Lower bounds for the discrepancy of inversive congruential pseudorandom numbers
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- by Harald Niederreiter PDF
- Math. Comp. 55 (1990), 277-287 Request permission
Abstract:
The inversive congruential method is a uniform pseudorandom number generator which was introduced recently. For a prime modulus p the discrepancy $D_p^{(k)}$ of k-tuples of successive pseudorandom numbers generated by this method determines the statistical independence properties of these pseudorandom numbers. It was shown earlier by the author that \[ D_p^{(k)} = O({p^{ - 1/2}}{(\log p)^k})\quad {\text {for}}\;2 \leq k < p.\] Here it is proved that this bound is essentially best possible. In fact, for a positive proportion of the admissible parameters in the inversive congruential method the discrepancy $D_p^{(k)}$ is at least of the order of magnitude ${p^{ - 1/2}}$ for all $k \geq 2$.References
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Additional Information
- © Copyright 1990 American Mathematical Society
- Journal: Math. Comp. 55 (1990), 277-287
- MSC: Primary 65C10; Secondary 11K45
- DOI: https://doi.org/10.1090/S0025-5718-1990-1023766-0
- MathSciNet review: 1023766