Further lattice packings in high dimensions
Arie Arie Bos, John H. Conway, Neil J.A. Sloane · Mathematika · 1982
Barnes and Sloane recently described a “general construction” for lattice packings of equal spheres in Euclidean space. In the present paper we simplify and further generalize their construction, and make it suitable for iteration. As a result we obtain lattice packings in ℝm with density Δ satisfying , as m → ∞ where is the smallest value of k for which the k-th iterated logarithm of m is less than 1. These appear to be the densest lattices that have been explicitly constructed in high-dimensional space. New records are also established in a number of lower dimensions, beginning in dimension 96.