An Upper Bound for the d -Dimensional Analogue of Heilbronn's Triangle Problem
Peter Braß · SIAM Journal on Discrete Mathematics · 2005
In this paper it is shown that for any set of n points selected from the d-dimensional unit cube, d odd, the volume of the smallest simplex spanned by the set is $O(n^{-(1+{1\over 2d})})$, which is a slight improvement on the only known upper bound O(n -1 )$, although still far from the lower bound $\Omega(n^{-d}\log n)$.