Space-filling properties of good lattice point sets

We study space-filling properties of good lattice point sets and obtain some general theoretical results. We show that linear level permutation does not decrease the minimum distance for good lattice point sets, and we identify several classes of such sets with large minimum distance. Based on good lattice point sets, some maximin distance designs are also constructed.

[1]  Edwin R. van Dam,et al.  Bounds for Maximin Latin Hypercube Designs , 2007, Oper. Res..

[2]  Thomas J. Santner,et al.  The Design and Analysis of Computer Experiments , 2003, Springer Series in Statistics.

[3]  Runze Li,et al.  Design and Modeling for Computer Experiments , 2005 .

[4]  R Core Team,et al.  R: A language and environment for statistical computing. , 2014 .

[5]  K. Fang,et al.  Application of Threshold-Accepting to the Evaluation of the Discrepancy of a Set of Points , 1997 .

[6]  Dick den Hertog,et al.  Maximin Latin Hypercube Designs in Two Dimensions , 2007, Oper. Res..

[7]  H. Keng,et al.  Applications of number theory to numerical analysis , 1981 .

[8]  Jerome Sacks,et al.  Designs for Computer Experiments , 1989 .

[9]  M. D. McKay,et al.  A comparison of three methods for selecting values of input variables in the analysis of output from a computer code , 2000 .

[10]  M. E. Johnson,et al.  Minimax and maximin distance designs , 1990 .

[11]  Dennis K. J. Lin,et al.  Uniform fractional factorial designs , 2012, 1206.0897.

[12]  Yong-Dao Zhou,et al.  Space-Filling Fractional Factorial Designs , 2014 .

[13]  V. R. Joseph,et al.  ORTHOGONAL-MAXIMIN LATIN HYPERCUBE DESIGNS , 2008 .

[14]  T. J. Mitchell,et al.  Exploratory designs for computational experiments , 1995 .

[15]  Max D. Morris,et al.  Factorial sampling plans for preliminary computational experiments , 1991 .

[16]  K. Fang,et al.  Number-theoretic methods in statistics , 1993 .

[17]  Thomas Hochkirchen.  Design and Modeling for Computer Experiments by K.-T. Fang, R. Li and A. Sudjianto , 2006 .