Extremal systems of points and numerical integration on the sphere (Q1431333)

The purpose of this paper is to study certain results concerning the extremal systems of points on the unit sphere \(S^r\subseteq \mathbb{R}^{r+1}\), related to problems of numerical integration and geometrical properties of extremal systems. The authors consider the worst case cubature error in a certain Hilbert space and its relation to a generalized discrepancy. The minimum geodesic distance between pairs of points and the mesh norm are discussed. They also consider numerical examples.