Improved sphere packing lower bounds from Hurwitz lattices
type: Item
instance of: scholarly article
title: Improved sphere packing lower bounds from Hurwitz lattices
zbMATH Open document ID: 1228.11095
author: Stephanie Vance
published in: Advances in Mathematics
publication date: 2011-07-07T00:00:00Z
full work available at URL: https://arxiv.org/abs/1105.3779
review text: The lattice sphere packing density \(\delta _{n, L}\) measures the greatest proportion of \(\mathbb{R}^n\) that can be filled by non-overlapping open Euclidean balls of the same radii with centers at a lattice. The author improves the asymptotic lower bound for such a density in dimensions divisible by four, proving that \[ \delta _{4m, L} \geq \zeta (4m) \frac{24 m}{2^{4m} e (1-e^{-m})}. \] In the case \(n=4m\) this improves by a constant factor the bound \(\delta _{n, L} \geq 2 \zeta (n) (n-1) 2^{-n}\) proved by \textit{K.~Ball} [Int. Math. Res. Not. 1992, 217--221 (1992; Zbl 0776.52006)], who in turn improved the previously known estimate \(1.68 n 2^{-n}\) of \textit{H.~Davenport} and \textit{C. A.~Rogers} [Duke Math. J. 14, 367--375 (1947; Zbl 0030.34602)]. The new bound is proven using \((4m)\)-dimensional Hurwitz lattice sphere packings.
Mathematics Subject Classification ID: 11H31
Mathematics Subject Classification ID: 52C17
Mathematics Subject Classification ID: 05B40
Mathematics Subject Classification ID: 52C07
zbMATH DE Number: 5918260
zbMATH Keywords: lattice sphere packing
zbMATH Keywords: packing density
zbMATH Keywords: Hurwitz lattices
describes a project that uses: kepler98
MaRDI profile type: Publication
OpenAlex ID: W2008929884
arXiv ID: 1105.3779
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DOI: 10.1016/J.AIM.2011.04.016
description: scientific article