Sphere-packings, lattices, and groups
Sphere-packings, lattices, and groups
A search for good multiple recursive random number generators
ACM Transactions on Modeling and Computer Simulation (TOMACS)
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
Mersenne twister: a 623-dimensionally equidistributed uniform pseudo-random number generator
ACM Transactions on Modeling and Computer Simulation (TOMACS) - Special issue on uniform random number generation
Tables of linear congruential generators of different sizes and good lattice structure
Mathematics of Computation
Tables of maximally equidistributed combined LFSR generators
Mathematics of Computation
On the performance of birthday spacings tests with certain families of random number generators
Mathematics and Computers in Simulation - IMACS sponsored Special issue on the second IMACS seminar on Monte Carlo methods
Fast combined multiple recursive generators with multipliers of the form a = ±2q ±2r
Proceedings of the 32nd conference on Winter simulation
Efficient and portable multiple recursive generators of large order
ACM Transactions on Modeling and Computer Simulation (TOMACS)
TestU01: A C library for empirical testing of random number generators
ACM Transactions on Mathematical Software (TOMS)
Comparison of Point Sets and Sequences for Quasi-Monte Carlo and for Random Number Generation
SETA '08 Proceedings of the 5th international conference on Sequences and Their Applications
Large-Order Multiple Recursive Generators with Modulus 231-1
INFORMS Journal on Computing
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We study the structure and point out weaknesses of recently proposed random number generators based on special types of linear recurrences with small coefficients, which allow fast implementations. Our theoretical analysis is complemented by the results of simple empirical statistical tests that the generators fail decisively. Directions for improvement and alternative generators are also pointed out.