Dimension 32 Kissing number lower bound: 345408 This configuration is obtained using the construction by Edel, Rains, and Sloane (doi:10.37236/1360, arXiv:math/0207291), based on the following codes tabulated by Litsyn, Rains, and Sloane at https://www.eng.tau.ac.il/~litsyn/tableand/ and by Brouwer at https://www.win.tue.nl/~aeb/codes/Andw.html: Let C_(1,1) be a binary code of block length 32, minimal distance c_1 = 32, and constant weight 32 with 1 code word. Let C_(1,2) be a binary code of block length 32 and minimal distance 8 with 131072 code words. Let C_(2,1) be a binary code of block length 32, minimal distance c_2 = 8, and constant weight 8 with 1659 code words. Let C_(2,2) be a binary code of block length 8 and minimal distance 2 with 128 code words. Let C_(3,1) be a binary code of block length 32, minimal distance c_3 = 2, and constant weight 2 with 496 code words. Let C_(3,2) be a binary code of block length 2 and minimal distance 1 with 4 code words. Then the kissing configuration is the union over i = 0,1,2 of the 32-dimensional vectors with nonzero coordinates in the locations specified by C_(i,1), where the coordinates are all +-sqrt(c_1/c_i) with signs specified by C_(i,2). Dimension 33 Kissing number lower bound: 360640 This configuration is obtained using the construction by Edel, Rains, and Sloane (doi:10.37236/1360, arXiv:math/0207291), based on the following codes tabulated by Litsyn, Rains, and Sloane at https://www.eng.tau.ac.il/~litsyn/tableand/ and by Brouwer at https://www.win.tue.nl/~aeb/codes/Andw.html: Let C_(1,1) be a binary code of block length 33, minimal distance c_1 = 32, and constant weight 32 with 1 code word. Let C_(1,2) be a binary code of block length 32 and minimal distance 8 with 131072 code words. Let C_(2,1) be a binary code of block length 33, minimal distance c_2 = 8, and constant weight 8 with 1777 code words. Let C_(2,2) be a binary code of block length 8 and minimal distance 2 with 128 code words. Let C_(3,1) be a binary code of block length 33, minimal distance c_3 = 2, and constant weight 2 with 528 code words. Let C_(3,2) be a binary code of block length 2 and minimal distance 1 with 4 code words. Then the kissing configuration is the union over i = 0,1,2 of the 33-dimensional vectors with nonzero coordinates in the locations specified by C_(i,1), where the coordinates are all +-sqrt(c_1/c_i) with signs specified by C_(i,2). Dimension 34 Kissing number lower bound: 380868 This configuration is obtained using the construction by Edel, Rains, and Sloane (doi:10.37236/1360, arXiv:math/0207291), based on the following codes tabulated by Litsyn, Rains, and Sloane at https://www.eng.tau.ac.il/~litsyn/tableand/ and by Brouwer at https://www.win.tue.nl/~aeb/codes/Andw.html: Let C_(1,1) be a binary code of block length 34, minimal distance c_1 = 32, and constant weight 32 with 1 code word. Let C_(1,2) be a binary code of block length 32 and minimal distance 8 with 131072 code words. Let C_(2,1) be a binary code of block length 34, minimal distance c_2 = 8, and constant weight 8 with 1934 code words. Let C_(2,2) be a binary code of block length 8 and minimal distance 2 with 128 code words. Let C_(3,1) be a binary code of block length 34, minimal distance c_3 = 2, and constant weight 2 with 561 code words. Let C_(3,2) be a binary code of block length 2 and minimal distance 1 with 4 code words. Then the kissing configuration is the union over i = 0,1,2 of the 34-dimensional vectors with nonzero coordinates in the locations specified by C_(i,1), where the coordinates are all +-sqrt(c_1/c_i) with signs specified by C_(i,2). Dimension 35 Kissing number lower bound: 409548 This configuration is obtained using the construction by Edel, Rains, and Sloane (doi:10.37236/1360, arXiv:math/0207291), based on the following codes tabulated by Litsyn, Rains, and Sloane at