Institut de Mathématiques de Luminy

Abstract 2008-08

Faure Henri.
Star discrepancy of generalized two-dimensional Hammersley point sets

We generalize to arbitrary bases recent results on the star 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 discrepancy of these point sets and obtain simple generalizations which are the best presently known with regard to low star
discrepancy. This study is parallel to the recent one by F. Pillichshammer and the author on the Lp discrepancy of the same point sets (to appear in Monatsh. Math.).

AMS subject classification: 11K06, 11K38.
Key words: Star discrepancy, Hammersley point sets, van der Corput
sequences.

 

 

 

 

 

 


Last update : june 25, 2008, EL.