On the distribution of pseudorandom numbers and vectors generated by inversive methods
Inversive methods are attractive alternatives to linear methods for pseudorandom number generation. A particular attractive method is the digital inversive method introduced by \textit{J. Eichenauer-Herrmann} and \textit{H. Niederreiter} [ACM Trans. Model. Comput. Simul. 4, 339-349 (1994; Zbl 0847.11038)]. Extending their method in [Math. Comput. 70, 1569-1574 (2001; Zbl 0983.11048)] the authors prove bounds on the discrepancy of sequences of digital inversive pseudorandom numbers and inversive pseudorandom vectors in parts of the period. The proofs are based on a new bound for certain exponential sums. Similar results were obtained on the digital explicit inversive method in \textit{H. Niederreiter} and \textit{A. Winterhof} [Acta Arith. 93, 387-399 (2000; Zbl 0969.11040)] and \textit{M. B. Levin} [Math. Slovaca 50, 581-598 (2000; Zbl 0990.65005)], the compound inversive method in \textit{H. Niederreiter} and \textit{A. Winterhof} [Monatsh. Math. 132, 35-48 (2001; Zbl 0983.11047)], and the inversive congruential method with odd prime power modulus in \textit{H. Niederreiter} and \textit{I. E. Shparlinski} [Acta Arith. 92, 89-98 (2000; Zbl 0949.11036)]. For a recent survey paper on this topic see \textit{H. Niederreiter} and \textit{I. E. Shparlinski} [Fang, Kai-Tai (ed.) et al., Monte Carlo and quasi-Monte Carlo methods 2000. Proceedings of a conference, Hong Kong Baptist Univ., Hong Kong SAR, China, 2000. Berlin, Springer, 86-102 (2002; Zbl 1076.65008)].
scientific article; zbMATH DE number 1441260