  Given a finite set of points on the Euclidean sphere, the worst case
quadrature error in Sobolev spaces has recently been shown to provide upper
bounds on the covering radius of the point set. Moreover, quasi-Monte Carlo
integration points on the sphere achieve the asymptotically optimal covering
radius. Here, we extend these results to points on compact smooth Riemannian
manifolds and provide numerical experiments illustrating our findings for the
Grassmannian manifold.
