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On the discrepancy of inversive congruential pseudorandom numbers with prime power modulus. II. (English) Zbl 0810.11043

Summary: [Part I, cf. ibid. 71, 153-161 (1991; Zbl 0727.11027).]
One of the alternatives to linear congruential pseudorandom number generators with their known deficiencies is the inversive congruential method with prime power modulus. Recently [the author, J. Comput. Appl. Math. 40, 345-349 (1992; Zbl 0761.65001)], it was proved that pairs of inversive congruential pseudorandom numbers have nice statistical independence properties. In the present paper it is shown that a similar result cannot be obtained for \(k\)-tuples with \(k\geq 3\) since their discrepancy is too large. The method of proof relies on the evaluation of certain exponential sums. In view of the present result the inversive congruential method with prime power modulus seems to be not absolutely suitable for generating uniform pseudorandom numbers.

MSC:

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

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