The Theory And Application Of Latin Matrix

Latin square and frequency square are the important concepts in DOE and combinatorics, which are of important value in the research of password theory and the balanced incomplete block design. With the help of Multilateral Matrix theory, this paper promotes the concept of Latin square for Latin matrix, and gives the definition of frequency matrix for the first time. This paper studies Latin matrix as the key object, and gives the Structure, Counting of Latin matrix and upper and lower bounds of Pairwise Latin Matrixes etc. After the introduction of Latin Matrix in chapter2, chapter3and chapter4give the application of Latin Matrix, which contain the structure of orthogonal arrays and balance block design. By using the application examples of orthogonal arrays and balance block design, we try to illustrate the value of Latin Matrix.