Maximalj-Simplices in the Reald-Dimensional Unit Cube

For each positive even integerjthere is an infinite arithmetic sequence of dimensionsdfor which we construct aj-simplex of maximum volume in thed-dimensional unit cube. For fixedd, all of these maximalj-simplices have the same Gram matrix, which is a multiple ofI+J. Forjeven, a new upper bound for the volume of aj-simplex in thed-dimensional unit cube is given