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Distribution of Digital Explicit Inversive Pseudorandom Numbers and Their Binary Threshold Sequence

In: Monte Carlo and Quasi-Monte Carlo Methods 2008

Author

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  • Zhixiong Chen

    (Putian University, Key Laboratory of Applied Mathematics)

  • Domingo Gomez

  • Arne Winterhof

Abstract

We study the distribution of s-dimensional points of digital explicit inversive pseudorandom numbers with arbitrary lags. We prove a discrepancy bound and derive results on the pseudorandomness of the binary threshold sequence derived from digital explicit inversive pseudorandom numbers in terms of bounds on the correlation measure of order k and the linear complexity profile. The proofs are based on bounds on exponential sums and earlier relations of Mauduit, Niederreiter and Sárközy between discrepancy and correlation measure of order k and of Brandstätter and the third author between correlation measure of order k and linear complexity profile, respectively.

Suggested Citation

  • Zhixiong Chen & Domingo Gomez & Arne Winterhof, 2009. "Distribution of Digital Explicit Inversive Pseudorandom Numbers and Their Binary Threshold Sequence," Springer Books, in: Pierre L' Ecuyer & Art B. Owen (ed.), Monte Carlo and Quasi-Monte Carlo Methods 2008, pages 249-258, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-04107-5_14
    DOI: 10.1007/978-3-642-04107-5_14
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