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Polynomial Arithmetic Analogue of Hickernell Sequences

In: Monte Carlo and Quasi-Monte Carlo Methods 2002

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  • Shu Tezuka

    (IBM Tokyo Research Laboratory)

Abstract

Summary Recently, Hickernell introduced a new class of low-discrepancy sequences which is an infinite version of good lattice points. His sequences are constructed from multiplying the van der Corput sequence by an integer vector. In this paper, we define the polynomial arithmetic analogue of Hickernell sequences by using polynomials over finite fields GF(b), and show that this new type of sequences constitute a class of digital (t, s)-sequences. Then, we give two versions of matrix representation for their generator matrices, and prove that for the first version, there do not exist (0, s)-sequences for any base b ≥ 2 and any dimension s ≥ 2, and that for the second version, there do not exist (0, s)-sequences in base b = 2 for any s ≥ 2.

Suggested Citation

  • Shu Tezuka, 2004. "Polynomial Arithmetic Analogue of Hickernell Sequences," Springer Books, in: Harald Niederreiter (ed.), Monte Carlo and Quasi-Monte Carlo Methods 2002, pages 451-459, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-18743-8_28
    DOI: 10.1007/978-3-642-18743-8_28
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