L<sub>p</sub>- and S<sub>p,q</sub><sup>r</sup>B-discrepancy of (order 2) digital nets
L<sub>p</sub>- and S<sub>p,q</sub><sup>r</sup>B-discrepancy of (order 2) digital nets
Dick proved that all order $2$ digital nets satisfy optimal upper bounds of the $L_2$-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 $S_{p,q}^r B$-discrepancy for a certain parameter range and enlarge that range …