Covering of spheres by spherical caps and worst-case error for equal weight cubature in Sobolev spaces

Johann S. Brauchart, Josef Dick, Edward B. Saff +3

We prove that the covering radius of an $N$-point subset $X_N$ of the unit sphere $S^d\subset R^{d+1}$ is bounded above by a power of the worst-case error for equal weight cubatur…