高强度正交表迫切需要好的构造方法因为具有附加的令人期望的统计性质，而且在这一领域有许多尚未解决的挑战性问题。本项目利用可分辨正交表、正交表的大集和广义差集矩阵等组合结构，使得有限域或剩余类环空间或者其子空间的直积的正交分化块数和基础正交表的水平数相匹配，通过Kronecker和提出高强度正交表新的递归构造方法。研究汉明距离、交互作用列、线性正交表、弹性函数、高强度差集矩阵，提高高强度正交表的饱和率。建立一套较完整的构造体系，在这个体系中，可以进行高强度正交表加、减、乘、除、并列、替换等多种运算，构造大量新的具有非素数幂水平列的高强度正交表和混合正交表。进一步研究它们的统计性质与组合性质，应用于均匀设计、大数据分析与处理、计算机试验设计、信息网络安全和量子纠缠态的构造。本项目将使得高强度正交表的构造理论更加丰富，应用前景更为广阔。

An orthogonal array of strength greater than two is called to be an orthogonal array with high strength. Hedayat, Sloane and Stufken in their monograph “Orthogonal Arrays: Theory and Applications" state that while strength t = 2 is arguably the most important case for statistical applications, there is an urgent need for better methods for strength t> =3 since orthogonal arrays with high strength have additional desirable statistical properties and there are challenging unsolved mathematical and statistical problems in this area. By use of resolvable orthogonal arrays, large set of orthogonal arrays and generalized difference schemes, this project makes the number of orthogonal partition blocks of product of spaces of a finite field and spaces of a residue class ring or their subspaces equal to the level number of basic orthogonal arrays. And we propose a new general recursive construction method of orthogonal arrays with high strength by mean of Kronecker sum. This method facilitates the construction of larger orthogonal arrays from smaller arrays. By studying Hamming distance, interaction columns, linear orthogonal arrays，inner structure, resilient functions and difference schemes with high strength we further improve the percent saturation of orthogonal arrays with high strength. We will establish a complete system for the construction of orthogonal arrays with high strength, in which there are addition, subtraction, multiplication, division, joining operation of columns and replacement method of such arrays. A lot of new high strength orthogonal arrays and mixed orthogonal arrays having factors with non-prime power number of levels will be obtained. By investigating statistical and combinatorial properties of orthogonal arrays with high strength, we will apply them to uniform designs, computer experimental designs, analyses and process of big data, information and net security, construction of quantum entangled states, etc. This project will enrich construction theory of orthogonal arrays with high strength and make them have wider applications. Therefore, it will play an important role in theory and application in experimental designs.