PreprintCC BY 4.0arXiv
Improved lattice-packing bounds in small dimensions
Abstract
We strengthen the upper bound on the density of a lattice packing in small dimensions. A lattice cannot have too many short vectors; we modify the Cohn--Elkies linear program accordingly by allowing the auxiliary function to be positive on a short interval beyond the minimum distance. For 11 ≤ n ≤ 16, our bound is tighter than the three-point bound of Cohn, de Laat and Salmon. For n ∈ [17, 23] ∪ [25, 40] ∪ [43, 57] ∪ [62, 75]∪ [83, 91], our bound lies below the published numerical values of the Cohn--Elkies bound.
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BibTeX
@misc{zubrilina2026improved,
title = {{Improved lattice-packing bounds in small dimensions}},
author = {Nina Zubrilina},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.35830},
eprint = {2610.35830},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.35830},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Improved lattice-packing bounds in small dimensions
AU - Nina Zubrilina
PY - 2026
DA - 2026/10/26
PB - arXiv
DO - 10.48550/arxiv.2610.35830
UR - https://arxiv.org/abs/2610.35830
AB - We strengthen the upper bound on the density of a lattice packing in small dimensions. A lattice cannot have too many short vectors; we modify the Cohn--Elkies linear program accordingly by allowing the auxiliary function to be positive on a short interval beyond the minimum distance. For 11 ≤ n ≤ 16, our bound is tighter than the three-point bound of Cohn, de Laat and Salmon. For n ∈ [17, 23] ∪ [25, 40] ∪ [43, 57] ∪ [62, 75]∪ [83, 91], our bound lies below the published numerical values of the Cohn--Elkies bound.
ER -