Spherical Designs via Brouwer Fixed Point Theorem

• Authors: Andriy V. Bondarenko;Maryna S. Viazovska
• Venue: SIAM Journal on Discrete Mathematics
• Year: 2010

For each $N\geq c_{d}t^{\frac{2d(d+1)}{d+2}}$ we prove the existence of a spherical $t$-design on $S^{d}$ consisting of $N$ points, where $c_{d}$ is a constant depending only on $d$.