Construction Of Uniform Designs With Large Size

With development of the society and information technology, the theory of uniform designs is more and more systematical and complete. Nowadays uniform designs are widely used in various area, particularly in computer experiments. As a important space-filling design method, uniform design is also robust to the modeling assumption. However,due to the complexity of problem, most of uniform design construction methods are inefficient, even useless for large size or high dimensional design construction. In this paper, several methods are discussed and compared for constructing large size and high dimensional uniform design.First of all, centered discrepancy, which is a measurement of uniformity and is called CD, is described briefly. Then, based on the centered discrepancy, several construction methods, for example, random permuting method (RPM), mixture method (MM), NTLBG method, are compared under the CD. Finally, we analyze the uniformity of the optimal design obtained by the NTLBG method, and compare CD value of the optimal design obtained by above methods with the optimal designs obtained by TA method, and pglp method. An application of those construction methods are also shown.