On the second smallest distance between finitely many points on the sphere (Q1122145)

Let \(s_ 2(n)\) be the supremum of the numbers s which have the property that on the two-dimensional unit sphere one can place n different points \(P_ 1,...,P_ n\) such that any spherical distance \(P_ iP_ j\) (i,j\(\in \{1,...,n\}\), \(i\neq j)\) which is not the minimal distance among all distances of the considered point set is at least s. The authors deal with the problem of finding \(s_ 2(n)\) as well as of the corresponding extremal arrangement of points. For \(n=9\) they succeeded in solving it, while for \(n\geq 9\) they merely obtained an upper bound for \(s_ 2(n)\).