Asymptotically optimal spherical codes

A new class of spherical codes is presented which are designed analogously to laminated lattice construction. For many minimum angular separations, these “laminated spherical codes” outperform the best known spherical codes. In fact, for fixed dimension k⩽49, the density of the laminated spherical code approaches the density of the (k-1)-dimensional laminated lattice Λ_k-1, as the minimum angular separation θ→0. In particular, the three-dimensional laminated spherical code is asymptotically optimal, in the sense that its density approaches the Fejes Toth (1959) upper bound as θ→0. The laminated spherical codes are also structured, which simplifies decoding