Constructions of mixed orthogonal arrays of strength three

Abstract

Symmetric orthogonal arrays and mixed (or asymmetric) orthogonal arrays are useful in the design of various experiments. They are also a fundamental tool in the construction of various combinatorial configurations. In this paper, we obtain some difference matrices of strength three and provide some new constructions of mixed orthogonal arrays of strength three by using difference matrices and Hadamard matrices. As an application, we obtain some new mixed orthogonal arrays of strength three, and some of them are tight.