The L2-discrepancy measures the irregularity of the distribution of a finite point set. In this note, we prove lower bounds for the L2-discrepancy of arbitrary N-point sets. Our main focus is on theâ€¦ (More)

In a celebrated construction, Chen and Skriganov gave explicit examples of point sets achieving the best possible L2-norm of the discrepancy function. We consider the discrepancy function of theâ€¦ (More)

We investigate quasi-Monte Carlo rules for the numerical integration of multivariate periodic functions from Besov spaces Sp,q B(T d)with dominating mixed smoothness 1/p < r < 2. We show that order 2â€¦ (More)

We investigate quasi-Monte Carlo rules for the numerical integration of multivariate periodic functions from Besov spaces S p,qB(T) with dominating mixed smoothness 1/p < r < 2. We show that order 2â€¦ (More)

The L2-discrepancy measures the irregularity of the distribution of a finite point set. In this note we prove lower bounds for the L2 discrepancy of arbitrary N -point sets. Our main focus is on theâ€¦ (More)