Spherical Designs via Brouwer Fixed Point Theorem

Andriy V. Bondarenko, Maryna S. Viazovska
2010 SIAM Journal on Discrete Mathematics  
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 $d$.
doi:10.1137/080738313 fatcat:fckijaayarbixhddsd232iydey