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)tn , 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.

DOI: 10.1016/j.jat.2007.12.001

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Cite this paper

@article{Bondarenko2008NewAE, title={New asymptotic estimates for spherical designs}, author={Andriy V. Bondarenko and Maryna S. Viazovska}, journal={Journal of Approximation Theory}, year={2008}, volume={152}, pages={101-106} }