The $L\log L$-Luxemburg Discrepancy for Nonnegative Weights Suffers from the Curse of Dimensionality

We study the normalized discrepancy in the Luxemburg norm generated by $Φ(s)=s\log(1+s)$. For arbitrary nonnegative quadrature weights, we prove that the associated information complexity suffers from the curse of dimensionality: for every $\varepsilon\in(0,1)$, there exist constants $c_\varepsilon>