D-optimal weighing designs for four and five objects

For j = 4 and j = 5 and all d j, the maximum value of det XXT, where X runs through all j d (0,1)-matrices, is determined along with a matrix X0 for which the maximum determinant is attained. In the theory of statistical designs, X0 is called a D-optimal design matrix. Design matrices that were previously thought to be D-optimal, are shown here to be D-optimal.