On the enumeration of some D-optimal designs

Abstract

Two matrices with elements taken from the set {-1,1} are Hadamard equivalent if one can be converted into the other by a sequence of permutations of rows and columns, and negations of rows and columns. In this paper we summarize what is known about the number of equivalence classes of matrices having maximal determinant. We establish that there are 7 equivalence classes for matrices of order 21 and that there are at least 9,884 equivalence classes for matrices of order 26. The latter result is obtained primarily using a switching technique for producing new designs from old.