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A Lower Bound on the Density of Sphere Packings via Graph Theory
Using graph-theoretic methods we give a new proof that for all sufficiently
large , there exist sphere packings in of density at least
, exceeding the classical Minkowski bound by a factor linear in .
This matches up to a constant the best known lower bounds on the density of
sphere packings due to Rogers, Davenport-Rogers, and Ball. The suggested method
makes it possible to describe the points of such a packing with complexity
, which is significantly lower than in the other approaches.Comment: 6 pages, 2 postscript figure