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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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Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License
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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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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.