On a new method for constructing good point sets on spheres (Q1209835)

The author presents a method of distributing a large number \(N\) of points \(P_ 1,\dots,P_ N\) over the unit sphere \(S^{d-1}\) (in \(d\)- dimensional Euclidean space, \(d\geq 3\)) in a ``uniform'' way -- in the sense that the point set \(\{P_ 1,\dots,P_ N\}\) is essentially optimal for a certain ``discrepancy concept'' defined by means of distance functions (``potentials'') and distance functionals (``energies''). By combining this constructive method with a probabilistic approach (due to J. Beck) he obtains almost best possible approximations of balls \(B^ d\) (\(3\leq d\leq 6\)) by zonotopes which are generated (as the Minkowski sum) by \(N\) line segments of equal length.