Large triangles in the d-dimensional unit-cube

We consider a variant of Heilbronn's triangle problem by asking for fixed dimension d greater than or equal to 2 for a distribution of n points in the d-dimensional unit-cube [0, 1](d) such that the minimum (2-dimensional) area of a triangle among these n points is maximal. Denoting this maximum value by Delta(d)(off-line) (n) and Delta(d)(on-line) (n) for the off-line and the on-line situation, respectively, we will show that c(1) (.)(log n)(1/(d-1)) /n(2/(d-1)) less than or equal to Delta(d)(off-line)(n) less than or equal to C-1/n(2/d) and c(2)/n(2/(d-1)) less than or equal to Delta(d)(on-line)(n) less than or equal to C-2/n(2/d) for constants c(1), c(2), C-1, C-2 > 0 which depend on d only.