For pt. I see ibid., vol.43, no.6, p.1774-85, 1997. New spherical codes called laminated spherical codes are constructed in dimensions 2-49 using a technique similar to the construction of laminated lattices. Each spherical code is recursively constructed from existing spherical codes in one lower dimension. Laminated spherical codes outperform the best known spherical codes in the minimum distance sense for many code sizes. The density of a laminated spherical code approaches the density of the laminated lattice in one lower dimension, as the minimum distance approaches zero. 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 the minimum distance approaches zero. Laminated spherical codes perform asymptotically as well as wrapped spherical codes in those dimensions where laminated lattices are optimal sphere packings.
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