https://www.eng.tau.ac.il/~litsyn/tableand/ and by Brouwer at https://www.win.tue.nl/~aeb/codes/Andw.html: Let C_(1,1) be a binary code of block length 35, minimal distance c_1 = 32, and constant weight 32 with 1 code word. Let C_(1,2) be a binary code of block length 32 and minimal distance 8 with 131072 code words. Let C_(2,1) be a binary code of block length 35, minimal distance c_2 = 8, and constant weight 8 with 2157 code words. Let C_(2,2) be a binary code of block length 8 and minimal distance 2 with 128 code words. Let C_(3,1) be a binary code of block length 35, minimal distance c_3 = 2, and constant weight 2 with 595 code words. Let C_(3,2) be a binary code of block length 2 and minimal distance 1 with 4 code words. Then the kissing configuration is the union over i = 0,1,2 of the 35-dimensional vectors with nonzero coordinates in the locations specified by C_(i,1), where the coordinates are all +-sqrt(c_1/c_i) with signs specified by C_(i,2). Dimension 36 Kissing number lower bound: 484568 This configuration is obtained using the construction by Edel, Rains, and Sloane (doi:10.37236/1360, arXiv:math/0207291), based on the following codes tabulated by Litsyn, Rains, and Sloane at https://www.eng.tau.ac.il/~litsyn/tableand/ and by Brouwer at https://www.win.tue.nl/~aeb/codes/Andw.html: Let C_(1,1) be a binary code of block length 36, minimal distance c_1 = 32, and constant weight 32 with 1 code word. Let C_(1,2) be a binary code of block length 32 and minimal distance 8 with 131072 code words. Let C_(2,1) be a binary code of block length 36, minimal distance c_2 = 8, and constant weight 8 with 2742 code words. Let C_(2,2) be a binary code of block length 8 and minimal distance 2 with 128 code words. Let C_(3,1) be a binary code of block length 36, minimal distance c_3 = 2, and constant weight 2 with 630 code words. Let C_(3,2) be a binary code of block length 2 and minimal distance 1 with 4 code words. Then the kissing configuration is the union over i = 0,1,2 of the 36-dimensional vectors with nonzero coordinates in the locations specified by C_(i,1), where the coordinates are all +-sqrt(c_1/c_i) with signs specified by C_(i,2). Dimension 37 Kissing number lower bound: 494312 This configuration is obtained using the construction by Edel, Rains, and Sloane (doi:10.37236/1360, arXiv:math/0207291), based on the following codes tabulated by Litsyn, Rains, and Sloane at https://www.eng.tau.ac.il/~litsyn/tableand/ and by Brouwer at https://www.win.tue.nl/~aeb/codes/Andw.html: Let C_(1,1) be a binary code of block length 37, minimal distance c_1 = 32, and constant weight 32 with 1 code word. Let C_(1,2) be a binary code of block length 32 and minimal distance 8 with 131072 code words. Let C_(2,1) be a binary code of block length 37, minimal distance c_2 = 8, and constant weight 8 with 2817 code words. Let C_(2,2) be a binary code of block length 8 and minimal distance 2 with 128 code words. Let C_(3,1) be a binary code of block length 37, minimal distance c_3 = 2, and constant weight 2 with 666 code words. Let C_(3,2) be a binary code of block length 2 and minimal distance 1 with 4 code words. Then the kissing configuration is the union over i = 0,1,2 of the 37-dimensional vectors with nonzero coordinates in the locations specified by C_(i,1), where the coordinates are all +-sqrt(c_1/c_i) with signs specified by C_(i,2). Dimension 38 Kissing number lower bound: 566652 This configuration is obtained using the construction by Edel, Rains, and Sloane (doi:10.37236/1360, arXiv:math/0207291), based on the following codes tabulated by Litsyn, Rains, and Sloane at https://www.eng.tau.ac.il/~litsyn/tableand/ and by Brouwer at https://www.win.tue.nl/~aeb/codes/Andw.html: Let C_(1,1) be a binary code of block length 38, minimal distance c_1 = 38, and constant weight 38 with 1 code word. Let C_(1,2) be a binary code