On the discrepancy of sequences in the unit-interval

In the first part of this paper we give an overview on known general bounds for the most important types of discrepancies of sequences in the unit-interval. It is pointed out that for all these types the van der Corput sequence, or a variant of it, provides an example with lowest possible order of discrepancy. In the second part we slightly improve the until now best known lower bound for the one-dimensional discrepancy constant with respect to extreme discrepancy given by R. Béjian in 1982.