Discrepancy of second order digital sequences in function spaces with   dominating mixed smoothness
  The discrepancy function measures the deviation of the empirical distribution of a point set in $[0,1]^d$ from the uniform distribution. In this paper, we study the classical discrepancy function with respect to the BMO and exponential Orlicz norms, as well as Sobolev, Besov and Triebel-Lizorkin norms with dominating mixed smoothness. We give sharp bounds for the discrepancy function under such norms with respect to infinite sequences. 
Josef Dick and Aicke Hinrichs and Lev Markhasin and Friedrich   Pillichshammer
math.NT