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 Λ in Euclidean space onto a finite subset of the unit sphere in one higher dimension. The mapping preserves much of the structure of Λ, and unlike previously proposed maps, the density of the wrapped spherical codes approaches the density of Λ 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 Λ is the densest possible sphere packing