Generalized Hofer-Niederreiter sequences and their discrepancy from an (u, e, s)-point of view

Recently Tezuka introduced the concept of (u, e, s)-sequences which generalizes (t, s)-sequences by Niederreiter. This generalization can be used to point out a deeper regularity of certain digital sequences, which can be exploited to obtain improvements on their discrepancy bounds. Earlier Larcher and Niederreiter introduced so-called (T , s)-sequences with similar consequences. In this paper we generalize both concepts by introducing (U , e, s)-sequences, we work out relations between the concept of (U , e, s)-sequences and the concepts of (t, s)-, (u, e, s)-, and (T , s)sequences, we introduce an explicit construction of (U , e, s)-sequences by generalizing Hofer-Niederreiter sequences, we give a discrepancy bound for (U , e, s)-sequences which is based on bounds for (u,m, e, s)-nets, and we relate our results to earlier ones.