Discrepancy bounds for hybrid sequences involving digital explicit inversive pseudorandom numbers

We consider hybrid sequences, that is, sequences in a multidimensional unit cube that are composed from low-discrepancy sequences and sequences of pseudorandom numbers. We establish the first nontrivial deterministic discrepancy bounds for three kinds of hybrid sequences that are obtained by “mixing” low-discrepancy sequences and digital explicit inversive sequences. Such hybrid sequences are of interest for high-dimensional numerical integration since they combine the advantages of Monte Carlo methods and quasi-Monte Carlo methods.