Preprint series: 03-32 , Preprints

MSC:

52C07 Lattices and convex bodies in $n$ dimensions, See Also {11H06, 11H31, 11P21}

11H31 Lattice packing and covering, See also {05B40, 52C15, 52C17}

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

Upload: 2003-08-29-08-29