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Mathematics of Computation

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Full orbit sequences in affine spaces via fractional jumps and pseudorandom number generation


Authors: Federico Amadio Guidi, Sofia Lindqvist and Giacomo Micheli
Journal: Math. Comp. 88 (2019), 2005-2025
MSC (2010): Primary 11B37, 15B33, 11T06, 11K38, 11K45, 11T23, 65C10, 37P25
DOI: https://doi.org/10.1090/mcom/3400
Published electronically: November 27, 2018
MathSciNet review: 3925495
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Abstract: Let $ n$ be a positive integer. In this paper we provide a general theory to produce full orbit sequences in the affine $ n$-dimensional space over a finite field. For $ n=1$ our construction covers the case of the Inversive Congruential Generators (ICG). In addition, for $ n>1$ we show that the sequences produced using our construction are easier to compute than ICG sequences. Furthermore, we prove that they have the same discrepancy bounds as the ones constructed using the ICG.


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Additional Information

Federico Amadio Guidi
Affiliation: Mathematical Institute, University of Oxford, Oxford, United Kingdom
Email: federico.amadio@maths.ox.ac.uk

Sofia Lindqvist
Affiliation: Mathematical Institute, University of Oxford, Oxford, United Kingdom
Email: sofia.lindqvist@maths.ox.ac.uk

Giacomo Micheli
Affiliation: Mathematical Institute, University of Oxford, Oxford, United Kingdom
Email: giacomo.micheli@maths.ox.ac.uk

DOI: https://doi.org/10.1090/mcom/3400
Keywords: Full orbit sequences, pseudorandom number generators, inversive congruential generators, discrepancy
Received by editor(s): May 8, 2018
Received by editor(s) in revised form: August 8, 2018
Published electronically: November 27, 2018
Additional Notes: The third author is the corresponding author.
The third author would like to thank the Swiss National Science Foundation grant number 171248.
Article copyright: © Copyright 2018 American Mathematical Society