New asymptotic estimates for spherical designs
Abstract
Let N(n, t) be the minimal number of points in a spherical t-design on the unit sphere Sn in Rn+1. For each n >= 3, we prove a new asymptotic upper bound N(n, t) <= C(n)tan, where C(n) is a constant depending only on n, a3 <= 4, a4 <= 7, a5 <= 9, a6 <= 11, a7 <= 12, a8 <= 16, a9 <= 19, a10 <= 22, and an < n/2*log2(2n), n > 10.
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