of block length 38 and minimal distance 10 with 180224 code words. Let C_(2,1) be a binary code of block length 38, minimal distance c_2 = 8, and constant weight 8 with 2997 code words. Let C_(2,2) be a binary code of block length 8 and minimal distance 2 with 128 code words. Let C_(3,1) be a binary code of block length 38, minimal distance c_3 = 2, and constant weight 2 with 703 code words. Let C_(3,2) be a binary code of block length 2 and minimal distance 1 with 4 code words. Then the kissing configuration is the union over i = 0,1,2 of the 38-dimensional vectors with nonzero coordinates in the locations specified by C_(i,1), where the coordinates are all +-sqrt(c_1/c_i) with signs specified by C_(i,2). Dimension 39 Kissing number lower bound: 755988 This configuration is obtained using the construction by Edel, Rains, and Sloane (doi:10.37236/1360, arXiv:math/0207291), based on the following codes tabulated by Litsyn, Rains, and Sloane at https://www.eng.tau.ac.il/~litsyn/tableand/ and by Brouwer at https://www.win.tue.nl/~aeb/codes/Andw.html: Let C_(1,1) be a binary code of block length 39, minimal distance c_1 = 39, and constant weight 39 with 1 code word. Let C_(1,2) be a binary code of block length 39 and minimal distance 10 with 327680 code words. Let C_(2,1) be a binary code of block length 39, minimal distance c_2 = 8, and constant weight 8 with 3323 code words. Let C_(2,2) be a binary code of block length 8 and minimal distance 2 with 128 code words. Let C_(3,1) be a binary code of block length 39, minimal distance c_3 = 2, and constant weight 2 with 741 code words. Let C_(3,2) be a binary code of block length 2 and minimal distance 1 with 4 code words. Then the kissing configuration is the union over i = 0,1,2 of the 39-dimensional vectors with nonzero coordinates in the locations specified by C_(i,1), where the coordinates are all +-sqrt(c_1/c_i) with signs specified by C_(i,2). Dimension 40 Kissing number lower bound: 1064368 This configuration is obtained using the construction by Edel, Rains, and Sloane (doi:10.37236/1360, arXiv:math/0207291), based on the following codes tabulated by Litsyn, Rains, and Sloane at https://www.eng.tau.ac.il/~litsyn/tableand/ and by Brouwer at https://www.win.tue.nl/~aeb/codes/Andw.html: Let C_(1,1) be a binary code of block length 40, minimal distance c_1 = 40, and constant weight 40 with 1 code word. Let C_(1,2) be a binary code of block length 40 and minimal distance 10 with 589824 code words. Let C_(2,1) be a binary code of block length 40, minimal distance c_2 = 8, and constant weight 8 with 3683 code words. Let C_(2,2) be a binary code of block length 8 and minimal distance 2 with 128 code words. Let C_(3,1) be a binary code of block length 40, minimal distance c_3 = 2, and constant weight 2 with 780 code words. Let C_(3,2) be a binary code of block length 2 and minimal distance 1 with 4 code words. Then the kissing configuration is the union over i = 0,1,2 of the 40-dimensional vectors with nonzero coordinates in the locations specified by C_(i,1), where the coordinates are all +-sqrt(c_1/c_i) with signs specified by C_(i,2). Dimension 41 Kissing number lower bound: 1170384 This configuration is obtained using the construction by Edel, Rains, and Sloane (doi:10.37236/1360, arXiv:math/0207291), based on the following codes tabulated by Litsyn, Rains, and Sloane at https://www.eng.tau.ac.il/~litsyn/tableand/ and by Brouwer at https://www.win.tue.nl/~aeb/codes/Andw.html: Let C_(1,1) be a binary code of block length 41, minimal distance c_1 = 40, and constant weight 40 with 1 code word. Let C_(1,2) be a binary code of block length 40 and minimal distance 10 with 589824 code words. Let C_(2,1) be a binary code of block length 41, minimal distance c_2 = 8, and constant weight 8 with 4510 code words. Let C_(2,2) be a binary code of block length 8 and minimal