthogonal union of 100 points in 22 dimensions and 21 points in 9 dimensions.
11⁢x−1
31 122 0.097075019140 Henry Cohn, 2024, needs more optimization.
31 123 0.097719944481 Henry Cohn, 2024, needs more optimization.
31 124 0.098246224233 Henry Cohn, 2024, needs more optimization.
31 125 0.098808971229 Henry Cohn, 2024, needs more optimization.
31 126 0.099578231743 Henry Cohn, 2024, needs more optimization.
31 127 0.100293341787 Henry Cohn, 2024, needs more optimization.
31 128 0.100771919550 Henry Cohn, 2024, needs more optimization.
31 129 0.101280472100 Henry Cohn, 2024, needs more optimization.
31 130 0.101888661101 Henry Cohn, 2024, needs more optimization.
31 131 0.102404682165 Henry Cohn, 2024, needs more optimization.
31 132 0.103128258506 Henry Cohn, 2024, needs more optimization.
31 133 0.103691560609 Henry Cohn, 2024, needs more optimization.
31 134 0.104159695240 Henry Cohn, 2024, needs more optimization.
31 135 0.104686167563 Henry Cohn, 2024, needs more optimization.
31 136 0.105357288574 Henry Cohn, 2024, needs more optimization.
31 137 0.105714227034 Henry Cohn, 2024, needs more optimization.
31 138 0.106290145479 Henry Cohn, 2024, needs more optimization.
31 139 0.107089609510 Henry Cohn, 2024, needs more optimization.
31 140 0.107606620308 Henry Cohn, 2024, needs more optimization.
31 141 0.108080608008 Henry Cohn, 2024, needs more optimization.
31 142 0.108654540648 Henry Cohn, 2024, needs more optimization.
31 143 0.109370683000 Henry Cohn, 2024, needs more optimization.
31 144 0.109697861349 Henry Cohn, 2024, needs more optimization.
31 145 0.110397023389 Henry Cohn, 2024, needs more optimization.
31 146 0.110805420329 Henry Cohn, 2024, needs more optimization.
31 147 0.111552213817 Henry Cohn, 2024, needs more optimization.
31 148 0.112152438495 Henry Cohn, 2024, needs more optimization.
31 149 0.112977234084 Henry Cohn, 2024, needs more optimization.
31 150 0.113482238343 Henry Cohn, 2024, needs more optimization.
31 151 0.114126591977 Henry Cohn, 2024, needs more optimization.
31 152 0.114377592776 Henry Cohn, 2024, needs more optimization.
31 153 0.115029108950 Henry Cohn, 2024, needs more optimization.
31 154 0.115831577419 Henry Cohn, 2024, needs more optimization.
31 155 0.116222191649 Henry Cohn, 2024, needs more optimization.
31 156 0.117139993281 Henry Cohn, 2024, needs more optimization.
31 157 0.117597806524 Henry Cohn, 2024, needs more optimization.
31 158 0.118116098225 Henry Cohn, 2024, needs more optimization.
31 159 0.118845328001 Henry Cohn, 2024, needs more optimization.
31 160 0.119481156688 Henry Cohn, 2024, needs more optimization.
31 161 0.120313792397 Henry Cohn, 2024, needs more optimization.
31 162 0.120662393999 Henry Cohn, 2024, needs more optimization.
31 163 0.121451145415 Henry Cohn, 2024, needs more optimization.
31 164 0.122040188717 Henry Cohn, 2024, needs more optimization.
31 165 0.122618688933 Henry Cohn, 2024, needs more optimization.
31 166 0.123448505215 Henry Cohn, 2024, needs more optimization.
31 167 0.123905695105 Henry Cohn, 2024, needs more optimization.
31 168 0.124687469129 Henry Cohn, 2024, needs more optimization.
31 169 0.125288921229 Henry Cohn, 2024, needs more optimization.
31 170 0.125847524493 Henry Cohn, 2024, needs more optimization.
31 171 0.126383179192 Henry Cohn, 2024, needs more optimization.
31 172 0.127186509311 Henry Cohn, 2024, needs more optimization.
31 173 0.127812369839 Henry Cohn, 2024, needs more optimization.
31 174 0.128446474676 Henry Cohn, 2024, needs more optimization.
31 175 0.128919345703 Henry Cohn, 2024, needs more optimization.
31 176 0.129487896380 Henry Cohn, 2024, needs more optimization.
31 177 0.130232363346 Henry Cohn, 2024, needs more optimization.
31 178 0.130767653339 Henry Cohn, 2024, needs more optimization.
31 179 0.131421943519 Henry Cohn, 2024, needs more optimization.
31 180 0.132109727595 Henry Cohn, 2024, needs more optimization.
31 181 0.132704266308 Henry Cohn, 2024, needs more optimization.
31 182 0.133165647800 Henry Cohn, 2024, needs more optimization.
31 183 0.133592906924 Henry Cohn, 2024, needs more optimization.
31 184 0.134020981501 Henry Cohn, 2024, needs more optimization.
31 185 0.134819608867 Henry Cohn, 2024, needs more optimization.
31 186 0.135253824767 Henry Cohn, 2024, needs more optimization.
31 187 0.135928069478 Henry Cohn, 2024, needs more optimization.
31 188 0.136205963392 Henry Cohn, 2024, needs more optimization.
31 189 0.136962974548 Henry Cohn, 2024, needs more optimization.
31 190 0.137448448528 Henry Cohn, 2024, needs more optimization.
31 191 0.137837860167 Henry Cohn, 2024, needs more optimization.
31 193 0.138785604708 Henry Cohn, 2024, needs more optimization.
31 194 0.140517513526 Henry Cohn, 2024, needs more optimization.
31 195 0.140935909114 Henry Cohn, 2024, needs more optimization.
31 196 0.141316824826 Henry Cohn, 2024, needs more optimization.
31 197 0.141847796372 Henry Cohn, 2024, needs more optimization.
31 198 0.142279490316 Henry Cohn, 2024, needs more optimization.
31 199 0.142828718057 Henry Cohn, 2024, needs more optimization.
31 200 0.143269451825 Henry Cohn, 2024, needs more optimization.
31 201 0.143706997294 Henry Cohn, 2024, needs more optimization.
31 202 0.144239005653 Henry Cohn, 2024, needs more optimization.
31 203 0.144617491652 Henry Cohn, 2024, needs more optimization.
31 204 0.145128823816 Henry Cohn, 2024, needs more optimization.
31 205 0.145517912716 Henry Cohn, 2024, needs more optimization.
31 206 0.145575641944 Henry Cohn, 2024, needs more optimization.
31 207 0.146329758147 Henry Cohn, 2024, needs more optimization.
31 208 0.146864325913 Henry Cohn, 2024, needs more optimization.
31 209 0.147262573039 Henry Cohn, 2024, needs more optimization.
31 210 0.147503329767 Henry Cohn, 2024, needs more optimization.
31 211 0.148099035183 Henry Cohn, 2024, needs more optimization.
31 212 0.148575653909 Henry Cohn, 2024, needs more optimization.
31 213 0.149001101947 Henry Cohn, 2024, needs more optimization.
31 214 0.149377664890 Henry Cohn, 2024, needs more optimization.
31 215 0.149818840342 Henry Cohn, 2024, needs more optimization.
31 216 0.150141225449 Henry Cohn, 2024, needs more optimization.
31 217 0.150565632725 Henry Cohn, 2024, needs more optimization.
31 218 0.151001290779 Henry Cohn, 2024, needs more optimization.
31 219 0.151414478873 Henry Cohn, 2024, needs more optimization.
31 220 0.151920067751 Henry Cohn, 2024, needs more optimization.
31 221 0.152227113807 Henry Cohn, 2024, needs more optimization.
31 222 0.152643547278 Henry Cohn, 2024, needs more optimization.
31 223 0.153005061428 Henry Cohn, 2024, needs more optimization.
31 224 0.153475245617 Henry Cohn, 2024, needs more optimization.
31 225 0.153892482011 Henry Cohn, 2024, needs more optimization.
31 226 0.154182110246 Henry Cohn, 2024, needs more optimization.
31 227 0.154525004309 Henry Cohn, 2024, needs more optimization.
31 228 0.154958112347 Henry Cohn, 2024, needs more optimization.
31 229 0.155354568156 Henry Cohn, 2024, needs more optimization.
31 230 0.155727219690 Henry Cohn, 2024, needs more optimization.
31 231 0.156129912047 Henry Cohn, 2024, needs more optimization.
31 232 0.156442290659 Henry Cohn, 2024, needs more optimization.
31 233 0.156971275864 Henry Cohn, 2024, needs more optimization.
31 234 0.157310611332 Henry Cohn, 2024, needs more optimization.
31 235 0.157581277503 Henry Cohn, 2024, needs more optimization.
31 236 0.157972322934 Henry Cohn, 2024, needs more optimization.
