On kissing numbers and spherical codes in high dimensions

TL;DR

This paper establishes improved lower bounds on kissing numbers and spherical codes in high dimensions, advancing understanding of sphere packings and code sizes with a significant linear factor enhancement.

Contribution

It provides a new lower bound for kissing numbers and spherical codes that surpasses previous bounds by a linear factor in the dimension.

Findings

Lower bound on kissing number: ^{3/2} imes (2/\u221a{3})^d

Improved lower bound on spherical codes with acute angle 

Linear factor enhancement over classical bounds

Abstract

We prove a lower bound of $\Omega (d^{3/2} \cdot (2/\sqrt{3})^d)$ on the kissing number in dimension $d$. This improves the classical lower bound of Chabauty, Shannon, and Wyner by a linear factor in the dimension. We obtain a similar linear factor improvement to the best known lower bound on the maximal size of a spherical code of acute angle $\theta$ in high dimensions.