A0366
Title: A construction method for Maximin L1-distance Latin hypercube designs
Authors: Ru Yuan - Zhongnan University of Economics and Law (China) [presenting]
Yuhao Yin - University of California Los Angeles (United States)
Hongquan Xu - University of California Los Angeles (United States)
Min-Qian Liu - Nankai University (China)
Abstract: Maximin distance designs are a kind of space-filling design and are widely used in computer experiments. However, although much work has been done on constructing such designs, doing so for a large number of rows and columns remains challenging. A theoretical construction method is proposed that generates a maximin $L_1$-distance Latin hypercube design with a run size that is close to the number of columns or half the number of columns. The theoretical results show that some of the constructed designs are both maximin $L_1$-distance and equidistant designs, which means that their pairwise $L_1$-distances are all equal and that they are uniform projection designs. Other designs are asymptotically optimal under the maximin $L_1$-distance criterion. Moreover, the proposed method is efficient for constructing high-dimensional Latin hypercube designs that perform well under the maximin $L_1$-distance criterion.