distance 2 with 128 code words. Let C_(3,1) be a binary code of block length 41, minimal distance c_3 = 2, and constant weight 2 with 820 code words. Let C_(3,2) be a binary code of block length 2 and minimal distance 1 with 4 code words. Then the kissing configuration is the union over i = 0,1,2 of the 41-dimensional vectors with nonzero coordinates in the locations specified by C_(i,1), where the coordinates are all +-sqrt(c_1/c_i) with signs specified by C_(i,2). Dimension 42 Kissing number lower bound: 1250676 This configuration is obtained using the construction by Edel, Rains, and Sloane (doi:10.37236/1360, arXiv:math/0207291), based on the following codes tabulated by Litsyn, Rains, and Sloane at https://www.eng.tau.ac.il/~litsyn/tableand/ and by Brouwer at https://www.win.tue.nl/~aeb/codes/Andw.html: Let C_(1,1) be a binary code of block length 42, minimal distance c_1 = 40, and constant weight 40 with 1 code word. Let C_(1,2) be a binary code of block length 40 and minimal distance 10 with 589824 code words. Let C_(2,1) be a binary code of block length 42, minimal distance c_2 = 8, and constant weight 8 with 5136 code words. Let C_(2,2) be a binary code of block length 8 and minimal distance 2 with 128 code words. Let C_(3,1) be a binary code of block length 42, minimal distance c_3 = 2, and constant weight 2 with 861 code words. Let C_(3,2) be a binary code of block length 2 and minimal distance 1 with 4 code words. Then the kissing configuration is the union over i = 0,1,2 of the 42-dimensional vectors with nonzero coordinates in the locations specified by C_(i,1), where the coordinates are all +-sqrt(c_1/c_i) with signs specified by C_(i,2). Dimension 43 Kissing number lower bound: 1745692 This configuration is obtained using the construction by Edel, Rains, and Sloane (doi:10.37236/1360, arXiv:math/0207291), based on the following codes tabulated by Litsyn, Rains, and Sloane at https://www.eng.tau.ac.il/~litsyn/tableand/ and by Brouwer at https://www.win.tue.nl/~aeb/codes/Andw.html: Let C_(1,1) be a binary code of block length 43, minimal distance c_1 = 43, and constant weight 43 with 1 code word. Let C_(1,2) be a binary code of block length 43 and minimal distance 11 with 1048576 code words. Let C_(2,1) be a binary code of block length 43, minimal distance c_2 = 8, and constant weight 8 with 5418 code words. Let C_(2,2) be a binary code of block length 8 and minimal distance 2 with 128 code words. Let C_(3,1) be a binary code of block length 43, minimal distance c_3 = 2, and constant weight 2 with 903 code words. Let C_(3,2) be a binary code of block length 2 and minimal distance 1 with 4 code words. Then the kissing configuration is the union over i = 0,1,2 of the 43-dimensional vectors with nonzero coordinates in the locations specified by C_(i,1), where the coordinates are all +-sqrt(c_1/c_i) with signs specified by C_(i,2). Dimension 44 Kissing number lower bound: 2948552 This configuration is obtained using the construction by Edel, Rains, and Sloane (doi:10.37236/1360, arXiv:math/0207291), based on the following codes tabulated by Litsyn, Rains, and Sloane at https://www.eng.tau.ac.il/~litsyn/tableand/ and by Brouwer at https://www.win.tue.nl/~aeb/codes/Andw.html: Let C_(1,1) be a binary code of block length 44, minimal distance c_1 = 44, and constant weight 44 with 1 code word. Let C_(1,2) be a binary code of block length 44 and minimal distance 11 with 2097152 code words. Let C_(2,1) be a binary code of block length 44, minimal distance c_2 = 8, and constant weight 8 with 6622 code words. Let C_(2,2) be a binary code of block length 8 and minimal distance 2 with 128 code words. Let C_(3,1) be a binary code of block length 44, minimal distance c_3 = 2, and constant weight 2 with 946 code words. Let C_(3,2) be a binary code of block length 2 and minimal distance 1 with 4 code