On the density of cyclotomic lattices constructed from codes

Abstract

Recently, Venkatesh improved the best known lower bound for lattice sphere packings by a factor $\log \log n$ for infinitely many dimensions $n$. Here we prove an effective version of this result, in the sense that we exhibit, for the same set of dimensions, finite families of lattices containing a lattice reaching this bound. Our construction uses codes over cyclotomic fields, lifted to lattices via Construction A.

References in corpus (1)

• Improved sphere packing lower bounds from Hurwitz lattices

Cited by in corpus (2)

• Generating dense packings of hard spheres by soft interaction design
• Coloring the Voronoi tessellation of lattices