The Existence Of Mixed Orthogonal Arrays MOA(N;a~6b~1,2) With Seven Factors

Orthogonal array is a combinatorial structure introduced by the statistician C.R.Rao in 1947 when he studied experimental designs. Many constructions and results of or-thogonal array, further research problems and abundant of references are listed both in ?Orthogonal Arrays:Theory and Applications? ([7]) written by A.S.Hedayat, N.J.A.Sloane and J.Stufken and in?The CRC Handbook of Combinatorial Designs? ([2])written by R.J.R.Abel?C.J.Colbourn and J.H.Dinitz. The publication of these books promotes the study of orthogonal array.In this paper, we mainly investigate the mixed orthogonal arrays MOA(N;a~6b~1,2) with seven factors of strength two and obtain a few new constructions.Firstly, we introduce the research background of the full paper, containing some basic concepts, and we list the main work of this paper. According to the equivalent of the relationship between the mixed orthogonal arrays and the orthogonal Latin squares, we get the values of the main research factors and discuss the different cases based on the values. If the mixed orthogonal arrays with N times experiments is existence, then the type of mixed orthogonal arrays with arbitrary multiples of N must be exist, so we want to get the number of experiment N as small as possible. But if the minimum number of N does not exist, we consider the existence of multiples of N.Secondly, we investigate some of the construction methods, give the proof of con-struction 2.1.5, and prove the existence of MOA(302;30651,2) and MOA(302;30661,2). According to the known mixed orthogonal arrays and through the corresponding construc-tion methods, such as constructions 2.1.1,2.1.4,2.1.8,2.1.9 and so on, we get a kind of mixed orthogonal arrays by these constructions.Finally, we conclude the main results and give some mixed orthogonal arrays with seven factors. We also put forward some problems.