On the density of cyclotomic lattices constructed from codes
Philippe Moustrou · International Journal of Number Theory · 2016
Recently, Venkatesh improved the best known lower bound for lattice sphere packings by a factor [Formula: see text] for infinitely many dimensions [Formula: see text]. 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. We also prove a similar result for families of symplectic lattices.