Eichenauer-Herrmann, Jürgen; Grothe, Holger; Niederreiter, Harald; Topuzoǧlu, Alev On the lattice structure of a nonlinear generator with modulus \(2^{\alpha}\). (English) Zbl 0702.65006 J. Comput. Appl. Math. 31, No. 1, 81-85 (1990). Let \(Z_ m=\{0,1,...,m-1\}\), \(Z^*_{2^{\alpha}}=\{1,3,...,2^{\alpha}-1\}\) for m,\(\alpha\in N\). Define a nonlinear generator by \(x_{n+1}\equiv ax_ n^{-1}+b(mod 2^{\alpha})\) (1), \(n\geq 0\), where \(x^{-1}\) is the unique element in \(Z^*_{2^{\alpha}}\) with x \(x^{-1}\equiv 1 mod(2^{\alpha})\) for \(x\in Z^*_{2^{\alpha}}\) and \(x_ 0\in Z^*_{2^{\alpha}}\). Assumptions such that (1) has maximal period length \(2^{\alpha -1}\) are given. It is proved that the set of consecutive pseudorandom numbers forms a superposition of shifted lattices. The lattice bases are determined. Reviewer: W.Grecksch Cited in 15 Documents MSC: 65C10 Random number generation in numerical analysis Keywords:nonlinear pseudorandom numbers; lattice structure; superposition of shifted lattices PDFBibTeX XMLCite \textit{J. Eichenauer-Herrmann} et al., J. Comput. Appl. Math. 31, No. 1, 81--85 (1990; Zbl 0702.65006) Full Text: DOI References: [1] Eichenauer, J.; Lehn, J., On the structure of quadratic congruential sequences, Manuscripta Math., 58, 129-140 (1987) · Zbl 0598.65004 [2] Eichenauer, J.; Lehn, J.; Topuzoǧlu, A., A nonlinear congruential pseudorandom number generator with power of two modulus, Math. Comp., 51, 757-759 (1988) · Zbl 0701.65008 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.