ASYMPTOTICALLY DENSE SPHERICAL CODES .1. WRAPPED SPHERICAL CODES

A new class of spherical codes called wrapped spherical codes is const ructed by ''wrapping'' any sphere packing Lambda in Euclidean space on to a finite subset of the unit sphere in one higher dimension. The map ping preserves much of the structure of Lambda, and unlike previously proposed maps, the density of wrapped spherical codes approaches the d ensity of Lambda as the minimum distance approaches zero. We show that this implies that the asymptotically maximum spherical coding density is achieved by wrapped spherical codes whenever Lambda is the densest possible sphere packing.