Numerical construction of spherical t-designs by Barzilai-Borwein method

A point set X-N on the unit sphere is a spherical t-design is equivalent to the nonnegative quantity A(N,t+1) vanished. We show that if X-N is a stationary point set of A(N,t+1) and the minimal singular value of basis matrix is positive, then X-N is a spherical t-design. Moreover, the numerical construction of spherical t-designs is valid by using Barzilai-Borwein method. We obtain numerical spherical t-designs with N = (t + 2)(2) points for t + 1 up to 127. (C) 2019 IMACS. Published by Elsevier B.V. All rights reserved.