A note on E. Thiémard's algorithm to compute bounds for the star discrepancy

  • Authors:

  • Tim Pillards;Ronald Cools

  • Affiliations:

  • Department of Computer Science, Katholieke Universiteit Leuven, Celestijnenlaan 200A, B-3001 Heverlee, Belgium;Department of Computer Science, Katholieke Universiteit Leuven, Celestijnenlaan 200A, B-3001 Heverlee, Belgium

  • Venue:
  • Journal of Complexity
  • Year:
  • 2005

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Abstract

Thiémard (J. Complexity 17(4) (2001) 850) suspects that his upper bound for the discrepancy B(P, x) is bounded below by a measure for the tightness of the partition P. We present a counterexample but also prove that for a certain class of partitions the assumption is valid. The partitions used in Thiémard's algorithm are all part of this class.