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)(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)(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.