Wrap-around L2-discrepancy of random sampling, latin hypercube and uniform designs

Kai Tai Fang*, Chang Xing Ma

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review

57 Citations (Scopus)


For comparing random designs and Latin hypercube designs, this paper considers a wrap-around version of the L2-discrepancy (WD). The theoretical expectation and variance of this discrepancy are derived for these two designs. The expectation and variance of Latin hypercube designs are significantly lower than those of the corresponding random designs. We also study construction of the uniform design under the WD and show that one-dimensional uniform design under this discrepancy can be any set of equidistant points. For high dimensional uniform designs we apply the threshold accepting heuristic for finding low discrepancy designs. We also show that the conjecture proposed by K. T. Fang, D. K. J. Lin, P. Winker, and Y. Zhang (2000, Technometrics) is true under the WD when the design is complete.

Original languageEnglish
Pages (from-to)608-624
Number of pages17
JournalJournal of Complexity
Issue number4
Publication statusPublished - Dec 2001
Externally publishedYes

Scopus Subject Areas

  • Algebra and Number Theory
  • Statistics and Probability
  • Numerical Analysis
  • Mathematics(all)
  • Control and Optimization
  • Applied Mathematics

User-Defined Keywords

  • Latin hypercube design
  • quasi Monte-Carlo methods
  • threshold accepting heuristic
  • uniform design
  • wrap-around discrepancy


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