1;3409;0c A Note on Polynomial Arithmetic Analogue of Halton Sequences

A Note on Polynomial Arithmetic Analogue of Halton Sequences

ACM Transactions on Modeling and Computer Simulation, vol. 4, no. 3, 1994
Pages: 279-284DOI: 10.1145/189443.189447

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bibtex

In this article, we investigate (O, k )-sequences in a prime power base b > h obtained from Halton sequences with respect to polynomial arithmetic over finite fields. We show that for 1 < h < k, the generator matrix of the hth coordinate of these sequences can be characterized in terms of the Pascal’s triangle. To be precise, the (i, J) element of the matrix is equal to where i, j > 1, and b ~, . . . . b~ are distinct elements in Fb. This result provides us with useful information for practical implementation of this class of low discrepancy sequences and also sheds light on a theoretical connection between the Pascal’s triangle and low-discrepancy sequences first explored by Faure for the analysis of his sequences