31 237 0.158436941690 Henry Cohn, 2024, needs more optimization.
31 238 0.158722912007 Henry Cohn, 2024, needs more optimization.
31 239 0.159134215691 Henry Cohn, 2024, needs more optimization.
31 240 0.159449147752 Henry Cohn, 2024, needs more optimization.
31 241 0.159872757455 Henry Cohn, 2024, needs more optimization.
31 242 0.160137677192 Henry Cohn, 2024, needs more optimization.
31 243 0.160601336290 Henry Cohn, 2024, needs more optimization.
31 244 0.160954172170 Henry Cohn, 2024, needs more optimization.
31 245 0.161226997296 Henry Cohn, 2024, needs more optimization.
31 246 0.161565914214 Henry Cohn, 2024, needs more optimization.
31 247 0.162022492877 Henry Cohn, 2024, needs more optimization.
31 248 0.162169362083 Henry Cohn, 2024, needs more optimization.
31 249 0.162588869348 Henry Cohn, 2024, needs more optimization.
31 250 0.162836466551 Henry Cohn, 2024, needs more optimization.
31 251 0.163383781125 Henry Cohn, 2024, needs more optimization.
31 252 0.163732013348 Henry Cohn, 2024, needs more optimization.
31 253 0.164021659254 Henry Cohn, 2024, needs more optimization.
31 254 0.164345760369 Henry Cohn, 2024, needs more optimization.
31 255 0.164642139929 Henry Cohn, 2024, needs more optimization.
31 256 0.164968075706 Henry Cohn, 2024, needs more optimization.
31 257 0.165349600149 Henry Cohn, 2024, needs more optimization.
31 258 0.165686698520 Henry Cohn, 2024, needs more optimization.
31 259 0.166073504195 Henry Cohn, 2024, needs more optimization.
31 260 0.166358574980 Henry Cohn, 2024, needs more optimization.
31 307 0.166666666667 Orthogonal union of 275 points in 22 dimensions and 32 points in 9 dimensions.
6⁢x−1
31 308 0.180525091271 Orthogonal union of 275 points in 22 dimensions and 33 points in 9 dimensions.
31 309 0.181109867605 Henry Cohn, 2024, needs more optimization.
31 310 0.181491048684 Henry Cohn, 2024, needs more optimization.
31 311 0.181581671886 Henry Cohn, 2024, needs more optimization.
31 318 0.181818181819 Orthogonal union of 297 points in 24 dimensions and 21 points in 7 dimensions.
11⁢x−2
31 321 0.182743997632 Orthogonal union of 297 points in 24 dimensions and 24 points in 7 dimensions.
19⁢x2+2⁢x−1
31 322 0.184421713382 Henry Cohn, 2024, needs more optimization.
31 323 0.184586428135 Henry Cohn, 2024, needs more optimization.
31 324 0.184981691361 Henry Cohn, 2024, needs more optimization.
31 325 0.185346405250 Henry Cohn, 2024, needs more optimization.
31 327 0.185702381203 Henry Cohn, 2024, needs more optimization.
31 328 0.186048196914 Henry Cohn, 2024, needs more optimization.
31 329 0.186238939955 Henry Cohn, 2024, needs more optimization.
31 330 0.186721546630 Henry Cohn, 2024, needs more optimization.
31 332 0.186747271002 Henry Cohn, 2024, needs more optimization.
31 333 0.187220281464 Henry Cohn, 2024, needs more optimization.
31 334 0.187596613063 Henry Cohn, 2024, needs more optimization.
31 335 0.187650616818 Henry Cohn, 2024, needs more optimization.
31 336 0.188177704925 Henry Cohn, 2024, needs more optimization.
31 337 0.188337360243 Henry Cohn, 2024, needs more optimization.
31 338 0.188495469140 Henry Cohn, 2024, needs more optimization.
31 339 0.188610427409 Henry Cohn, 2024, needs more optimization.
31 340 0.188972850141 Henry Cohn, 2024, needs more optimization.
31 341 0.189089410334 Henry Cohn, 2024, needs more optimization.
31 342 0.189446827262 Henry Cohn, 2024, needs more optimization.
31 343 0.189704671556 Henry Cohn, 2024, needs more optimization.
31 344 0.189968168578 Henry Cohn, 2024, needs more optimization.
31 345 0.190263938719 Henry Cohn, 2024, needs more optimization.
31 346 0.190409000274 Henry Cohn, 2024, needs more optimization.
31 347 0.190613295985 Henry Cohn, 2024, needs more optimization.
31 348 0.190892686114 Henry Cohn, 2024, needs more optimization.
31 349 0.191086893092 Henry Cohn, 2024, needs more optimization.
31 350 0.191423905678 Henry Cohn, 2024, needs more optimization.
31 351 0.191651726279 Henry Cohn, 2024, needs more optimization.
31 352 0.191911263542 Henry Cohn, 2024, needs more optimization.
31 353 0.191979380122 Henry Cohn, 2024, needs more optimization.
31 354 0.192103883717 Henry Cohn, 2024, needs more optimization.
31 355 0.192481261865 Henry Cohn, 2024, needs more optimization.
31 356 0.192604296025 Henry Cohn, 2024, needs more optimization.
31 357 0.192938500194 Henry Cohn, 2024, needs more optimization.
31 358 0.193250315321 Henry Cohn, 2024, needs more optimization.
31 359 0.193431716382 Henry Cohn, 2024, needs more optimization.
31 360 0.193707326182 Henry Cohn, 2024, needs more optimization.
31 361 0.193786959851 Henry Cohn, 2024, needs more optimization.
31 362 0.194174794969 Henry Cohn, 2024, needs more optimization.
31 363 0.194187833021 Henry Cohn, 2024, needs more optimization.
31 364 0.194521532005 Henry Cohn, 2024, needs more optimization.
31 366 0.194875823032 Henry Cohn, 2024, needs more optimization.
31 367 0.194978546441 Henry Cohn, 2024, needs more optimization.
31 368 0.195408006100 Henry Cohn, 2024, needs more optimization.
31 369 0.195613430467 Henry Cohn, 2024, needs more optimization.
31 370 0.195827731156 Henry Cohn, 2024, needs more optimization.
31 371 0.195895053059 Henry Cohn, 2024, needs more optimization.
31 372 0.196328380253 Henry Cohn, 2024, needs more optimization.
31 373 0.196342936885 Henry Cohn, 2024, needs more optimization.
31 374 0.196660414901 Henry Cohn, 2024, needs more optimization.
31 375 0.196669459325 Henry Cohn, 2024, needs more optimization.
31 376 0.196892905688 Henry Cohn, 2024, needs more optimization.
31 377 0.197261103432 Henry Cohn, 2024, needs more optimization.
31 378 0.197500599404 Henry Cohn, 2024, needs more optimization.
31 380 0.197730549472 Henry Cohn, 2024, needs more optimization.
31 381 0.198142375563 Henry Cohn, 2024, needs more optimization.
31 382 0.198240644322 Henry Cohn, 2024, needs more optimization.
31 384 0.198471420781 Henry Cohn, 2024, needs more optimization.
31 385 0.198768261803 Henry Cohn, 2024, needs more optimization.
31 386 0.199094295427 Henry Cohn, 2024, needs more optimization.
31 387 0.199422221706 Henry Cohn, 2024, needs more optimization.
31 388 0.199607645210 Henry Cohn, 2024, needs more optimization.
31 389 0.199867344867 Henry Cohn, 2024, needs more optimization.
31 581 0.2 Orthogonal union of 552 points in 23 dimensions and 29 points in 8 dimensions.
5⁢x−1
31 582 0.203916279404 Orthogonal union of 552 points in 23 dimensions and 30 points in 8 dimensions.
31 583 0.219706528517 Orthogonal union of 552 points in 23 dimensions and 31 points in 8 dimensions.
31 585 0.227325452024 Orthogonal union of 552 points in 23 dimensions and 33 points in 8 dimensions.
95⁢x2−4⁢x−4
31 586 0.231571616436 Henry Cohn, 2024, needs more optimization.
31 587 0.231696388312 Henry Cohn, 2024, needs more optimization.
31 589 0.231911877884 Henry Cohn, 2024, needs more optimization.
31 591 0.232237122221 Henry Cohn, 2024, needs more optimization.
31 592 0.232341355735 Henry Cohn, 2024, needs more optimization.
31 594 0.232543050068 Henry Cohn, 2024, needs more optimization.
31 595 0.232685488430 Henry Cohn, 2024, needs more optimization.
31 596 0.232977081309 Henry Cohn, 2024, needs more optimization.
31 597 0.233204517559 Henry Cohn, 2024, needs more optimization.
31 598 0.233225681557 Henry Cohn, 2024, needs more optimization.
31 599 0.233397642396 Henry Cohn, 2024, needs more optimization.
31 600 0.233469669538 Henry Cohn, 2024, needs more optimization.
