几类新的拉丁超立方体设计的构造研究

Latin hypercube designs are one of the most commonly used designs in computer experiments. It not only has important theoretical significance, but also has great practical value. With the rapid development of science and technology, the demands of some experiments on designs are becoming increasingly higher, and the structures of the designs are becoming more and more complex. In order to do experiments efficiently, we hope that the designs have some excellent characteristics, and can hold enough factors. This project will improve the Latin hypercube designs from the point of this view, including: 1) the construction of Latin hypercube designs with both of the uniformity in high dimensions and column-orthogonality by using the excellent uniformity in high dimensions of strong orthogonal arrays and MNOAs. 2) the construction of sliced Latin hypercube designs under some new criterions that we will propose. We expect to obtain some system construction methods for the above complex experiment designs so that the practitioners can use the designs directly.

拉丁超立方体设计是计算机试验中应用最广泛的设计之一，它不仅在理论研究上有重要意义，在实际应用中也有重大价值。随着科学技术的快速发展，一些试验对设计的要求越来越高，需要的设计结构也越来越复杂。为了能够更加有效率地进行试验，我们希望设计具有一定的优良性，并且能够容纳足够多的因子。从这个角度出发，本项目拟对拉丁超立方体设计进行改进，包括：1) 利用MNOA和强正交表优良的高维投影均匀性，构造同时具有高维投影均匀性和列正交性的拉丁超立方体设计；2) 提出一些新的准则，并在这些准则下构造分片拉丁超立方体设计。期望通过本项目能得到以上复杂设计的系统构造方法，以供实际工作者直接使用。