ELA, Volume 4, pp. 48-73, November 1998, abstract.

D-optimal weighing designs for four and five objects

Michael G. Neubauer, William Watkins, and Joel Zeitlin

For j=4 and j=5 and all d greater than or equal to j, the maximum 
value of det XX^T, where X runs through all j times d (0,1)-matrices, 
is determined along with a matrix X_0 for which the maximum determinant 
is attained.  In the theory of statistical designs, X_0 is called a 
D-optimal design matrix.  Design matrices that were previously thought 
to be D-optimal, are shown here to be D-optimal.