Improvements on low discrepancy one-dimensional sequences and two-dimensional point sets

We obtain significant improvements for the star discrepancy D* of generalized van der Corput sequences by means of linear digit scramblings (see Section 5.2 for the definition). We also find a new lower bound for the extreme discrepancy D of these sequences which permits to show that linearly-scrambled sequences are set in a good place among generalized van der Corput sequences. Finally, we derive the corresponding properties for generalized Hammersley point sets in arbitrary bases and link recent developments in base 2 by Kritzer, Larcher and Pillichshammer to former studies of Bejian and the author.