Lattices with exponentially large kissing numbers do exist

TL;DR

This paper revises a previous lattice construction claiming exponentially large kissing numbers, providing a corrected method that achieves similar results but with smaller constants, clarifying the theoretical understanding of lattice kissing numbers.

Contribution

It corrects and refines a prior lattice construction to establish the existence of lattices with large kissing numbers, addressing previous gaps in the argument.

Findings

Corrected lattice construction with large kissing numbers

Achieved similar results with smaller constants

Clarified theoretical bounds on lattice kissing numbers

Abstract

This note corrects the paper \cite{ex}, where lattice sequences having exponentially large kissing numbers were constructed. However it was noted in \cite{dif} that the arguments in that paper are not sufficient. Here we correct the construction which leads to similar results, albeit with much smaller constants.