Reposted by Ansgar Burchards
New record for density of sphere packings in ℝ^n. Pretty big breakthrough!
arxiv.org/abs/2504.05042
arxiv.org
Lattice packing of spheres in high dimensions using a stochastically evolving ellipsoid
We prove that in any dimension $n$ there exists an origin-symmetric ellipsoid ${\mathcal{E}} \subset {\mathbb{R}}^n$ of volume $ c n^2 $ that contains no points of ${\mathbb{Z}}^n$ other than the orig...