Lattice Packings of Cross-polytopes Constructed from Sidon Sets
share
A family of lattice packings of n-dimensional cross-polytopes (ℓ_1 balls) is constructed by using the notion of Sidon sets in finite Abelian groups. The resulting density exceeds that of any prior construction by a factor of at least 2^Θ( n /ln n ) in the asymptotic regime n →∞.
READ FULL TEXT