Iterative Constructions Of Orthogonal Arrays Of Strength T And Orthogonal Partitions

Constructions of asymmetric orthogonal arrays of strength two has been an area of intense research. Relatively less is known on the construction of symmetric orthogonal arrays and asymmetric orthogonal arrays of strength larger than two because finding OAs of strength larger than two is tougher than finding OAs of strength two. But strength larger than 3 OAs are more useful than strength 2 OAs as their characteristics allow us to study the interaction of certain factors in the factorial design. Specifically, orthogonal arrays and orthogonal partitions play an important role in communications and coding theory.In this letter, we mainly apply orthogonal partitions to the construction of symmetric OAs and asymmetric OAs of strength t. We also construct the orthogonal partitions by using orthogonal arrays and orthogonal Latin squares. And the orthogonal arrays constructed by the method are tight or possess the higher percent saturations. The outline of this letter is as follows.Chapter 1 introduces the current research status and development of orthogonal parti-tions and orthogonal arrays, as well some basic concepts, main lemma and some corollaries required for our presentation and analysis are presented.Chapter 2 generalized the concept of orthogonal partition, and by using orthogonal Latin squares, then presents the iterative constructions of orthogonal arrays of strength t and orthogonal partitions.Chapter 3 proposes the methods for constructing high strength orthogonal arrays and high strength mixed orthogonal arrays. The main content of this paper are proposes in Chapter 4, and we put forward some suggestions.