Efficient algorithms for computing the L2-discrepancy
Mathematics of Computation
Monte Carlo Variance of Scrambled Net Quadrature
SIAM Journal on Numerical Analysis
The weighted spectral test: diaphony
ACM Transactions on Modeling and Computer Simulation (TOMACS) - Special issue on uniform random number generation
A generalized discrepancy and quadrature error bound
Mathematics of Computation
Fourier Analysis of Uniform Random Number Generators
Journal of the ACM (JACM)
Testing multivariate uniformity and its applications
Mathematics of Computation
Parallel linear congruential generators with Sophie-Germain moduli
Parallel Computing
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This paper presents the limit laws of discrepancies defined via exponential sums, and algorithms (with error bounds) to approximate the corresponding distribution functions. The results cover the weighted and the nonweighted spectral test of Hellekalek and various instances of the general discrepancies of Hiekernell and Hoogland and Kleiss for the exponential function system, as well as classical quantities like the spectral test, diaphony, and the Zaremba figure of merit.