Lower bounds for wrap-around L2-discrepancy and constructions of symmetrical uniform designs

Kai Tai Fang*, Yu Tang, Jianxing Yin

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review

37 Citations (Scopus)


The wrap-around L2-discrepancy has been used in quasi-Monte Carlo methods, especially in experimental designs. In this paper, explicit lower bounds of the wrap-around L2-discrepancy of U-type designs are obtained. Sufficient conditions for U-type designs to achieve their lower bounds are given. Taking advantage of these conditions, we consider the perfect resolvable balanced incomplete block designs, and use them to construct uniform designs under the wrap-around L2-discrepancy directly. We also propose an efficient balance-pursuit heuristic, by which we find many new uniform designs, especially with high levels. It is seen that the new algorithm is more powerful than existing threshold accepting ones in the literature.

Original languageEnglish
Pages (from-to)757-771
Number of pages15
JournalJournal of Complexity
Issue number5
Publication statusPublished - Oct 2005
Externally publishedYes

Scopus Subject Areas

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

User-Defined Keywords

  • Lower bound
  • Perfect RBIBD
  • Uniform designs
  • Wrap-around L-discrepancy


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