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Lower bounds for the discrepancy of inversive congruential pseudorandom numbers with power of two modulus. (English) Zbl 0762.65001
The discrepancy $$D_{m/2}^{(k)}$$ of $$k$$-tuples of consecutive pseudorandom numbers generated by the inversive congruential method with modulus $$m=2^ \omega$$ with maximum period length $$m/2$$ is studied. It is shown that for a given modulus $$m$$ there exist multipliers in the inversive congruential method such that $$D_{m/2}^{(k)}$$ is at least of the order of magnitude $$m^{-1/2}$$ for all dimensions $$k\geq 2$$ and all increments $$b$$. Therefore, the upper bound $$D_{m/2}^{(2)}=O(m^{-1/2}(\log m)^ 2)$$ is in general best possible up to the logarithmic factor.
Reviewer: V.Burjan (Praha)

##### MSC:
 65C10 Random number generation in numerical analysis 11K45 Pseudo-random numbers; Monte Carlo methods
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##### References:
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