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Further lattice packings in high dimensions

Published online by Cambridge University Press:  26 February 2010

A. Bos ,
J. H. Conway  and
N. J. A. Sloane
A. Bos
Affiliation:
Corporate ISA, N. V. Philips' Gloeilampenfabrieken, 5600 MD, Eindhoven, Netherlands
J. H. Conway
Affiliation:
Department of Pure Mathematics and Mathematical Statistics, University of Cambridge, Cambridge, CB2 1SB
N. J. A. Sloane
Affiliation:
Mathematics and Statistics Research Center, Bell Laboratories, Murray Hill, NJ 07974, U.S.A.
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Abstract

Barnes and Sloane recently described a “general construction” for lattice packings of equal spheres in Euclidean space. In the present paper we simplify and further generalize their construction, and make it suitable for iteration. As a result we obtain lattice packings in ℝm with density Δ satisfying , as m → ∞ where is the smallest value of k for which the k-th iterated logarithm of m is less than 1. These appear to be the densest lattices that have been explicitly constructed in high-dimensional space. New records are also established in a number of lower dimensions, beginning in dimension 96.

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Type
Research Article
Information
Mathematika , Volume 29 , Issue 2 , December 1982 , pp. 171 - 180
Copyright
Copyright © University College London 1982

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