Construction of Optimal Orthogonal Partition

Abstract

Orthogonal partitions play a crucial role in orthogonal array theory, design of experiments and quantum information theory. The optimisation of orthogonal partitions can improve the saturation percentages of orthogonal arrays (OAs) obtained by the orthogonal partition method. In particular, optimal orthogonal partitions of strength 1 are of great practical utility. However, there is still a scarcity of results about orthogonal partitions, especially optimal ones. In this paper, the definition of an optimal orthogonal partition is proposed, and we construct optimal orthogonal partitions of OAs by several construction methods, such as orthogonal partition method, difference scheme construction, generalised product construction and construction. As an application, we obtain various optimal orthogonal partitions and OAs with higher saturation percentages.