5 research outputs found
New asymptotic estimates for spherical designs
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 10.Comment: 12 page
Spherical designs via Brouwer fixed point theorem
For each N>=c_d*n^{2d*(d+1)/(d+2)} we prove the existence of a spherical
n-design on S^d consisting of N points, where c_d is a constant depending only
on .Comment: 17 page