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

Authors:
Kai-Tai Fang;Yu Tang;Jianxing Yin
Affiliations:
Department of Mathematics, Hong Kong Baptist University, Hong Kong, PR China;Department of Mathematics, Hong Kong Baptist University, Hong Kong, PR China and Department of Mathematics, Suzhou University, Suzhou 215006, PR China;Department of Mathematics, Suzhou University, Suzhou 215006, PR China
Venue:
Journal of Complexity
Year:
2005

Citing 4
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Abstract

The wrap-around L"2-discrepancy has been used in quasi-Monte Carlo methods, especially in experimental designs. In this paper, explicit lower bounds of the wrap-around L"2-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 L"2-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.