Generalized good lattice point sets
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Good lattice point (GLP) sets are frequently used in quasi-Monte Carlo method and computer experiments. However, the space-filling property of GLP sets needs to be improved especially when the number of factors is large. This paper shows that the generalized GLP (GGLP) sets, constructed simply and fast by the linear level permutation of the GLP sets, have better space-filling property than the GLP sets and the orthogonal Latin hypercube designs (OLHD) in the sense of maximin distance criterion and uniformity criterion, especially for high dimensional cases. Unlike the OLHD, the number of runs of the GGLP sets can be chosen as any integer. It is also shown that the GLP sets are better than Latin hypercube designs as the starting design for linear and nonlinear level permutation. The GGLP sets are recommended for the designs with large number of factors and/or large number of runs.
KeywordsGGLP GLP Linear level permutation Maximin distance Mixture discrepancy
Part of the research was done when the corresponding author was visiting Department of Statistics at University of California, Los Angeles. The authors would like to thank Prof. Hongquan Xu and Prof. Hongliang Lai for their help. This paper was supported by CEMEE State Key Laboratory fund project (CEMEE2015Z0301A1) and NNSF of China (11471229).
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