31 601 0.233647985134 Henry Cohn, 2024, needs more optimization.
31 602 0.233752211511 Henry Cohn, 2024, needs more optimization.
31 603 0.233932452204 Henry Cohn, 2024, needs more optimization.
31 604 0.233973504830 Henry Cohn, 2024, needs more optimization.
31 605 0.234059341948 Henry Cohn, 2024, needs more optimization.
31 607 0.234379580958 Henry Cohn, 2024, needs more optimization.
31 608 0.234620240134 Henry Cohn, 2024, needs more optimization.
31 609 0.234652191200 Henry Cohn, 2024, needs more optimization.
31 611 0.234739212583 Henry Cohn, 2024, needs more optimization.
31 612 0.234885765345 Henry Cohn, 2024, needs more optimization.
31 613 0.235128703694 Henry Cohn, 2024, needs more optimization.
31 614 0.235330014238 Henry Cohn, 2024, needs more optimization.
31 616 0.235401970871 Henry Cohn, 2024, needs more optimization.
31 617 0.235654990746 Henry Cohn, 2024, needs more optimization.
31 618 0.235889068590 Henry Cohn, 2024, needs more optimization.
31 620 0.236017122801 Henry Cohn, 2024, needs more optimization.
31 621 0.236113113448 Henry Cohn, 2024, needs more optimization.
31 622 0.236235616268 Henry Cohn, 2024, needs more optimization.
31 623 0.236461931630 Henry Cohn, 2024, needs more optimization.
31 625 0.236590725586 Henry Cohn, 2024, needs more optimization.
31 626 0.236875543864 Henry Cohn, 2024, needs more optimization.
31 628 0.236884343789 Henry Cohn, 2024, needs more optimization.
31 629 0.236896294496 Henry Cohn, 2024, needs more optimization.
31 631 0.237298608507 Henry Cohn, 2024, needs more optimization.
31 633 0.237600131117 Henry Cohn, 2024, needs more optimization.
31 634 0.237850822916 Henry Cohn, 2024, needs more optimization.
31 635 0.237902492647 Henry Cohn, 2024, needs more optimization.
31 637 0.238028250166 Henry Cohn, 2024, needs more optimization.
31 638 0.238114687449 Henry Cohn, 2024, needs more optimization.
31 640 0.238319821440 Henry Cohn, 2024, needs more optimization.
31 641 0.238594886352 Henry Cohn, 2024, needs more optimization.
31 642 0.238613911178 Henry Cohn, 2024, needs more optimization.
31 643 0.238769614665 Henry Cohn, 2024, needs more optimization.
31 644 0.238999572995 Henry Cohn, 2024, needs more optimization.
31 646 0.239138128367 Henry Cohn, 2024, needs more optimization.
31 647 0.239238960876 Henry Cohn, 2024, needs more optimization.
31 649 0.239414719170 Henry Cohn, 2024, needs more optimization.
31 650 0.239660880989 Henry Cohn, 2024, needs more optimization.
31 652 0.239826612310 Henry Cohn, 2024, needs more optimization.
31 654 0.239962267656 Henry Cohn, 2024, needs more optimization.
31 655 0.240310917698 Henry Cohn, 2024, needs more optimization.
31 656 0.240411853923 Henry Cohn, 2024, needs more optimization.
31 657 0.240492867635 Henry Cohn, 2024, needs more optimization.
31 658 0.240589820521 Henry Cohn, 2024, needs more optimization.
31 659 0.240883446132 Henry Cohn, 2024, needs more optimization.
31 661 0.240971944638 Henry Cohn, 2024, needs more optimization.
31 662 0.241114237807 Henry Cohn, 2024, needs more optimization.
31 664 0.241310145194 Henry Cohn, 2024, needs more optimization.
31 665 0.241589644382 Henry Cohn, 2024, needs more optimization.
31 667 0.241591034300 Henry Cohn, 2024, needs more optimization.
31 669 0.241851236085 Henry Cohn, 2024, needs more optimization.
31 671 0.242113042907 Henry Cohn, 2024, needs more optimization.
31 672 0.242346708862 Henry Cohn, 2024, needs more optimization.
31 673 0.242366458036 Henry Cohn, 2024, needs more optimization.
31 674 0.242413621504 Henry Cohn, 2024, needs more optimization.
31 675 0.242489201932 Henry Cohn, 2024, needs more optimization.
31 676 0.242603171767 Henry Cohn, 2024, needs more optimization.
31 677 0.242715613815 Henry Cohn, 2024, needs more optimization.
31 678 0.242892537063 Henry Cohn, 2024, needs more optimization.
31 681 0.243038756036 Henry Cohn, 2024, needs more optimization.
31 682 0.243233567865 Henry Cohn, 2024, needs more optimization.
31 683 0.243488158287 Henry Cohn, 2024, needs more optimization.
31 684 0.243519802387 Henry Cohn, 2024, needs more optimization.
31 685 0.243642416666 Henry Cohn, 2024, needs more optimization.
31 686 0.243861042657 Henry Cohn, 2024, needs more optimization.
31 687 0.243971361564 Henry Cohn, 2024, needs more optimization.
31 688 0.244069229107 Henry Cohn, 2024, needs more optimization.
31 689 0.244133717245 Henry Cohn, 2024, needs more optimization.
31 690 0.244200802725 Henry Cohn, 2024, needs more optimization.
31 691 0.244225811196 Henry Cohn, 2024, needs more optimization.
31 692 0.244471194626 Henry Cohn, 2024, needs more optimization.
31 693 0.244730550504 Henry Cohn, 2024, needs more optimization.
31 695 0.244785309322 Henry Cohn, 2024, needs more optimization.
31 696 0.244974956353 Henry Cohn, 2024, needs more optimization.
31 697 0.244980860198 Henry Cohn, 2024, needs more optimization.
31 699 0.245180843147 Henry Cohn, 2024, needs more optimization.
31 700 0.245399098290 Henry Cohn, 2024, needs more optimization.
31 701 0.245405276324 Henry Cohn, 2024, needs more optimization.
31 702 0.245663733239 Henry Cohn, 2024, needs more optimization.
31 704 0.245697980685 Henry Cohn, 2024, needs more optimization.
31 705 0.246018978338 Henry Cohn, 2024, needs more optimization.
31 709 0.246035194411 Henry Cohn, 2024, needs more optimization.
31 710 0.246432907525 Henry Cohn, 2024, needs more optimization.
31 711 0.246591531164 Henry Cohn, 2024, needs more optimization.
31 713 0.246688381635 Henry Cohn, 2024, needs more optimization.
31 714 0.246825125573 Henry Cohn, 2024, needs more optimization.
31 715 0.246955103034 Henry Cohn, 2024, needs more optimization.
31 716 0.247121766265 Henry Cohn, 2024, needs more optimization.
31 717 0.247226189770 Henry Cohn, 2024, needs more optimization.
31 718 0.247439934616 Henry Cohn, 2024, needs more optimization.
31 720 0.247464563846 Henry Cohn, 2024, needs more optimization.
31 721 0.247551705070 Henry Cohn, 2024, needs more optimization.
31 722 0.247721915266 Henry Cohn, 2024, needs more optimization.
31 723 0.247727024977 Henry Cohn, 2024, needs more optimization.
31 725 0.248017759018 Henry Cohn, 2024, needs more optimization.
31 726 0.248225052297 Henry Cohn, 2024, needs more optimization.
31 728 0.248328830933 Henry Cohn, 2024, needs more optimization.
31 730 0.248463996459 Henry Cohn, 2024, needs more optimization.
31 731 0.248601993439 Henry Cohn, 2024, needs more optimization.
31 732 0.248727036596 Henry Cohn, 2024, needs more optimization.
31 733 0.249019117022 Henry Cohn, 2024, needs more optimization.
31 735 0.249063954894 Henry Cohn, 2024, needs more optimization.
31 736 0.249213959744 Henry Cohn, 2024, needs more optimization.
31 737 0.249322990462 Henry Cohn, 2024, needs more optimization.
31 738 0.249338794717 Henry Cohn, 2024, needs more optimization.
31 739 0.249397797457 Henry Cohn, 2024, needs more optimization.
31 741 0.249710890250 Henry Cohn, 2024, needs more optimization.
31 742 0.249798138250 Henry Cohn, 2024, needs more optimization.
31 743 0.249989510379 Henry Cohn, 2024, needs more optimization.
31 938 0.25 Orthogonal union of 891 points in 22 dimensions and 47 points in 9 dimensions.
4⁢x−1
31 939 0.254741941811 Orthogonal union of 891 points in 22 dimensions and 48 points in 9 dimensions.
31 940 0.261827927697 Orthogonal union of 891 points in 22 dimensions and 49 points in 9 dimensions.
31 943 0.267191024627 Orthogonal union of 891 points in 22 dimensions and 52 points in 9 dimensions.
