Asymptotically dense spherical codes. I. Wrapped spherical codes

A new class of spherical codes called wrapped spherical codes is constructed by "wrapping" any sphere packing /spl Lambda/ in Euclidean space onto a finite subset of the unit sphere in one higher dimension. The mapping preserves much of the structure of /spl Lambda/, and unlike previously proposed maps, the density of the wrapped spherical codes approaches the density of /spl 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 /spl Lambda/ is the densest possible sphere packing.