PreprintCC BY-SA 4.0arXiv
A lattice family with kissing numbers τ(ℒn) ≥ e2 √n
Abstract
For all prime powers q≥5, we construct lattices ℒq⊆ℤq with kissing numbers τ(ℒq)≥ (1/2πe2+o(1))√q e2√q. The same asymptotic bound holds on a set of integer dimensions of natural density $1$, and in every sufficiently large integer dimension n with an additional factor e−1/2n1/40. The construction is an extension of a previous construction by Bennett-Peikert based on Reed-Solomon codes.
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BibTeX
@misc{laarhoven2026lattice,
title = {{A lattice family with kissing numbers $τ(\mathcalL_n) \ge e^2 \sqrtn$}},
author = {Thijs Laarhoven and Scott Duke Kominers},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2609.13608},
eprint = {2609.13608},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.13608},
note = {CC BY-SA 4.0},
}
RIS
TY - UNPB
TI - A lattice family with kissing numbers τ(ℒ_n) ≥ e^2 √n
AU - Thijs Laarhoven
AU - Scott Duke Kominers
PY - 2026
DA - 2026/10/01
PB - arXiv
DO - 10.48550/arxiv.2609.13608
UR - https://arxiv.org/abs/2609.13608
AB - For all prime powers q≥5, we construct lattices ℒ_q⊆ℤ^q with kissing numbers τ(ℒ_q)≥ (1/2πe^2+o(1))√q e^2√q. The same asymptotic bound holds on a set of integer dimensions of natural density $1$, and in every sufficiently large integer dimension n with an additional factor e^−1/2n^1/40. The construction is an extension of a previous construction by Bennett-Peikert based on Reed-Solomon codes.
ER -