On lattices equivalent to their duals
type: Item
instance of: scholarly article
title: On lattices equivalent to their duals
zbMATH Open document ID: 0810.11041
author: N. J. A. Sloane
author: J. H. Conway
published in: Journal of Number Theory
publication date: 1994-09-28T00:00:00Z
review text: The authors call a lattice in Euclidean \(n\)-space isodual if it is isometric to its dual. A lattice similar to its dual (e.g., any for \(n=2\)) can be rescaled to become isodual, and certain even lattices similar to their duals (interesting from the point of view of modular forms) hold the sphere packing records for \(n=4\), 8, 12, 16, 24, 32 and 48. The present paper, however, mainly deals with the case \(n=3\): using their version of the Selling parameters to describe cubic lattices, the authors find that a ``mean'' of the face-centered and body-centered cubic lattices (called the m.c.c. lattice) solves both the isodual packing and covering problems. The paper also lists the densest isodual lattices known for \(n= 5\), 6, 7, 9, 10, 11 and 14.
Mathematics Subject Classification ID: 11H31
Mathematics Subject Classification ID: 11H06
Mathematics Subject Classification ID: 52C07
zbMATH DE Number: 645305
zbMATH Keywords: isodual covering
zbMATH Keywords: Selling parameters
zbMATH Keywords: cubic lattices
zbMATH Keywords: isodual packing
zbMATH Keywords: densest isodual lattices
reviewed by: Heinz-Georg Quebbemann
MaRDI profile type: Publication
full work available at URL: jnth.1994.1073
OpenAlex ID: W2047689836
DOI: 10.1006/JNTH.1994.1073
description: scientific article; zbMATH DE number 645305