A lower bound on packing density
If \(H\subseteq\mathbb{R}^n\) is a bounded, convex body which is symmetric through each of the coordinate hyperplanes, then there exist codes which give rise, via Construction A of Leech and Sloane to lattice-packings of H whose density \(\Delta\) satisfies the logarithmic Minkowski-Hlawka bound, \(\liminf_{n\to \infty}\log_2^n\sqrt{\Delta}\geq -1.\) This follows as a corollary of our main result, Theorem 9, a general way of obtaining lower bounds on the lattice-packing densities of various bodies. Unfortunately, when n is at all large, it is computationally prohibitive (although theoretically possible) to exhibit the arrangements explicitly.
scientific article; zbMATH DE number 4077342
scientific article