有序正交阵列及相关课题研究

Ordered orthogonal arrays are the combinatorial depictions of (T,M,S)-nets which have wide applications in the quasi-Monte Carlo methods of numerical integration and etc.. they also have intimate connections with orthogonal arrys which have very important theoretical and using values ,and are the core research objects in design theory. Recently, using ordered orthogonal arrays, orthogonal arrays of strength 3 and some combinatorial methods, for the fixed parameters T, M,S, the applicant of this project give a bulk of existence results on (T,M,S)-nets. This train of think on nets is new and interesting. Based on this breakthrough point , in this project, we will research the constructions and existence of ordered orthogonal arrays of strength greater than or equal to 3 and sevearl important related combinatorial configurations in design theory, which include ordered orhogonal arrays, orthogonal arrays, difference matrices, some other arrys with special property and some applications. By acquiring substantial results and progress, research on these difficult topics will push the further develop of design theory.

有序正交阵列是广泛用于数值计算的拟蒙特卡罗算法等许多方面的(T , M, S)-网的组合刻画。它们与设计理论中有着非常重要的理论和应用价值的核心研究对象- - -正交阵列有着密切的联系。最近，借助于强度为3有序正交阵列, 正交阵列和组合设计方法，项目申请人对固定参数T，M，S，，任意基对应的Nes给出了一批存在性结果。这种研究（T， M, S）-网的思路是新颖而有趣的。以此为切入点，本项目对强度≥3的有序正交阵列和设计理论相关的一些重要组合构形的构造方法和存在性进行研究，主要内容包括到有序正交阵列，正交阵列，差矩阵，其它一些有特殊性质的阵列和一些应用等。对这些困难问题进行研究和探索，取得一些实质性的研究承诺过过，将推动组合设计理论的进一步发展。

有序正交阵列与设计理论中具有重要的理论和应用价值的核心研究对象之一----正交阵列有着密切的联系。它们也是广泛用于数值计算的拟蒙特卡罗算法等许多方面的(T , M, S)-网的组合刻画。本项目以有序正交阵列为切入点，对设计理论相关的一些重要组合构形的构造方法和存在性进行研究，主要内容包括到有序正交阵列，正交阵列，差矩阵，及其它一些有特殊性质的阵列和一些应用等等。对这些困难问题进行研究和探索，取得一些实质性的研究成果，将推动组合设计理论的进一步发展。