Improved kissing numbers in seventeen through twenty-one dimensions

TL;DR

This paper improves the known lower bounds for kissing numbers in dimensions 17 to 21 by constructing new sphere packings that surpass previous records, using a novel sign modification technique rather than Leech lattice cross sections.

Contribution

The authors introduce a new method of modifying lattice vectors to construct larger sphere packings, improving the lower bounds of kissing numbers in multiple dimensions.

Findings

Kissing number in 17D is at least 5730

Kissing number in 18D is at least 7654

Kissing number in 19D is at least 11692

Abstract

We prove that the kissing numbers in 17, 18, 19, 20, and 21 dimensions are at least 5730, 7654, 11692, 19448, and 29768, respectively. The previous records were set by Leech in 1967, and we improve on them by 384, 256, 1024, 2048, and 2048. Unlike the previous constructions, the new configurations are not cross sections of the Leech lattice minimal vectors. Instead, they are constructed by modifying the signs in the lattice vectors to open up more space for additional spheres.