A lower bound on packing density
type: Item
instance of: scholarly article
title: A lower bound on packing density
zbMATH Open document ID: 0659.10033
DOI: 10.1007/BF01393834
author: J. A. Rush
published in: Inventiones Mathematicae
publication date: 1989-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/143740
review text: 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.
Mathematics Subject Classification ID: 11H31
Mathematics Subject Classification ID: 52C17
Mathematics Subject Classification ID: 11H06
zbMATH DE Number: 4077342
zbMATH Keywords: convex body
zbMATH Keywords: construction A
zbMATH Keywords: logarithmic Minkowski-Hlawka bound
zbMATH Keywords: lower bounds
zbMATH Keywords: lattice-packing densities
MaRDI profile type: Publication
cites work: Q5611106
cites work: Q4039784
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description: scientific article; zbMATH DE number 4077342