The sphere packing problem in dimension 8

TL;DR

This paper proves that the densest way to pack equal-sized spheres in 8-dimensional space is achieved by the $E_8$-lattice, establishing it as the optimal packing configuration.

Contribution

It provides a rigorous proof that the $E_8$-lattice packing is the densest sphere packing in 8 dimensions, resolving a long-standing mathematical conjecture.

Findings

$E_8$-lattice achieves maximal packing density in 8D

No other packing surpasses the $E_8$-lattice density

Confirms the optimality of the $E_8$-lattice in sphere packing

Abstract

In this paper we prove that no packing of unit balls in Euclidean space $\mathbb{R}^8$ has density greater than that of the $E_8$-lattice packing.