New asymptotic estimates for spherical designs

Details New asymptotic estimates for spherical designs New asymptotic estimates for spherical designs

2008-11-02

arxiv.org/abs/0811.0168v1

Journal of Approximation Theory Volume 152, Issue 1, May 2008, Pages 101-106

Mathematics

Numerical Analysis

12 pages

Scientific paper

Let N(n, t) be the minimal number of points in a spherical t-design on the
unit sphere S^n in R^{n+1}. For each n >= 3, we prove a new asymptotic upper
bound N(n, t) <= C(n)t^{a_n}, where C(n) is a constant depending only on n, a_3
<= 4, a_4 <= 7, a_5 <= 9, a_6 <= 11, a_7 <= 12, a_8 <= 16, a_9 <= 19, a_10 <=
22, and a_n < n/2*log_2(2n), n > 10.

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