L_p- and S_{p,q}^rB-discrepancy of (order 2) digital nets
Numerical Analysis
2015-09-02 v4 Algebraic Geometry
Abstract
Dick proved that all order digital nets satisfy optimal upper bounds of the -discrepancy. We give an alternative proof for this fact using Haar bases. Furthermore, we prove that all digital nets satisfy optimal upper bounds of the -discrepancy for a certain parameter range and enlarge that range for order digitals nets. -, - and -discrepancy is considered as well.
Keywords
Cite
@article{arxiv.1402.4424,
title = {L_p- and S_{p,q}^rB-discrepancy of (order 2) digital nets},
author = {Lev Markhasin},
journal= {arXiv preprint arXiv:1402.4424},
year = {2015}
}