New lattice sphere packings denser than Mordell-Weil lattices

Abstract

1) We present new lattice sphere packings in Euclid spaces of many dimensions in the range 3332 − 4096, which are denser than known densest Mordell-Weil lattice sphere packings in these dimensions. Moreover it is proved that if there were some nice linear binary codes we could construct lattices denser than Mordell-Weil lattices of the many dimensions in the range 128 − 3272.2) Lattice sphere packings of many dimensions in the range 4098 − 8232 better than present records are presented. Some new dense lattice sphere packings of moderate dimensions 84, 85, 86, 181 − 189 denser than any previously known sphere packings of these dimensions are also given.3) New lattices with densities at least 8 times of the densities of Craig lattices of the dimensions p−1, where p is a prime satisfying p−1 ≥ 1222, are constructed. Some of these lattices provide new record sphere packings.The construction is based on the analogues of Craig lattices.