Research On Mixed Orthogonal Arrays And Generalized Transversal Design And Generalized Net Design

Orthogonal arrays has a very high availability in experiment design, its application greatly increased the economic and technical standards. Therefore, foreign and domestic mathematicians have made great efforts in the methods of orthogonal construction theory. The proposing of the concepts of frequency square has injected new vitality in the con-struction of orthogonal arrays and has given a huge developing scope to orthogonal arrays. Transversal design and net design can be used to construct the frequency square. So, this paper will combines the characteristics of mixed orthogonal array, make further research on transversal design,net design and frequency square.The details are as follows:Chapter one is to introduce the development of the orthogonal construction theory, and the basic knowledge needed in this paper.Chapter two is to introduce the definitions of transversal design and net design, on the basis of which mixed orthogonal arrays and proposed the concepts of the generalized designs and generalized net design. Some examples are given to show the existence of generalized transversal design and generalized net design.Chapter three studies the theorems and properties of the generalized transversal design and generalized net design, use those theorem and the mixed orthogonal arrays to construct some orthogonal frequency square. Then parts of lower bounds of the orthogonal frequency square are updated again. In the end, it draws a conclusion of this paper, and proposes some problems to solve.