On the distribution properties of Niederreiter–Halton sequences

We study the distribution properties of sequences which are a generalization of the well-known van der Corput–Halton sequence on the one hand, and digital (T,s)-sequences in the sense of Niederreiter on the other. In this paper we completely answer the question under which conditions such a sequence is uniformly distributed in the s-dimensional unit cube, by using methods based on the q-additive property of the weighted q-ary sum-of-digits function.