1;3409;0c Polynomial Arithmetic Analogue of Halton Sequences

Polynomial Arithmetic Analogue of Halton Sequences

ACM Transactions on Modeling and Computer Simulation, vol. 3, no. 2, 1993
Pages: 99-107DOI: 10.1145/169702.169694

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We introduce the radical inverse function with respect to polynomial arithmetic over finite fields, and thereby construct a polynomial arithmetic analogue of Halton sequences. Next, we generalize the definition of Niederreiter sequences so that his key lemma [Niederreiter 1988, Lemma 4] still holds. We then prove that our analogous Halton sequences constitute a new class of low-discrepancy sequences viewed as a special subclass of the generalized Niederreiter sequences