Advertisement
Published in:
2009 | OriginalPaper | Chapter
L 2 Discrepancy of Two-Dimensional Digitally Shifted Hammersley Point Sets in Base b
Authors : Henri Faure, Friedrich Pillichshammer
Published in: Monte Carlo and Quasi-Monte Carlo Methods 2008
Publisher: Springer Berlin Heidelberg
Activate our intelligent search to find suitable subject content or patents.
Select sections of text to find matching patents with Artificial Intelligence. powered by
Select sections of text to find additional relevant content using AI-assisted search. powered by
We give an exact formula for the
L
2
discrepancy of two-dimensional digitally shifted Hammersley point sets in base
b
. This formula shows that for certain bases
b
and certain shifts the
L
2
discrepancy is of best possible order with respect to the general lower bound due to Roth. Hence, for the first time, it is proved that, for a thin, but infinite subsequence of bases
b
starting with 5,19,71,…, a single permutation only can achieve this best possible order, unlike previous results of White (1975) who needs
b
permutations and Faure & Pillichshammer (2008) who need 2 permutations.