The distribution of the discrepancy of scrambled digital (\(t\),\(m\),\(s\))-nets (Q1873034)

The authors compare the empirical distribution of the squared discrepancy of scrambled digital \((t,m,s)\)-nets with the theoretical asymptotic normal distribution. More precisely, in Section 2 they provide a general description of the discrepancy and derive the theoretical asymptotic distribution of the square discrepancy of scrambled nets. Section~3 explains the procedure for fitting the empirical distribution of the square discrepancy of scrambled nets to the theoretical asymptotic distribution. Section~4 discusses the experimental results. Finally, Section~5 contains some concluding results. Furthermore, the authors discuss the variance and the empirical distribution of the square discrepancy of Owen's scrambling and a variant, linear scrambling.