New Sphere Packings from the Antipode Construction

TL;DR

This paper introduces new non-lattice sphere packings in specific dimensions using the antipode construction, achieving record densities that outperform previous results.

Contribution

It presents the first application of the antipode method to construct record-breaking sphere packings in multiple dimensions.

Findings

Record-breaking densities in dimensions 19, 20, 21, 23, 44, 45, and 47.

Novel application of antipode construction to non-lattice packings.

Improved sphere packing densities over all previously known configurations.

Abstract

In this note, we construct non-lattice sphere packings in dimensions $19$, $20$, $21$, $23$, $44$, $45$, and $47$, demonstrating record densities that surpass all previously documented results in these dimensions. The construction involves applying the antipode method to suboptimal cross-sections of $\Lambda_{24}$ and $P_{48p}$ respectively in those dimensions.