On the constant in Klartag's theorem for lattice packings in high dimensions

Abstract

In 2025, Boaz Klartag proved that there exists a lattice sphere packing in ${\mathbb{R}}^n$ whose density is at least \[ c n^2 2^{-n}, \] where $c>0$ is an absolute constant. Our aim is to refine the analysis of Klartag's argument and to show that the constant can be taken as \[ c = \frac{1}{2e} - o(1), \qquad n\to\infty. \]

arXiv comment8 pages