Recent trends in random number and random vector generation
Annals of Operations Research
Random number generation and quasi-Monte Carlo methods
Random number generation and quasi-Monte Carlo methods
New methods for pseudorandom numbers and pseudorandom vector generation
WSC '92 Proceedings of the 24th conference on Winter simulation
On the statistical independence of nonlinear congruential pseudorandom numbers
ACM Transactions on Modeling and Computer Simulation (TOMACS)
On a new class of pseudorandom numbers for simulation methods
Journal of Computational and Applied Mathematics
Linear and inversive pseudorandom numbers for parallel and distributed simulation
PADS '98 Proceedings of the twelfth workshop on Parallel and distributed simulation
Average Discrepancy, Hyperplanes, and Compound Pseudorandom Numbers
Finite Fields and Their Applications
Average Behaviour of Compound Nonlinear Congruential Pseudorandom Numbers
Finite Fields and Their Applications
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The present paper deals with a general compound method for generating uniform pseudorandom numbers. Equidistribution and statistical independence properties of the generated sequences are studied based on the discrepancy of certain point sets. A unified approach to the analysis of the full period and of (relatively large) parts of the period is worked out, which rests on bounds for certain exponential sums over finite fields. This calculus is applied to the compound nonlinear congruential method and to the compound explicit inversive congruential method, which have been introduced recently. Known upper bounds for the discrepancy over the full period are improved and new upper bounds for the discrepancy over parts of the period are established.