D-optimal augmented designs and the existence of tight orthogonal arrays with high strength

Abstract

In this paper, in view of the Rao’s inequalities on the parameters of an orthogonal array, we define some extended matrices for asymmetric orthogonal arrays of strength t(t≥2). According to these matrices, necessary conditions for the existence of tight asymmetric orthogonal arrays of strengths 2 and 4 described by Mukerjee and Wu (1995) are generalized to the existence of tight asymmetric orthogonal arrays of strength t, and examples of the nonexistence of tight asymmetric orthogonal arrays with high strength are interpreted. Furthermore, some conditions on the additional p runs are determined, which guarantee that the orthogonal array plus p run design is D-optimal.