Pages: 279-284
, DOI: 10.1145/189443.189447

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 Pascalâ€™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 Pascalâ€™s triangle and low-discrepancy sequences first explored by Faure for the analysis of his sequences