On a generalization of Craig lattices

Abstract

In this paper we introduce generalized Craig lattices, which allows us to construct lattices in Euclidean spaces of many dimensions in the range 3332-4096 which are denser than the densest known Mordell-Weil lattices. Moreover we prove that if there were some nice linear binary codes we could construct lattices even denser in the range 128-3272. We also construct some dense lattices of dimensions in the range 4098-8232. Finally we also obtain some new lattices of moderate dimensions such as 68,84,85,86, which are denser than the previously known densest lattices.