Adelic constructions of low discrepancy sequences

Abstract

In [Fr2, Skr], Frolov and Skriganov showed that low discrepancy point sets in the multidimensional unit cube $[0,1{)}^s$ can be obtained from admissible lattices in ${\mathbb{R}}^s$. In this paper, we get a similar result for the case of $({\mathbb{F}}_q((x^{-1})){)}^s$. Then we combine this approach with Halton’s construction of low discrepancy sequences.