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Publication Date:
July 2005
ISSN:
1615-7168
DOI:
10.1515/advg.2005.5.1.137

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Advances in Geometry

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Free Planes in Lattice Sphere Packings

Martin Henk

Citation Information: Advances in Geometry. Volume 5, Issue 1, Pages 137–144, ISSN (Online) 1615-7168, ISSN (Print) 1615-715X, DOI: 10.1515/advg.2005.5.1.137, July 2005

Publication History:
Received:
6 October, 2003
Revised:
12 February, 2004
Published Online:
2005-07-27

Abstract

We show that for every lattice packing of n-dimensional spheres there exists an (n/log2(n))-dimensional affine plane which does not meet any of the spheres in their interior, provided n is large enough. Such an affine plane is called a free plane and our result improves on former bounds.

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