The exponent of discrepancy is at most 1.4778...

Grzegorz W. Wasilkowski, Henryk Woźniakowski

Research output: Contribution to journalArticlepeer-review

10 Scopus citations


We study discrepancy with arbitrary weights in the L2 norm over the d-dimensional unit cube. The exponent p* of discrepancy is defined as the smallest p for which there exists a positive number K such that for all d and all ε ≤ 1 there exist Kε-p points with discrepancy at most ε. It is well known that p* ∈ (1, 2]. We improve the upper bound by showing that p* ≤ 1.4778842. This is done by using; relations between discrepancy and integration in the average case setting with the Wiener sheet measure. Our proof is not constructive. The known constructive bound on the exponent p* is 2.454.

Original languageEnglish
Pages (from-to)1125-1132
Number of pages8
JournalMathematics of Computation
Issue number219
StatePublished - Jul 1997


  • Average case
  • Discrepancy
  • Multivariate integration

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Computational Mathematics
  • Applied Mathematics


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