Dick proved that all order 2 digital nets satisfy optimal upper bounds of
the L2β-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 Sp,qrβB-discrepancy for a certain parameter range and enlarge that
range for order 2 digitals nets. Lpβ-, Sp,qrβF- and SprβH-discrepancy is considered as well