71⁢x2−4⁢x−4
31 944 0.267727681714 Henry Cohn, 2024, needs more optimization.
31 945 0.267776015657 Henry Cohn, 2024, needs more optimization.
31 946 0.267901457984 Henry Cohn, 2024, needs more optimization.
31 947 0.267907660859 Henry Cohn, 2024, needs more optimization.
31 948 0.268025695886 Henry Cohn, 2024, needs more optimization.
31 949 0.268182725232 Henry Cohn, 2024, needs more optimization.
31 952 0.268345318030 Henry Cohn, 2024, needs more optimization.
31 953 0.268351338118 Henry Cohn, 2024, needs more optimization.
31 954 0.268588984195 Henry Cohn, 2024, needs more optimization.
31 955 0.268595370931 Henry Cohn, 2024, needs more optimization.
31 957 0.268779350759 Henry Cohn, 2024, needs more optimization.
31 959 0.268804932669 Henry Cohn, 2024, needs more optimization.
31 960 0.268864067760 Henry Cohn, 2024, needs more optimization.
31 962 0.269160269937 Henry Cohn, 2024, needs more optimization.
31 964 0.269199680105 Henry Cohn, 2024, needs more optimization.
31 966 0.269327873096 Henry Cohn, 2024, needs more optimization.
31 967 0.269537951080 Henry Cohn, 2024, needs more optimization.
31 970 0.269718073733 Henry Cohn, 2024, needs more optimization.
31 971 0.269864849783 Henry Cohn, 2024, needs more optimization.
31 973 0.269917561961 Henry Cohn, 2024, needs more optimization.
31 974 0.269991926062 Henry Cohn, 2024, needs more optimization.
31 977 0.270156054479 Henry Cohn, 2024, needs more optimization.
31 978 0.270294435234 Henry Cohn, 2024, needs more optimization.
31 979 0.270407979154 Henry Cohn, 2024, needs more optimization.
31 980 0.270439468354 Henry Cohn, 2024, needs more optimization.
31 981 0.270475218932 Henry Cohn, 2024, needs more optimization.
31 982 0.270710547337 Henry Cohn, 2024, needs more optimization.
31 984 0.270760911425 Henry Cohn, 2024, needs more optimization.
31 985 0.270870745903 Henry Cohn, 2024, needs more optimization.
31 986 0.270943507332 Henry Cohn, 2024, needs more optimization.
31 987 0.271045769738 Henry Cohn, 2024, needs more optimization.
31 989 0.271098666820 Henry Cohn, 2024, needs more optimization.
31 990 0.271201775081 Henry Cohn, 2024, needs more optimization.
31 992 0.271300459765 Henry Cohn, 2024, needs more optimization.
31 994 0.271469037651 Henry Cohn, 2024, needs more optimization.
31 995 0.271603919944 Henry Cohn, 2024, needs more optimization.
31 996 0.271649484461 Henry Cohn, 2024, needs more optimization.
31 997 0.271687018777 Henry Cohn, 2024, needs more optimization.
31 999 0.271805124316 Henry Cohn, 2024, needs more optimization.
31 1000 0.271970137410 Henry Cohn, 2024, needs more optimization.
31 1001 0.271972108837 Henry Cohn, 2024, needs more optimization.
31 1003 0.272020036007 Henry Cohn, 2024, needs more optimization.
31 1004 0.272266277009 Henry Cohn, 2024, needs more optimization.
31 1005 0.272276289281 Henry Cohn, 2024, needs more optimization.
31 1006 0.272477939776 Henry Cohn, 2024, needs more optimization.
31 1008 0.272526265698 Henry Cohn, 2024, needs more optimization.
31 1010 0.272596493835 Henry Cohn, 2024, needs more optimization.
31 1024 0.272727272728 Code with 1024 points in 22 dimensions.
11⁢x−3
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 0.029445000129 Henry Cohn, 2024, needs more optimization.
32 67 0.037581109828 Henry Cohn, 2024, needs more optimization.
32 68 0.040223214988 Henry Cohn, 2024, needs more optimization.
32 69 0.042684924285 Henry Cohn, 2024, needs more optimization.
32 70 0.043196421683 Henry Cohn, 2024, needs more optimization.
32 71 0.043562764207 Henry Cohn, 2024, needs more optimization.
32 72 0.043961874787 Henry Cohn, 2024, needs more optimization.
32 73 0.044524842229 Henry Cohn, 2024, needs more optimization.
32 74 0.047103741147 Henry Cohn, 2024, needs more optimization.
32 75 0.049032547437 Henry Cohn, 2024, needs more optimization.
32 76 0.050188725890 Henry Cohn, 2024, needs more optimization.
32 77 0.051454696848 Henry Cohn, 2024, needs more optimization.
32 78 0.052486824885 Henry Cohn, 2024, needs more optimization.
32 79 0.053704909815 Henry Cohn, 2024, needs more optimization.
32 80 0.055095466381 Henry Cohn, 2024, needs more optimization.
32 81 0.056196826671 Henry Cohn, 2024, needs more optimization.
32 82 0.057505095775 Henry Cohn, 2024, needs more optimization.
32 83 0.058540043699 Henry Cohn, 2024, needs more optimization.
32 84 0.059806915819 Henry Cohn, 2024, needs more optimization.
32 85 0.060934954661 Henry Cohn, 2024, needs more optimization.
32 86 0.062192889993 Henry Cohn, 2024, needs more optimization.
32 87 0.063398319830 Henry Cohn, 2025, needs more optimization.
32 88 0.064385294642 Henry Cohn, 2025, needs more optimization.
32 89 0.065598655681 Henry Cohn, 2025, needs more optimization.
32 90 0.066441658045 Henry Cohn, 2025, needs more optimization.
32 91 0.067805877850 Henry Cohn, 2025, needs more optimization.
32 92 0.068771649322 Henry Cohn, 2024, needs more optimization.
32 93 0.069849010021 Henry Cohn, 2025, needs more optimization.
32 94 0.070671826659 Henry Cohn, 2025, needs more optimization.
32 95 0.071741773798 Henry Cohn, 2025, needs more optimization.
32 96 0.073112859514 Henry Cohn, 2025, needs more optimization.
32 97 0.073938556941 Henry Cohn, 2025, needs more optimization.
32 98 0.074776041191 Henry Cohn, 2024, needs more optimization.
32 99 0.075692955783 Henry Cohn, 2024, needs more optimization.
32 100 0.076403325571 Henry Cohn, 2025, needs more optimization.
32 101 0.077413818722 Henry Cohn, 2024, needs more optimization.
32 102 0.078270744042 Henry Cohn, 2024, needs more optimization.
32 103 0.079123429158 Henry Cohn, 2024, needs more optimization.
32 104 0.080102471268 Henry Cohn, 2024, needs more optimization.
32 105 0.081099277422 Henry Cohn, 2024, needs more optimization.
32 106 0.081695409363 Henry Cohn, 2024, needs more optimization.
32 107 0.082188092332 Henry Cohn, 2024, needs more optimization.
32 108 0.083160548753 Henry Cohn, 2024, needs more optimization.
32 109 0.083806345170 Henry Cohn, 2024, needs more optimization.
32 110 0.084697338620 Henry Cohn, 2024, needs more optimization.
32 111 0.085505482267 Henry Cohn, 2024, needs more optimization.
32 112 0.086022845124 Henry Cohn, 2024, needs more optimization.
32 118 0.086322451079 Henry Cohn, 2024, needs more optimization.
32 121 0.087115245525 Henry Cohn, 2024, needs more optimization.
32 123 0.090909090910 Orthogonal union of 100 points in 22 dimensions and 23 points in 10 dimensions.
11⁢x−1
32 124 0.094247880572 Henry Cohn, 2024, needs more optimization.
32 125 0.094921797910 Henry Cohn, 2024, needs more optimization.
32 126 0.095236820600 Henry Cohn, 2024, needs more optimization.
32 127 0.095959875042 Henry Cohn, 2024, needs more optimization.
32 128 0.096665133236 Henry Cohn, 2024, needs more optimization.
32 129 0.097207373205 Henry Cohn, 2024, needs more optimization.
32 130 0.097753212820 Henry Cohn, 2024, needs more optimization.
32 131 0.098399111068 Henry Cohn, 2024, needs more optimization.
32 132 0.098917249661 Henry Cohn, 2024, needs more optimization.
32 133 0.099580461460 Henry Cohn, 2024, needs more optimization.
32 134 0.100174414427 Henry Cohn, 2024, needs more optimization.
32 135 0.100846028147 Henry Cohn, 2024, needs more optimization.
32 136 0.100973164693 Henry Cohn, 2024, needs more optimization.
32 137 0.101677931946 Henry Cohn, 2024, needs more optimization.
32 138 0.102174312781 Henry Cohn, 2024, needs more optimization.
32 139 0.102635526755 Henry Cohn, 2024, needs more optimization.
32 140 0.103260536468 Henry Cohn, 2024, needs more optimization.
