Star Extreme Discrepancy of Generalized Two-dimensional Hammersley Point Sets

We generalize to arbitrary bases recent results on the star extreme discrepancy of digitally shifted two-dimensional Hammersley point sets in base 2 by Kritzer, Larcher and Pillichshammer. The key idea is to link our fundamental formula for the discrepancy function of generalized van der Corput sequences to the corresponding quantity for generalized two-dimensional Hammersley point sets. In that way, we can derive precise formulas for the star extreme discrepancy of these point sets and obtain simple generalizations which are the best presently known with regard to low star extreme discrepancy. This study is parallel to the recent one by F. Pillichshammer and the author on the (star) Lp discrepancy (p < ∞) of the same point sets (to appear in Monatsh. Math.). Communicated by Yukio Ohkubo