Year: 2026
Type: preprint
Abstract: Among lattices normalized to have packing radius one, the known shallowest depths of the deep holes in $7$-, $8$-, $9$- and $10$-dimensional lattices are $\sqrt{7/3}$, $\sqrt2$, $\sqrt{5/2}$ and $\sqrt{8/3}$, given by $E_7^*$, $E_8$, the laminated lattices $Λ_9$ and $Λ_{10}$, respectively. This paper presents new lattices in these dimensions with shallower deep holes. It also answers two problems of J. Martinet about short representatives of the classes of $Λ/2Λ$ in $7,8,9,10$ and $12$ dimensions.
Source: arXiv (Cornell University)
Authors: Li, Yiming, Zong, Chuanming
Institution: Tianjin University
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Awards: G2245778657, G4800798109
OpenAlex ID: W7214051699