32 141 0.103792451631 Henry Cohn, 2024, needs more optimization.
32 142 0.104263655246 Henry Cohn, 2024, needs more optimization.
32 143 0.105090699344 Henry Cohn, 2024, needs more optimization.
32 144 0.105487786149 Henry Cohn, 2024, needs more optimization.
32 145 0.106023935628 Henry Cohn, 2024, needs more optimization.
32 146 0.106451586146 Henry Cohn, 2024, needs more optimization.
32 147 0.106855065256 Henry Cohn, 2024, needs more optimization.
32 148 0.107630510421 Henry Cohn, 2024, needs more optimization.
32 149 0.108142113287 Henry Cohn, 2024, needs more optimization.
32 150 0.108781514535 Henry Cohn, 2024, needs more optimization.
32 151 0.109157616876 Henry Cohn, 2024, needs more optimization.
32 152 0.109732207821 Henry Cohn, 2024, needs more optimization.
32 153 0.110301066396 Henry Cohn, 2024, needs more optimization.
32 154 0.110697436038 Henry Cohn, 2024, needs more optimization.
32 155 0.111393501673 Henry Cohn, 2024, needs more optimization.
32 156 0.112249864991 Henry Cohn, 2024, needs more optimization.
32 157 0.112712035944 Henry Cohn, 2024, needs more optimization.
32 158 0.113343333855 Henry Cohn, 2024, needs more optimization.
32 159 0.113911844059 Henry Cohn, 2024, needs more optimization.
32 160 0.114306405210 Henry Cohn, 2024, needs more optimization.
32 161 0.114922705925 Henry Cohn, 2024, needs more optimization.
32 162 0.115511600197 Henry Cohn, 2024, needs more optimization.
32 163 0.116024300457 Henry Cohn, 2024, needs more optimization.
32 164 0.116788199149 Henry Cohn, 2024, needs more optimization.
32 165 0.117075026109 Henry Cohn, 2024, needs more optimization.
32 166 0.117783678450 Henry Cohn, 2024, needs more optimization.
32 167 0.118516318213 Henry Cohn, 2024, needs more optimization.
32 168 0.119104852945 Henry Cohn, 2024, needs more optimization.
32 169 0.119608492518 Henry Cohn, 2024, needs more optimization.
32 170 0.120232877287 Henry Cohn, 2024, needs more optimization.
32 171 0.121023216114 Henry Cohn, 2024, needs more optimization.
32 172 0.121611033286 Henry Cohn, 2024, needs more optimization.
32 173 0.121956368117 Henry Cohn, 2024, needs more optimization.
32 174 0.122547527589 Henry Cohn, 2024, needs more optimization.
32 175 0.123463526284 Henry Cohn, 2024, needs more optimization.
32 176 0.123940542063 Henry Cohn, 2024, needs more optimization.
32 177 0.124475117668 Henry Cohn, 2024, needs more optimization.
32 178 0.125047188332 Henry Cohn, 2024, needs more optimization.
32 179 0.125586736264 Henry Cohn, 2024, needs more optimization.
32 180 0.126109622396 Henry Cohn, 2024, needs more optimization.
32 181 0.126636017575 Henry Cohn, 2024, needs more optimization.
32 182 0.127292733138 Henry Cohn, 2024, needs more optimization.
32 183 0.127945851948 Henry Cohn, 2024, needs more optimization.
32 184 0.128637668533 Henry Cohn, 2024, needs more optimization.
32 185 0.128862548357 Henry Cohn, 2024, needs more optimization.
32 186 0.129570358424 Henry Cohn, 2024, needs more optimization.
32 187 0.130181855496 Henry Cohn, 2024, needs more optimization.
32 188 0.130556308761 Henry Cohn, 2024, needs more optimization.
32 189 0.131219899361 Henry Cohn, 2024, needs more optimization.
32 190 0.131765273811 Henry Cohn, 2024, needs more optimization.
32 191 0.132284294857 Henry Cohn, 2024, needs more optimization.
32 192 0.133539596390 Henry Cohn, 2024, needs more optimization.
32 193 0.134262654550 Henry Cohn, 2024, needs more optimization.
32 194 0.134734966983 Henry Cohn, 2024, needs more optimization.
32 195 0.135356632875 Henry Cohn, 2024, needs more optimization.
32 198 0.135660128288 Henry Cohn, 2024, needs more optimization.
32 199 0.136147798396 Henry Cohn, 2024, needs more optimization.
32 200 0.137776910845 Henry Cohn, 2024, needs more optimization.
32 201 0.138145244190 Henry Cohn, 2024, needs more optimization.
32 202 0.138698566178 Henry Cohn, 2024, needs more optimization.
32 203 0.139049101340 Henry Cohn, 2024, needs more optimization.
32 204 0.139532715272 Henry Cohn, 2024, needs more optimization.
32 205 0.139962970787 Henry Cohn, 2024, needs more optimization.
32 206 0.140497985862 Henry Cohn, 2024, needs more optimization.
32 207 0.140798351884 Henry Cohn, 2024, needs more optimization.
32 208 0.141264126184 Henry Cohn, 2024, needs more optimization.
32 209 0.141793837027 Henry Cohn, 2024, needs more optimization.
32 210 0.142213422531 Henry Cohn, 2024, needs more optimization.
32 211 0.142547029999 Henry Cohn, 2024, needs more optimization.
32 212 0.142921282669 Henry Cohn, 2024, needs more optimization.
32 213 0.143478434195 Henry Cohn, 2024, needs more optimization.
32 214 0.143970521276 Henry Cohn, 2024, needs more optimization.
32 215 0.144438908349 Henry Cohn, 2024, needs more optimization.
32 216 0.144707754364 Henry Cohn, 2024, needs more optimization.
32 217 0.145042920166 Henry Cohn, 2024, needs more optimization.
32 218 0.145535448958 Henry Cohn, 2024, needs more optimization.
32 219 0.145830852675 Henry Cohn, 2024, needs more optimization.
32 220 0.146268599081 Henry Cohn, 2024, needs more optimization.
32 221 0.146589218423 Henry Cohn, 2024, needs more optimization.
32 222 0.147058620143 Henry Cohn, 2024, needs more optimization.
32 223 0.147575978269 Henry Cohn, 2024, needs more optimization.
32 224 0.147893722575 Henry Cohn, 2024, needs more optimization.
32 225 0.148336614844 Henry Cohn, 2024, needs more optimization.
32 226 0.148740823797 Henry Cohn, 2024, needs more optimization.
32 227 0.149119180421 Henry Cohn, 2024, needs more optimization.
32 228 0.149503717718 Henry Cohn, 2024, needs more optimization.
32 229 0.149888163970 Henry Cohn, 2024, needs more optimization.
32 230 0.150195661057 Henry Cohn, 2024, needs more optimization.
32 231 0.150532568870 Henry Cohn, 2024, needs more optimization.
32 232 0.150984979068 Henry Cohn, 2024, needs more optimization.
32 233 0.151315512910 Henry Cohn, 2024, needs more optimization.
32 234 0.151729667577 Henry Cohn, 2024, needs more optimization.
32 235 0.152125018866 Henry Cohn, 2024, needs more optimization.
32 236 0.152379915816 Henry Cohn, 2024, needs more optimization.
32 237 0.152815509942 Henry Cohn, 2024, needs more optimization.
32 238 0.153184479457 Henry Cohn, 2024, needs more optimization.
32 239 0.153506480395 Henry Cohn, 2024, needs more optimization.
32 240 0.153846007417 Henry Cohn, 2024, needs more optimization.
32 241 0.154264314863 Henry Cohn, 2024, needs more optimization.
32 242 0.154557308165 Henry Cohn, 2024, needs more optimization.
32 243 0.154898848382 Henry Cohn, 2024, needs more optimization.
32 244 0.155326952843 Henry Cohn, 2024, needs more optimization.
32 245 0.155752868427 Henry Cohn, 2024, needs more optimization.
32 246 0.156019507652 Henry Cohn, 2024, needs more optimization.
32 247 0.156273834445 Henry Cohn, 2024, needs more optimization.
32 248 0.156620129479 Henry Cohn, 2024, needs more optimization.
32 249 0.157012952011 Henry Cohn, 2024, needs more optimization.
32 250 0.157251038643 Henry Cohn, 2024, needs more optimization.
32 251 0.157766492949 Henry Cohn, 2024, needs more optimization.
32 252 0.157901053151 Henry Cohn, 2024, needs more optimization.
32 253 0.158385754120 Henry Cohn, 2024, needs more optimization.
32 254 0.158777723258 Henry Cohn, 2024, needs more optimization.
32 255 0.159040612079 Henry Cohn, 2024, needs more optimization.
32 256 0.159351432473 Henry Cohn, 2024, needs more optimization.
32 257 0.159772984822 Henry Cohn, 2024, needs more optimization.
