Combinatorial arrangements analogous to orthogonal arrays

Abstract

In this paper are considered some combinatorial arrangements analogous to orthogonal arrays introduced by the author several years ago (Rao, 1946a). In an orthogonal array, all combinations of s elements taken d at a time allowing repetitions occur an equal number of times in every set of d rows of the array. By not allowing repetitions and relaxing the condition that the combinations should be ordered certain new arrangements called orthogonal arrays of Type I and Type II have been obtained. Their relationships with orthogonal latin squares and their use in the construction of BIB designs have been discussed.