The Existence Of A Class Of Mixed Orthogonal Arrays

Orthogonal array is an important object in the combinatiorial design theory and experimental design theory. Orthogonal array is a combinatorial structure introduced by the statistician C. R. Rao in1947. This combinatorial structure is used for orthogonal experiment design. After then, many combination mathematicians and statisticians de-voted themselves to the research of orthogonal array. And they applied them to a lot of fields, such as agriculture, medicine, manufacture, computer science and cryptography etc. With the rapid development of modern science and technology, different levels of factors are needed, which deduced the conception of mixed orthogonal arrays.A. S. Hedayat, N. J. A. Sloane and J. Stufken published the monograph of Orthogonal Arrays:Theory and Applications in1999. In this book, they submitted an open prob-lem. For factor number larger than4, is there a mixed orthogonal array of strength two? Until now, the existence of the mixed orthogonal array of strength two and at most five factors has been solved. In this paper, we mainly investigated the mixed orthogonal array with six factors.In this paper, we discussed different cases according to the relationship between the level of factors. We proved that the necessary conditions on existence of the mixed orthog-onal array with six factors and strength two was also sufficient with several exceptions and possible exceptions.