Improved sphere packing lower bounds from Hurwitz lattices

TL;DR

This paper establishes an improved asymptotic lower bound for sphere packing density in dimensions divisible by four, enhancing previous bounds for various lattice packings including Hurwitz lattices.

Contribution

It introduces a new asymptotic lower bound for sphere packing density in certain dimensions, specifically improving bounds for Hurwitz lattices.

Findings

Enhanced lower bounds for sphere packing density in dimensions divisible by four.

Improved bounds for lattice and Hurwitz lattice sphere packings.

Asymptotic bounds surpass previous results by a constant factor.

Abstract

In this paper we prove an asymptotic lower bound for the sphere packing density in dimensions divisible by four. This asymptotic lower bound improves on previous asymptotic bounds by a constant factor and improves not just lower bounds for the sphere packing density, but also for the lattice sphere packing density and, in fact, the Hurwitz lattice sphere packing density.