Abstract
Let {x n } be pseudorandom numbers inI=[0,1) of the maximal period, generated by the modified inversive method with modulusM, M=2α. We show that, for anys≥2, the set of all nonoverlappings-tuples X ns =(x ns ,x ns +1, ...,x ns +s−1) ∈I s,n=0,1, ..., (M/2)−1, is the same as the intersection ofI s with a union of some number of grids with explicitly known shift vectors and lattice bases. Our arguments follow closely those in the paper by Eichnauer-Herrmann, Grothe, Niederreiter and Topuzoglu.
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Kato, T., Wu, LM. & Yanagihara, N. On the lattice structure of pseudo random numbers generated by the modified inversive congruential generator with modulus 2α . Japan J. Indust. Appl. Math. 14, 33–38 (1997). https://doi.org/10.1007/BF03167308
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DOI: https://doi.org/10.1007/BF03167308