New asymptotic estimates for spherical designs
Numerical Analysis
2008-11-04 v1 General Mathematics
Abstract
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.
Keywords
Cite
@article{arxiv.0811.0168,
title = {New asymptotic estimates for spherical designs},
author = {Andriy V. Bondarenko and Maryna S. Viazovska},
journal= {arXiv preprint arXiv:0811.0168},
year = {2008}
}
Comments
12 pages