We study the star discrepancy of (t, m, 2)-nets and (t, 2)-sequences in arbitrary base b. We give best possible upper bounds on the star discrepancy of (t, m, 2)-nets and show new upper bounds on the star discrepancy of (t, 2)-sequences. By these results, which shall be obtained by combinatorial arguments, we improve existing upper bounds on the star discrepancy of such point sets.
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A best possible upper bound on the star discrepancy of (t, m, 2)-nets
∗The first author is supported by the Australian Research Council under its Center of Excellence Program.
†School of Mathematics, University of New South Wales, Sydney 2052, Australia.
‡The second author is supported by the Austrian Research Foundation (FWF), Projects P17022-N12 and S8311-MAT.
§Corresponding Author, Department of Mathematics, University of Salzburg, Hellbrunnerstr. 34, A-5020 Salzburg, Austria.
Citation Information: Monte Carlo Methods and Applications mcma. Volume 12, Issue 1, Pages 1–17, ISSN (Online) 1569-3961, ISSN (Print) 0929-9629, DOI: 10.1515/156939606776886643,
Publication History:
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Key Words: (t, m, s)-net,; (t, s)-sequence,; star discrepancy
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