32 258 0.160063230154 Henry Cohn, 2024, needs more optimization.
32 259 0.160266246413 Henry Cohn, 2024, needs more optimization.
32 260 0.160631309327 Henry Cohn, 2024, needs more optimization.
32 261 0.161012077093 Henry Cohn, 2024, needs more optimization.
32 262 0.161325379980 Henry Cohn, 2024, needs more optimization.
32 263 0.161686152400 Henry Cohn, 2024, needs more optimization.
32 264 0.162009838139 Henry Cohn, 2024, needs more optimization.
32 265 0.162374169559 Henry Cohn, 2024, needs more optimization.
32 266 0.162557386348 Henry Cohn, 2024, needs more optimization.
32 267 0.162954522975 Henry Cohn, 2024, needs more optimization.
32 268 0.163207571615 Henry Cohn, 2024, needs more optimization.
32 269 0.163653068082 Henry Cohn, 2024, needs more optimization.
32 270 0.163899338951 Henry Cohn, 2024, needs more optimization.
32 271 0.164208689279 Henry Cohn, 2024, needs more optimization.
32 272 0.164503719952 Henry Cohn, 2024, needs more optimization.
32 273 0.164774713052 Henry Cohn, 2024, needs more optimization.
32 274 0.165033604073 Henry Cohn, 2024, needs more optimization.
32 275 0.165217983186 Henry Cohn, 2024, needs more optimization.
32 276 0.166022529605 Henry Cohn, 2024, needs more optimization.
32 277 0.166200669321 Henry Cohn, 2024, needs more optimization.
32 278 0.166553492236 Henry Cohn, 2024, needs more optimization.
32 315 0.166666666667 Orthogonal union of 275 points in 22 dimensions and 40 points in 10 dimensions.
6⁢x−1
32 316 0.176776695297 Orthogonal union of 275 points in 22 dimensions and 41 points in 10 dimensions.
32⁢x2−1
32 317 0.177434414004 Henry Cohn, 2024, needs more optimization.
32 318 0.177525070508 Henry Cohn, 2024, needs more optimization.
32 319 0.177871468801 Henry Cohn, 2024, needs more optimization.
32 320 0.178057661503 Henry Cohn, 2024, needs more optimization.
32 321 0.178401510411 Henry Cohn, 2024, needs more optimization.
32 322 0.178537993649 Henry Cohn, 2024, needs more optimization.
32 323 0.178813747175 Henry Cohn, 2024, needs more optimization.
32 324 0.179162237291 Henry Cohn, 2024, needs more optimization.
32 325 0.179336524553 Henry Cohn, 2024, needs more optimization.
32 326 0.179567679022 Henry Cohn, 2024, needs more optimization.
32 327 0.179882263989 Henry Cohn, 2024, needs more optimization.
32 328 0.180019787896 Henry Cohn, 2024, needs more optimization.
32 329 0.180409425373 Henry Cohn, 2024, needs more optimization.
32 330 0.180605040041 Henry Cohn, 2024, needs more optimization.
32 331 0.180953870471 Henry Cohn, 2024, needs more optimization.
32 332 0.181050238542 Henry Cohn, 2024, needs more optimization.
32 333 0.181377084619 Henry Cohn, 2024, needs more optimization.
32 334 0.181618823461 Henry Cohn, 2024, needs more optimization.
32 335 0.181939599240 Henry Cohn, 2024, needs more optimization.
32 336 0.182166937330 Henry Cohn, 2024, needs more optimization.
32 337 0.182288508505 Henry Cohn, 2024, needs more optimization.
32 338 0.182669192576 Henry Cohn, 2024, needs more optimization.
32 339 0.182752922385 Henry Cohn, 2024, needs more optimization.
32 340 0.183128825383 Henry Cohn, 2024, needs more optimization.
32 341 0.183134452524 Henry Cohn, 2024, needs more optimization.
32 342 0.183572250098 Henry Cohn, 2024, needs more optimization.
32 343 0.183939631778 Henry Cohn, 2024, needs more optimization.
32 344 0.184063300540 Henry Cohn, 2024, needs more optimization.
32 345 0.184276442783 Henry Cohn, 2024, needs more optimization.
32 346 0.184345485462 Henry Cohn, 2024, needs more optimization.
32 347 0.184720958360 Henry Cohn, 2024, needs more optimization.
32 348 0.185044256953 Henry Cohn, 2024, needs more optimization.
32 349 0.185151368544 Henry Cohn, 2024, needs more optimization.
32 350 0.185358636655 Henry Cohn, 2024, needs more optimization.
32 351 0.185599868707 Henry Cohn, 2024, needs more optimization.
32 352 0.185913785245 Henry Cohn, 2024, needs more optimization.
32 353 0.186122529171 Henry Cohn, 2024, needs more optimization.
32 354 0.186357388389 Henry Cohn, 2024, needs more optimization.
32 356 0.186569391779 Henry Cohn, 2024, needs more optimization.
32 357 0.186898403779 Henry Cohn, 2024, needs more optimization.
32 359 0.187269281447 Henry Cohn, 2024, needs more optimization.
32 360 0.187665495727 Henry Cohn, 2024, needs more optimization.
32 361 0.187862075563 Henry Cohn, 2024, needs more optimization.
32 362 0.188193342813 Henry Cohn, 2024, needs more optimization.
32 363 0.188399705713 Henry Cohn, 2024, needs more optimization.
32 364 0.188687479451 Henry Cohn, 2024, needs more optimization.
32 365 0.188718130844 Henry Cohn, 2024, needs more optimization.
32 366 0.188752718226 Henry Cohn, 2024, needs more optimization.
32 367 0.189247448171 Henry Cohn, 2024, needs more optimization.
32 368 0.189437501174 Henry Cohn, 2024, needs more optimization.
32 369 0.189584168940 Henry Cohn, 2024, needs more optimization.
32 370 0.189749814625 Henry Cohn, 2024, needs more optimization.
32 371 0.189997342706 Henry Cohn, 2024, needs more optimization.
32 372 0.190321321543 Henry Cohn, 2024, needs more optimization.
32 373 0.190486476246 Henry Cohn, 2024, needs more optimization.
32 374 0.190757608834 Henry Cohn, 2024, needs more optimization.
32 375 0.190919909740 Henry Cohn, 2024, needs more optimization.
32 376 0.191174129092 Henry Cohn, 2024, needs more optimization.
32 377 0.191489276720 Henry Cohn, 2024, needs more optimization.
32 378 0.191549991097 Henry Cohn, 2024, needs more optimization.
32 379 0.191758494698 Henry Cohn, 2024, needs more optimization.
32 380 0.191897110776 Henry Cohn, 2024, needs more optimization.
32 381 0.192232831968 Henry Cohn, 2024, needs more optimization.
32 382 0.192397345485 Henry Cohn, 2024, needs more optimization.
32 384 0.192717660678 Henry Cohn, 2024, needs more optimization.
32 385 0.193073771554 Henry Cohn, 2024, needs more optimization.
32 386 0.193139872996 Henry Cohn, 2024, needs more optimization.
32 387 0.193408366636 Henry Cohn, 2024, needs more optimization.
32 388 0.193526809101 Henry Cohn, 2024, needs more optimization.
32 389 0.193906551804 Henry Cohn, 2024, needs more optimization.
32 390 0.194022685010 Henry Cohn, 2024, needs more optimization.
32 391 0.194196835388 Henry Cohn, 2024, needs more optimization.
32 392 0.194536482369 Henry Cohn, 2024, needs more optimization.
32 393 0.194697543244 Henry Cohn, 2024, needs more optimization.
32 394 0.194941780781 Henry Cohn, 2024, needs more optimization.
32 395 0.194954011507 Henry Cohn, 2024, needs more optimization.
32 396 0.195020840283 Henry Cohn, 2024, needs more optimization.
32 397 0.195307440545 Henry Cohn, 2024, needs more optimization.
32 399 0.195621885661 Henry Cohn, 2024, needs more optimization.
32 400 0.195926796484 Henry Cohn, 2024, needs more optimization.
32 401 0.196224906466 Henry Cohn, 2024, needs more optimization.
32 402 0.196423441896 Henry Cohn, 2024, needs more optimization.
32 403 0.196557565312 Henry Cohn, 2024, needs more optimization.
32 404 0.196819244400 Henry Cohn, 2024, needs more optimization.
32 405 0.196882588762 Henry Cohn, 2024, needs more optimization.
32 407 0.197164418759 Henry Cohn, 2024, needs more optimization.
32 408 0.197549069742 Henry Cohn, 2024, needs more optimization.
32 409 0.197690484099 Henry Cohn, 2024, needs more optimization.
32 410 0.197907284786 Henry Cohn, 2024, needs more optimization.
32 411 0.198200399473 Henry Cohn, 2024, needs more optimization.
32 412 0.198390416938 Henry Cohn, 2024, needs more optimization.
