Two matrix-based lattice construction techniques - Carmelo Interlando, J.; Da Nóbrega Neto, Trajano Pires [UNESP]; Flores, André Luiz; Dantas Lopes, José Othon (Elsevier, 2013)
Let m and n be integers greater than 1. Given lattices A and B of dimensions m and n, respectively, a technique for constructing a lattice from them of dimension m+n-1 is introduced. Furthermore, if A and B possess bases satisfying certain conditions, then a second technique yields a lattice of dimension m+n-2. The relevant parameters of the new lattices are given in terms of the respective parameters of A,B, and a lattice C isometric to a sublattice of A and B. Denser sphere packings than previously known ones in dimensions 52, 68, 84, 248, 520, and 4098 are obtained. © 2012 Elsevier Inc. All rights reserved.
Keywords: Generator matrices; Geometry of numbers; Lattices; Sphere packings; Generator matrix; Lattice construction; Sub-lattices; Crystal lattices; Number theory; Packing