On the exponent of discrepancies

Grzegorz W. Wasilkowski, Henryk WoźNiakowski

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


We study various discrepancies with arbitrary weights in the L2 norm over domains whose dimension is proportional to d. We are mostly interested in large d. The exponent p of discrepancy is defined as the smallest number for which there exists a positive number C such that for all d and ε there exist Cε-p points with discrepancy at most ε. We prove that for the most standard case of discrepancy anchored at zero, the exponent is at most 1.41274..., which slightly improves the previously known bound 1.47788.... For discrepancy anchored at α and for quadrant discrepancy at we prove that the exponent is at most 1.31662 ... for α = [1/2, ..., 1/2]. For unanchored discrepancy we prove that the exponent is at most 1.27113 .... The previous bound was 1.28898 .... It is known that for all these discrepancies the exponent is at least 1.

Original languageEnglish
Pages (from-to)983-992
Number of pages10
JournalMathematics of Computation
Issue number270
StatePublished - Apr 2010


  • Discrepancy
  • Multivariate integration

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Computational Mathematics
  • Applied Mathematics


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