A lower bound for Heilbronn's triangle problem in d

In this paper we show a lower bound for the generalization of Heilbronn's t riangle problem to d dimensions; namely, we show that there exists a set S of n points in the d-dimensional unit cube so that every d + 1 points of S define a simplex of volume Ohm (1/n(d)). We also show a constructive increm ental positioning of n points in a unit 3-cube for which every tetrahedron defined by four of these points has volume Ohm (1/n(4)).