How densely can spheres be packed with moderate effort in high dimensions?

TL;DR

This paper explores sphere packing densities in high dimensions using a novel algorithm, suggesting potential improvements over classical bounds and revealing that higher densities are achievable with moderate effort.

Contribution

It introduces a geometrical constraint satisfaction algorithm to generate dense sphere packings in up to 22 dimensions, surpassing previous lower bounds.

Findings

Density can be doubled relative to Ball's lower bound.

Exponential decay rate of density may be improved beyond Minkowski's 1/2.

Dense packings are achievable with moderate computational effort.

Abstract

We generate non-lattice packings of spheres in up to 22 dimensions using the geometrical constraint satisfaction algorithm RRR. Our aggregated data suggest that it is easy to double the density of Ball's lower bound, and more tentatively, that the exponential decay rate of the density can be improved relative to Minkowski's longstanding 1/2.