32 413 0.198420724273 Henry Cohn, 2024, needs more optimization.
32 414 0.198726918210 Henry Cohn, 2024, needs more optimization.
32 415 0.198843639897 Henry Cohn, 2024, needs more optimization.
32 416 0.198970756797 Henry Cohn, 2024, needs more optimization.
32 417 0.199296286106 Henry Cohn, 2024, needs more optimization.
32 418 0.199396138100 Henry Cohn, 2024, needs more optimization.
32 419 0.199634492278 Henry Cohn, 2024, needs more optimization.
32 421 0.199914469377 Henry Cohn, 2024, needs more optimization.
32 588 0.2 Orthogonal union of 552 points in 23 dimensions and 36 points in 9 dimensions.
5⁢x−1
32 589 0.213783378437 Orthogonal union of 552 points in 23 dimensions and 37 points in 9 dimensions.
32 590 0.217707451664 Orthogonal union of 552 points in 23 dimensions and 38 points in 9 dimensions.
32 591 0.222837046412 Orthogonal union of 552 points in 23 dimensions and 39 points in 9 dimensions.
32 592 0.225704407232 Orthogonal union of 552 points in 23 dimensions and 40 points in 9 dimensions.
32 593 0.226047015984 Henry Cohn, 2024, needs more optimization.
32 594 0.226137634576 Henry Cohn, 2024, needs more optimization.
32 595 0.226367289457 Henry Cohn, 2024, needs more optimization.
32 596 0.226502829657 Henry Cohn, 2024, needs more optimization.
32 599 0.226675090793 Henry Cohn, 2024, needs more optimization.
32 600 0.227111383934 Henry Cohn, 2024, needs more optimization.
32 601 0.227200566626 Henry Cohn, 2024, needs more optimization.
32 602 0.227330222611 Henry Cohn, 2024, needs more optimization.
32 603 0.227389899939 Henry Cohn, 2024, needs more optimization.
32 605 0.227504547370 Henry Cohn, 2024, needs more optimization.
32 606 0.227719624236 Henry Cohn, 2024, needs more optimization.
32 607 0.227847405275 Henry Cohn, 2024, needs more optimization.
32 608 0.228090701624 Henry Cohn, 2024, needs more optimization.
32 609 0.228256309547 Henry Cohn, 2024, needs more optimization.
32 611 0.228284427752 Henry Cohn, 2024, needs more optimization.
32 613 0.228569633437 Henry Cohn, 2024, needs more optimization.
32 615 0.228778022259 Henry Cohn, 2024, needs more optimization.
32 617 0.229052757688 Henry Cohn, 2024, needs more optimization.
32 619 0.229297488470 Henry Cohn, 2024, needs more optimization.
32 621 0.229543271117 Henry Cohn, 2024, needs more optimization.
32 622 0.229643716918 Henry Cohn, 2024, needs more optimization.
32 624 0.229743018969 Henry Cohn, 2024, needs more optimization.
32 625 0.230010543033 Henry Cohn, 2024, needs more optimization.
32 626 0.230276821171 Henry Cohn, 2024, needs more optimization.
32 627 0.230398006075 Henry Cohn, 2024, needs more optimization.
32 630 0.230414007155 Henry Cohn, 2024, needs more optimization.
32 631 0.230874286768 Henry Cohn, 2024, needs more optimization.
32 632 0.230955137435 Henry Cohn, 2024, needs more optimization.
32 633 0.231063778240 Henry Cohn, 2024, needs more optimization.
32 634 0.231115528761 Henry Cohn, 2024, needs more optimization.
32 635 0.231173539000 Henry Cohn, 2024, needs more optimization.
32 637 0.231327189794 Henry Cohn, 2024, needs more optimization.
32 638 0.231602000144 Henry Cohn, 2024, needs more optimization.
32 639 0.231708329111 Henry Cohn, 2024, needs more optimization.
32 640 0.231725087010 Henry Cohn, 2024, needs more optimization.
32 641 0.231965832368 Henry Cohn, 2024, needs more optimization.
32 642 0.232019278003 Henry Cohn, 2024, needs more optimization.
32 643 0.232200607314 Henry Cohn, 2024, needs more optimization.
32 644 0.232220466778 Henry Cohn, 2024, needs more optimization.
32 645 0.232466119406 Henry Cohn, 2024, needs more optimization.
32 646 0.232477010644 Henry Cohn, 2024, needs more optimization.
32 647 0.232737594620 Henry Cohn, 2024, needs more optimization.
32 648 0.232860114596 Henry Cohn, 2024, needs more optimization.
32 649 0.233001037835 Henry Cohn, 2024, needs more optimization.
32 651 0.233149800556 Henry Cohn, 2024, needs more optimization.
32 653 0.233310915510 Henry Cohn, 2024, needs more optimization.
32 654 0.233653076205 Henry Cohn, 2024, needs more optimization.
32 655 0.233711312428 Henry Cohn, 2024, needs more optimization.
32 656 0.233817869919 Henry Cohn, 2024, needs more optimization.
32 658 0.233827008703 Henry Cohn, 2024, needs more optimization.
32 660 0.234070735964 Henry Cohn, 2024, needs more optimization.
32 662 0.234359409527 Henry Cohn, 2024, needs more optimization.
32 663 0.234579746250 Henry Cohn, 2024, needs more optimization.
32 664 0.234608187710 Henry Cohn, 2024, needs more optimization.
32 665 0.234760088565 Henry Cohn, 2024, needs more optimization.
32 667 0.234877362071 Henry Cohn, 2024, needs more optimization.
32 668 0.235086576280 Henry Cohn, 2024, needs more optimization.
32 669 0.235271321100 Henry Cohn, 2024, needs more optimization.
32 671 0.235325125936 Henry Cohn, 2024, needs more optimization.
32 674 0.235582431971 Henry Cohn, 2024, needs more optimization.
32 675 0.235907901840 Henry Cohn, 2024, needs more optimization.
32 676 0.236079612447 Henry Cohn, 2024, needs more optimization.
32 679 0.236205073654 Henry Cohn, 2024, needs more optimization.
32 680 0.236511952690 Henry Cohn, 2024, needs more optimization.
32 681 0.236618858426 Henry Cohn, 2024, needs more optimization.
32 683 0.236660033823 Henry Cohn, 2024, needs more optimization.
32 685 0.236930200851 Henry Cohn, 2024, needs more optimization.
32 686 0.237164162830 Henry Cohn, 2024, needs more optimization.
32 688 0.237224391860 Henry Cohn, 2024, needs more optimization.
32 689 0.237506330706 Henry Cohn, 2024, needs more optimization.
32 690 0.237546588911 Henry Cohn, 2024, needs more optimization.
32 691 0.237560397073 Henry Cohn, 2024, needs more optimization.
32 692 0.237763744467 Henry Cohn, 2024, needs more optimization.
32 694 0.237882714131 Henry Cohn, 2024, needs more optimization.
32 695 0.238132995067 Henry Cohn, 2024, needs more optimization.
32 696 0.238242653253 Henry Cohn, 2024, needs more optimization.
32 697 0.238401323196 Henry Cohn, 2024, needs more optimization.
32 699 0.238508260038 Henry Cohn, 2024, needs more optimization.
32 700 0.238621085666 Henry Cohn, 2024, needs more optimization.
32 702 0.238729639573 Henry Cohn, 2024, needs more optimization.
32 703 0.238944253145 Henry Cohn, 2024, needs more optimization.
32 704 0.239034485380 Henry Cohn, 2024, needs more optimization.
32 706 0.239086590603 Henry Cohn, 2024, needs more optimization.
32 707 0.239383976627 Henry Cohn, 2024, needs more optimization.
32 708 0.239651219167 Henry Cohn, 2024, needs more optimization.
32 710 0.239703630321 Henry Cohn, 2024, needs more optimization.
32 711 0.239823017120 Henry Cohn, 2024, needs more optimization.
32 712 0.239832371417 Henry Cohn, 2024, needs more optimization.
32 713 0.239914071378 Henry Cohn, 2024, needs more optimization.
32 714 0.240131973793 Henry Cohn, 2024, needs more optimization.
32 716 0.240311271168 Henry Cohn, 2024, needs more optimization.
32 717 0.240422040886 Henry Cohn, 2024, needs more optimization.
32 719 0.240530548729 Henry Cohn, 2024, needs more optimization.
32 722 0.240714221732 Henry Cohn, 2024, needs more optimization.
32 723 0.240924821925 Henry Cohn, 2024, needs more optimization.
32 726 0.241309541637 Henry Cohn, 2024, needs more optimization.
32 727 0.241335311793 Henry Cohn, 2024, needs more optimization.
32 728 0.241573172596 Henry Cohn, 2024, needs more optimization.
32 730 0.241626040616 Henry Cohn, 2024, needs more optimization.
32 731 0.241763763371 Henry Cohn, 2024, needs more optimization.
