Acta Mathematica Hungarica

, Volume 109, Issue 3, pp 239–254 | Cite as

Star discrepancy estimates for digital (t, m, 2)-nets and digital (t, 2) -sequences over Z2

  • Josef Dick
  • Peter Kritzer
Article

Summary

We prove upper bounds on the star discrepancy of digital (t, m, 2)-nets and (t, 2)-sequences over Z2. The main tool is a decomposition lemma for digital (t, m, 2)-nets, which states that every digital (t, m, 2)-net is just the union of 2tdigitally shifted digital (0, m - t, 2)-nets. Using this result we generalize upper bounds on the star discrepancy of digital (0, m, 2) -nets and (0, 2) -sequences.

digital (t 2)-nets 2)-sequences star discrepancy 

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Copyright information

© Springer-Verlag/Akadémiai Kiadó 2005

Authors and Affiliations

  • Josef Dick
    • 1
  • Peter Kritzer
    • 2
  1. 1.School of Mathematics University of New South Wales
  2. 2.Department of Mathematics University of Salzburg

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