Volume-discrepancy estimates in one and two dimensions

  • Authors:

  • Y. -J. Xiao;H. Faure

  • Affiliations:

  • Université d'Evry-Val d'Essonne Bd des Coquibus F-91000 Evry, France and CERMA-ENPC, La Courtine F-93167 Noisy le Grand Cedex, France;Laboratoire de Mathématiques Discrètes C.N.R.S. UPR 9016 163 avenue de Luminy-Case 930 13288 Marseille Cedex 9, France

  • Venue:
  • Mathematical and Computer Modelling: An International Journal
  • Year:
  • 1996

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Abstract

In one dimension, we give an estimate for the lower bound of the volume-discrepancy (see [1]) for any sequence and an estimate for the volume-discrepancy of the Van der Corput sequences in base b = 2. In two dimensions, we estimate the volume-discrepancy for (0, 2)-sequences in base b = 2 and give an explicit minimal net.