Lattice Packings of Cross-polytopes Constructed from Sidon Sets

A family of lattice packings of $ n $-dimensional cross-polytopes ($ \ell_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^{ \Theta( \frac{ n }{ \ln n } ) } $ in the asymptotic regime $ n \to \infty $.