New lower bounds for kissing numbers in dimensions 32-35 and 37-39
Abstract
We show that the kissing numbers in dimensions 32, 33, 34, 35, 37, 38 and 39 are at least 352320, 370240, 390980, 415308, 499816, 605322 and 768916, improving the previous bounds 347584, 364736, 384836, 409676, 498024, 591900 and 763668. Except in dimension 38, the configurations are those of Edel, Rains and Sloane with new binary constant-weight codes of weight 8 and minimum distance 8 in the middle layer; each additional word adds 128 points. In dimension 38 we add 6855 antipodal pairs of vectors of the second shell of the Leech lattice to the empty equator of Kravatskiy's 591612-point configuration, where 144 pairs were known; this is an independent set problem in a regular graph of degree 11178 on 8386560 vertices. The codes and lines were found by local search, and all configurations were checked pair by pair in exact integer arithmetic.
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BibTeX
@misc{lin2026lower,
title = {{New lower bounds for kissing numbers in dimensions 32-35 and 37-39}},
author = {Qihong Lin},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.03682},
eprint = {2611.03682},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.03682},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - New lower bounds for kissing numbers in dimensions 32-35 and 37-39
AU - Qihong Lin
PY - 2026
DA - 2026/11/01
PB - arXiv
DO - 10.48550/arxiv.2611.03682
UR - https://arxiv.org/abs/2611.03682
AB - We show that the kissing numbers in dimensions 32, 33, 34, 35, 37, 38 and 39 are at least 352320, 370240, 390980, 415308, 499816, 605322 and 768916, improving the previous bounds 347584, 364736, 384836, 409676, 498024, 591900 and 763668. Except in dimension 38, the configurations are those of Edel, Rains and Sloane with new binary constant-weight codes of weight 8 and minimum distance 8 in the middle layer; each additional word adds 128 points. In dimension 38 we add 6855 antipodal pairs of vectors of the second shell of the Leech lattice to the empty equator of Kravatskiy's 591612-point configuration, where 144 pairs were known; this is an independent set problem in a regular graph of degree 11178 on 8386560 vertices. The codes and lines were found by local search, and all configurations were checked pair by pair in exact integer arithmetic.
ER -