On a refinement of Craig's lattices

Abstract

Let p be an odd prime. A family of (p - 1)-dimensional over-lattices yielding new record packings for several values of p in the interval [149... 3001] is presented. The result is obtained by modifying Craig's construction and considering conveniently chosen Z-submodules of Q(zeta), where zeta is a primitive pth root of unity. For p >= 59, it is shown that the center density of the (p - 1)-dimensional lattice in the new family is at least twice the center density of the (p - 1)-dimensional Craig lattice. (C) 2010 Elsevier B.V. All rights reserved.