Zurück zu den Preprints des Jahres 2003

by Henk, M..

Series: 2003-32, Preprints

MSC:

52C07 Lattices and convex bodies in $n$ dimensions

11H31 Lattice packing and covering

Abstract:
We show that for every lattice packing of $n$-dimensional spheres there exists an $(n/\log_2(n))$-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.

Keywords:
sphere packings, lattice, covering radii