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

Abstract

Owen proposed a method of scrambling ( t, m, s)-nets to eliminate statistical bias while retaining the low discrepancy property. Recently a central limit theorem has been proved for scrambled net quadrature. This article compares the empirical distribution of the square discrepancy of scrambled digital ( t, m, s)-nets with the theoretical asymptotic distribution suggested by the central limit theorem. Furthermore this article discusses the variance and the empirical distribution of the square discrepancy of Owen’s scrambling and a variant, linear scrambling.