Construction of Asymmetric Orthogonal Arrays With High Strength

ABSTRACT Orthogonal arrays (OAs) are a key research focus in combinatorial design theory and experimental design theory. They play a very important role in an increasing number of interdisciplinary fields, such as computer science, cryptography, multipartite quantum states and quantum information. And the open problems in many fields are closely related to the construction of orthogonal arrays with high strength and large size. At present, some open problems have been solved by using orthogonal arrays. There is an urgent need for developing such orthogonal arrays. This article introduces a general method for obtaining asymmetric orthogonal arrays with high strength. The proposed method is straightforward and constructive. The constructed OAs can be utilized to generate more OAs. Some selective OAs are tabulated for practical applications.