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Mean-square discrepancies of the Hammersley and Zaremba sequences for arbitrary radix

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Abstract

Theoretical formulae are obtained for estimating the discrepancy of a certain class of equidistributed sequences. Earlier results ofHalton andZaremba are generalized to arbitrary radix. The new discrepancy formulae are exact but more tractable than previously known versions. Significantly improved error-bounds for Quasi-Monte Carlo numerical integration result.

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Authors and Affiliations

  1. M.I.T. Lincoln Laboratory, 01776, Lexington, MA, USA

    Brian E. White

Authors
  1. Brian E. White
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Additional information

This work was performed at the University of Wisconsin, Madison, USA, with the support of the National Science Foundation.

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White, B.E. Mean-square discrepancies of the Hammersley and Zaremba sequences for arbitrary radix. Monatshefte für Mathematik 80, 219–229 (1975). https://doi.org/10.1007/BF01319918

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  • DOI: https://doi.org/10.1007/BF01319918

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