ON THE LATTICE STRUCTURE OF A NONLINEAR GENERATOR WITH MODULUS 2-ALPHA

Date

1990-07-24

Author

EICHENAUERHERRMANN, J
GROTHE, H
NIEDERREITER, H
TOPUZOGLU, A

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Nonlinear congruential pseudorandom number generators based on inversions have been introduced and analysed recently. These generators do not show the simple lattice structure of the widely used linear congruential generators which are too regular for certain simulation purposes. In the present paper a nonlinear congruential generator based on inversions with respect to a power of two modulus is considered. It is shown that the set of points formed by consecutive pseudorandom numbers has a more complicated lattice structure: it forms a superposition of shifted lattices. The corresponding lattice bases are explicitly determined and analysed.

Subject Keywords

Pseudorandom numbers, Nonlinear congruential method, Inversion modulo 2α, Lattice structure, Superposition of lattices

URI

https://hdl.handle.net/11511/67486

Journal

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

DOI

https://doi.org/10.1016/0377-0427(90)90338-z

Collections

Department of Mathematics, Article

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Citation Formats

J. EICHENAUERHERRMANN, H. GROTHE, H. NIEDERREITER, and A. TOPUZOGLU, “ON THE LATTICE STRUCTURE OF A NONLINEAR GENERATOR WITH MODULUS 2-ALPHA,” JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, pp. 81–85, 1990, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/67486.