New lower bounds for kissing numbers in dimensions $25−−31$

@misc{takhanov2026lower,
  title = {{New lower bounds for kissing numbers in dimensions $25$--$31$}},
  author = {Rustem Takhanov and Stanislav Yun},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.21591},
  eprint = {2609.21591},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.21591},
}

TY  - UNPB
TI  - New lower bounds for kissing numbers in dimensions $25−−31$
AU  - Rustem Takhanov
AU  - Stanislav Yun
PY  - 2026
DA  - 2026/09/23
PB  - arXiv
DO  - 10.48550/arxiv.2609.21591
UR  - https://arxiv.org/abs/2609.21591
AB  - The kissing number in dimension d is the largest number of non-overlapping congruent spheres that can simultaneously touch a central sphere of the same size. We study dimensions $25−31$, where the best previous constructions are based on Leech lifting from the optimal kissing configuration in dimension $24$. Our method exploits the absence of contacts between the unlifted bulk and the block consisting of lifted and auxiliary vectors. Rotating this block while keeping the bulk fixed creates room for two antipodal points in dimensions $26$, $27$, and $28$, and one point in dimension $29$. Three further modifications yield improvements in dimensions $25$, $30$ and $31$: (a) a nonorthogonal diagonal linear deformation of the lifted block admits two antipodal points in dimension $25$; (b) rotating the additional coordinates of the lifted vectors and then applying a small orthogonal transformation to the resulting lifted block as a whole admits two antipodal points in dimension $30$; (c) rotating only the additional coordinates of the lifted vectors admits four nonantipodal points in dimension $31$. Together, these constructions yield the new lower bounds τ_25≥ 197058, τ_26≥ 198552, τ_27≥ 200046, τ_28≥ 204522, τ_29≥ 209497, τ_30≥ 220442, and τ_31≥ 238354.
ER  -