Construction of high strength orthogonal arrays with repeated rows

Orthogonal arrays with repeated rows play a crucial role in the experimental design, combinatorial designs and computer science. However, there are few methods for studying high strength orthogonal arrays with repeated rows. In this paper, we construct asymmetric orthogonal arrays with repeated rows and high strength via product construction and orthogonal partition. Based on $ (u,u+v) $ construction, such symmetric arrays are obtained, many of which achieve the Mukerjee-Qian-Wu bound. The methods are useful for constructing symmetric or asymmetric orthogonal arrays with repeated rows of arbitrary strengths, numbers of levels and various sizes. The constructed arrays can be utilized to generate more arrays. The resulting arrays have a high degree of flexibility and many other desirable properties. Some selective arrays are tabulated for practical uses.