words. Then the kissing configuration is the union over i = 0,1,2 of the 44-dimensional vectors with nonzero coordinates in the locations specified by C_(i,1), where the coordinates are all +-sqrt(c_1/c_i) with signs specified by C_(i,2). Dimension 45 Kissing number lower bound: 3047160 This configuration is obtained using the construction by Edel, Rains, and Sloane (doi:10.37236/1360, arXiv:math/0207291), based on the following codes tabulated by Litsyn, Rains, and Sloane at https://www.eng.tau.ac.il/~litsyn/tableand/ and by Brouwer at https://www.win.tue.nl/~aeb/codes/Andw.html: Let C_(1,1) be a binary code of block length 45, minimal distance c_1 = 44, and constant weight 44 with 1 code word. Let C_(1,2) be a binary code of block length 44 and minimal distance 11 with 2097152 code words. Let C_(2,1) be a binary code of block length 45, minimal distance c_2 = 8, and constant weight 8 with 7391 code words. Let C_(2,2) be a binary code of block length 8 and minimal distance 2 with 128 code words. Let C_(3,1) be a binary code of block length 45, minimal distance c_3 = 2, and constant weight 2 with 990 code words. Let C_(3,2) be a binary code of block length 2 and minimal distance 1 with 4 code words. Then the kissing configuration is the union over i = 0,1,2 of the 45-dimensional vectors with nonzero coordinates in the locations specified by C_(i,1), where the coordinates are all +-sqrt(c_1/c_i) with signs specified by C_(i,2). Dimension 46 Kissing number lower bound: 5318060 This configuration is obtained using the construction by Edel, Rains, and Sloane (doi:10.37236/1360, arXiv:math/0207291), based on the following codes tabulated by Litsyn, Rains, and Sloane at https://www.eng.tau.ac.il/~litsyn/tableand/ and by Brouwer at https://www.win.tue.nl/~aeb/codes/Andw.html: Let C_(1,1) be a binary code of block length 46, minimal distance c_1 = 46, and constant weight 46 with 1 code word. Let C_(1,2) be a binary code of block length 46 and minimal distance 12 with 4194304 code words. Let C_(2,1) be a binary code of block length 46, minimal distance c_2 = 8, and constant weight 8 with 8747 code words. Let C_(2,2) be a binary code of block length 8 and minimal distance 2 with 128 code words. Let C_(3,1) be a binary code of block length 46, minimal distance c_3 = 2, and constant weight 2 with 1035 code words. Let C_(3,2) be a binary code of block length 2 and minimal distance 1 with 4 code words. Then the kissing configuration is the union over i = 0,1,2 of the 46-dimensional vectors with nonzero coordinates in the locations specified by C_(i,1), where the coordinates are all +-sqrt(c_1/c_i) with signs specified by C_(i,2). Dimension 47 Kissing number lower bound: 9741412 This configuration is obtained using the construction by Edel, Rains, and Sloane (doi:10.37236/1360, arXiv:math/0207291), based on the following codes tabulated by Litsyn, Rains, and Sloane at https://www.eng.tau.ac.il/~litsyn/tableand/ and by Brouwer at https://www.win.tue.nl/~aeb/codes/Andw.html: Let C_(1,1) be a binary code of block length 47, minimal distance c_1 = 47, and constant weight 47 with 1 code word. Let C_(1,2) be a binary code of block length 47 and minimal distance 12 with 8388608 code words. Let C_(2,1) be a binary code of block length 47, minimal distance c_2 = 8, and constant weight 8 with 10535 code words. Let C_(2,2) be a binary code of block length 8 and minimal distance 2 with 128 code words. Let C_(3,1) be a binary code of block length 47, minimal distance c_3 = 2, and constant weight 2 with 1081 code words. Let C_(3,2) be a binary code of block length 2 and minimal distance 1 with 4 code words. Then the kissing configuration is the union over i = 0,1,2 of the 47-dimensional vectors with nonzero coordinates in the locations specified by C_(i,1), where the coordinates are all +-sqrt(c_1/c_i) with signs specified by C_(i,2).