The Existence Of A Class Of Mixed Orthogonal Arrays With Seven Factors

The orthogonal array is an important object in combinatorial design theory, and it is applied to many fields, such as computer science, coding theory and cryptography etc. This paper mainly studies the existence of the mixed orthogonal arrays of strength two with seven factors and presents some new constructions. Consequently, a few new mixed orthogonal arrays are obtained.A.S.Hedayat, N.J.A.Sloane and J.Stufken published the monograph of Orthogonal Arrays:Theory and Applications in 1999. In this book, they proposed an open problem: is there a mixed orthogonal arrays of strength two with factor number larger than three? Up until to now, the existence of the mixed orthogonal arrays of strength two with factor number smaller than seven has been almost solved.This paper mainly studies the existence of the mixed orthogonal arrays of strength two with seven factors. The paper consists of four chapters and is organized as follows.Chapter 1 lists the research background of the paper, the related concepts and some existing results.Chapter 2 lists some basic constructions of mixed orthogonal arrays.Chapter 3 uses the construction method of transversal designs and some basic con-structions of mixed orthogonal arrays, and studies the existence of MOA(M; abcdef,2) (seven factors coprime), the existence of MOA(M; a7,2) and MOA(M; a5b1c1,2).Chapter 4 summarizes the main content of this paper and puts forward to some suggestions.