32 732 0.241985462970 Henry Cohn, 2024, needs more optimization.
32 733 0.242159273832 Henry Cohn, 2024, needs more optimization.
32 734 0.242207853630 Henry Cohn, 2024, needs more optimization.
32 735 0.242234548904 Henry Cohn, 2024, needs more optimization.
32 736 0.242416624983 Henry Cohn, 2024, needs more optimization.
32 737 0.242442206405 Henry Cohn, 2024, needs more optimization.
32 738 0.242542266041 Henry Cohn, 2024, needs more optimization.
32 739 0.242550207806 Henry Cohn, 2024, needs more optimization.
32 740 0.242917564767 Henry Cohn, 2024, needs more optimization.
32 742 0.242983931499 Henry Cohn, 2024, needs more optimization.
32 743 0.243175017635 Henry Cohn, 2024, needs more optimization.
32 744 0.243264779107 Henry Cohn, 2024, needs more optimization.
32 745 0.243348599264 Henry Cohn, 2024, needs more optimization.
32 746 0.243426349353 Henry Cohn, 2024, needs more optimization.
32 747 0.243510298210 Henry Cohn, 2024, needs more optimization.
32 748 0.243630339390 Henry Cohn, 2024, needs more optimization.
32 749 0.243759096517 Henry Cohn, 2024, needs more optimization.
32 750 0.243806395535 Henry Cohn, 2024, needs more optimization.
32 753 0.243989175422 Henry Cohn, 2024, needs more optimization.
32 755 0.244233021542 Henry Cohn, 2024, needs more optimization.
32 756 0.244374760375 Henry Cohn, 2024, needs more optimization.
32 758 0.244536548396 Henry Cohn, 2024, needs more optimization.
32 759 0.244754660708 Henry Cohn, 2024, needs more optimization.
32 761 0.244779416441 Henry Cohn, 2024, needs more optimization.
32 762 0.245036211022 Henry Cohn, 2024, needs more optimization.
32 763 0.245046675385 Henry Cohn, 2024, needs more optimization.
32 764 0.245239450207 Henry Cohn, 2024, needs more optimization.
32 765 0.245323029408 Henry Cohn, 2024, needs more optimization.
32 766 0.245461141753 Henry Cohn, 2024, needs more optimization.
32 768 0.245528148444 Henry Cohn, 2024, needs more optimization.
32 769 0.245832350925 Henry Cohn, 2024, needs more optimization.
32 771 0.245992234661 Henry Cohn, 2024, needs more optimization.
32 772 0.246017888762 Henry Cohn, 2024, needs more optimization.
32 775 0.246169811170 Henry Cohn, 2024, needs more optimization.
32 776 0.246348094537 Henry Cohn, 2024, needs more optimization.
32 778 0.246443480635 Henry Cohn, 2024, needs more optimization.
32 779 0.246622137023 Henry Cohn, 2024, needs more optimization.
32 781 0.246794469325 Henry Cohn, 2024, needs more optimization.
32 782 0.246938403137 Henry Cohn, 2024, needs more optimization.
32 783 0.247153080286 Henry Cohn, 2024, needs more optimization.
32 785 0.247198093842 Henry Cohn, 2024, needs more optimization.
32 786 0.247350672419 Henry Cohn, 2024, needs more optimization.
32 787 0.247449607206 Henry Cohn, 2024, needs more optimization.
32 788 0.247600455704 Henry Cohn, 2024, needs more optimization.
32 789 0.247626733138 Henry Cohn, 2024, needs more optimization.
32 790 0.247672493883 Henry Cohn, 2024, needs more optimization.
32 791 0.247829926400 Henry Cohn, 2024, needs more optimization.
32 792 0.247878036947 Henry Cohn, 2024, needs more optimization.
32 794 0.248074371391 Henry Cohn, 2024, needs more optimization.
32 796 0.248355864681 Henry Cohn, 2024, needs more optimization.
32 798 0.248391606992 Henry Cohn, 2024, needs more optimization.
32 799 0.248617693419 Henry Cohn, 2024, needs more optimization.
32 800 0.248618297797 Henry Cohn, 2024, needs more optimization.
32 801 0.248793062410 Henry Cohn, 2024, needs more optimization.
32 802 0.248957011510 Henry Cohn, 2024, needs more optimization.
32 804 0.248986295366 Henry Cohn, 2024, needs more optimization.
32 805 0.249169284511 Henry Cohn, 2024, needs more optimization.
32 806 0.249223193768 Henry Cohn, 2024, needs more optimization.
32 807 0.249339533418 Henry Cohn, 2024, needs more optimization.
32 808 0.249460854730 Henry Cohn, 2024, needs more optimization.
32 810 0.249627048848 Henry Cohn, 2024, needs more optimization.
32 811 0.249725919156 Henry Cohn, 2024, needs more optimization.
32 812 0.249847291662 Henry Cohn, 2024, needs more optimization.
32 814 0.249886159826 Henry Cohn, 2024, needs more optimization.
32 949 0.25 Orthogonal union of 891 points in 22 dimensions and 58 points in 10 dimensions.
4⁢x−1
32 950 0.253695768464 Orthogonal union of 891 points in 22 dimensions and 59 points in 10 dimensions.
32 951 0.256704396577 Orthogonal union of 891 points in 22 dimensions and 60 points in 10 dimensions.
32 952 0.258835264721 Orthogonal union of 891 points in 22 dimensions and 61 points in 10 dimensions.
32 954 0.261614645855 Henry Cohn, 2024, needs more optimization.
32 956 0.261648609109 Henry Cohn, 2024, needs more optimization.
32 957 0.261722453430 Henry Cohn, 2024, needs more optimization.
32 958 0.261863360736 Henry Cohn, 2024, needs more optimization.
32 960 0.261957631744 Henry Cohn, 2024, needs more optimization.
32 964 0.262226900961 Henry Cohn, 2024, needs more optimization.
32 965 0.262479775898 Henry Cohn, 2024, needs more optimization.
32 966 0.262539361811 Henry Cohn, 2024, needs more optimization.
32 967 0.262571836689 Henry Cohn, 2024, needs more optimization.
32 968 0.262652075423 Henry Cohn, 2024, needs more optimization.
32 970 0.262681528501 Henry Cohn, 2024, needs more optimization.
32 972 0.262879195145 Henry Cohn, 2024, needs more optimization.
32 975 0.263086534847 Henry Cohn, 2024, needs more optimization.
32 976 0.263225581849 Henry Cohn, 2024, needs more optimization.
32 979 0.263412817593 Henry Cohn, 2024, needs more optimization.
32 980 0.263570906780 Henry Cohn, 2024, needs more optimization.
32 981 0.263657928488 Henry Cohn, 2024, needs more optimization.
32 982 0.263781281716 Henry Cohn, 2024, needs more optimization.
32 984 0.263801504788 Henry Cohn, 2024, needs more optimization.
32 985 0.263910835391 Henry Cohn, 2024, needs more optimization.
32 986 0.264022219225 Henry Cohn, 2024, needs more optimization.
32 990 0.264132644245 Henry Cohn, 2024, needs more optimization.
32 992 0.264399670163 Henry Cohn, 2024, needs more optimization.
32 993 0.264473833538 Henry Cohn, 2024, needs more optimization.
32 994 0.264539495170 Henry Cohn, 2024, needs more optimization.
32 996 0.264546329404 Henry Cohn, 2024, needs more optimization.
32 997 0.264810116407 Henry Cohn, 2024, needs more optimization.
32 998 0.264873043701 Henry Cohn, 2024, needs more optimization.
32 1000 0.264875047324 Henry Cohn, 2024, needs more optimization.
32 1001 0.265007880035 Henry Cohn, 2024, needs more optimization.
32 1002 0.265083384539 Henry Cohn, 2024, needs more optimization.
32 1004 0.265293807842 Henry Cohn, 2024, needs more optimization.
32 1006 0.265379488959 Henry Cohn, 2024, needs more optimization.
32 1007 0.265387978983 Henry Cohn, 2024, needs more optimization.
32 1009 0.265508410278 Henry Cohn, 2024, needs more optimization.
32 1010 0.265667921371 Henry Cohn, 2024, needs more optimization.
32 1012 0.265679829911 Henry Cohn, 2024, needs more optimization.
32 1013 0.265946496377 Henry Cohn, 2024, needs more optimization.
32 1014 0.265995968496 Henry Cohn, 2024, needs more optimization.
32 1015 0.266059925491 Henry Cohn, 2024, needs more optimization.
32 1017 0.266101218859 Henry Cohn, 2024, needs more optimization.
32 1018 0.266287053678 Henry Cohn, 2024, needs more optimization.
32 1019 0.266339914714 Henry Cohn, 2024, needs more optimization.
32 1022 0.266358533949 Henry Cohn, 2024, needs more optimization.
32 1024 0.266505957750 Henry Cohn, 2024, needs more optimization.
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