678 research outputs found
L_p- and S_{p,q}^rB-discrepancy of (order 2) digital nets
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
- β¦