Pseudorandom vector generation by the inversive method
ACM Transactions on Modeling and Computer Simulation (TOMACS)
Digital inversive pseudorandom numbers
ACM Transactions on Modeling and Computer Simulation (TOMACS)
Compound inversive congruential pseudorandom numbers: an average-case analysis
Mathematics of Computation
On the distribution of inversive congruential pseudorandom numbers in parts of the period
Mathematics of Computation
On the distribution of the power generation
Mathematics of Computation
On the Distribution of Nonlinear Recursive Congruential Pseudorandom Numbers of Higher Orders
AAECC-13 Proceedings of the 13th International Symposium on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
Iterations of Multivariate Polynomials and Discrepancy of Pseudorandom Numbers
AAECC-14 Proceedings of the 14th International Symposium on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
Average Discrepancy, Hyperplanes, and Compound Pseudorandom Numbers
Finite Fields and Their Applications
The Period Lengths of Inversive Pseudorandom Vector Generations
Finite Fields and Their Applications
On the Distribution and Lattice Structure of Nonlinear Congruential Pseudorandom Numbers
Finite Fields and Their Applications
SETA '08 Proceedings of the 5th international conference on Sequences and Their Applications
Inversive pseudorandom numbers over Galois rings
European Journal of Combinatorics
Dynamical systems generated by rational functions
AAECC'03 Proceedings of the 15th international conference on Applied algebra, algebraic algorithms and error-correcting codes
Recent results on recursive nonlinear pseudorandom number generators
SETA'10 Proceedings of the 6th international conference on Sequences and their applications
Pseudorandom vector sequences derived from triangular polynomial systems with constant multipliers
WAIFI'10 Proceedings of the Third international conference on Arithmetic of finite fields
On the power generator and its multivariate analogue
Journal of Complexity
Multivariate permutation polynomial systems and nonlinear pseudorandom number generators
Finite Fields and Their Applications
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The inversive congruential method is an attractive alternative to the classical linear congruential method for pseudorandom number generation. The authors have recently introduced a new method for obtaining nontrivial upper bounds on the multidimensional discrepancy of inversive congruential pseudorandom numbers in parts of the period. This method has also been used to study the multidimensional distribution of several other similar families of pseudorandom numbers. Here we apply this method to show that, ''on average'' over all initial values, much stronger results than those known for ''individual'' sequences can be obtained.