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Free planes in lattice sphere packings

by Henk, M..

Series: 2003-32, Preprints

52C07 Lattices and convex bodies in $n$ dimensions
11H31 Lattice packing and covering

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.

sphere packings, lattice, covering radii