Points on manifolds with asymptotically optimal covering radius

Given a finite set of points on the Euclidean sphere, the worst case quadrature error for functions in Sobolev spaces has recently been shown to provide upper bounds on the covering radius of the point set. Moreover, sequences of Quasi-Monte Carlo (QMC) designs for Sobolev spaces on the sphere achieve asymptotically optimal covering radii. Here, we extend these results from sequences of QMC designs on the sphere to sequences of weighted QMC designs on compact smooth Riemannian manifolds. We also provide numerical experiments illustrating our findings for the Grassmannian manifold.