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Lattice computations for random numbers
Author(s):
Raymond
Couture;
Pierre
L'Ecuyer.
Journal:
Math. Comp.
69
(2000),
757-765.
MSC (1991):
Primary 65C10
Posted:
February 24, 1999
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Abstract:
We improve on a lattice algorithm of Tezuka for the computation of the  -distribution of a class of random number generators based on finite fields. We show how this is applied to the problem of constructing, for such generators, an output mapping yielding optimal  -distribution.
References:
- 1.
- R. Couture, P. L'Ecuyer, and S. Tezuka, On the distribution of
 -dimensional vectors for simple and combined Tausworthe sequences, Math. Comp. 60 (1993), no. 202, 749-761, S11-S16. MR 93h:11085 - 2.
- M. Fushimi and S. Tezuka, The -distribution of generalized feedback shift register pseudorandom numbers, Communications of the ACM 26 (1983), no. 7, 516-523.
- 3.
- J. R. Heringa, H. W. J. Blöte, and A. Compagner, New primitive trinomials of Mersenne-exponent degrees for random-number generation, Internat. J. of Modern Phys. C 3 (1992), no. 3, 561-564. MR 94a:11118
- 4.
- P. L'Ecuyer, Maximally equidistributed combined Tausworthe generators, Math. Comp. 65 (1996), no. 213, 203-213. MR 96d:65017
- 5.
- A. K. Lenstra, Factoring multivariate polynomials over finite fields, J. Comput. System Sci. 30 (1985), 235-248. MR 87a:11124
- 6.
- K. Mahler, An analogue to Minkowski's geometry of numbers in a field of series, Ann. of Math. 42 (1941), no. 2, 488-522. MR 2:350c
- 7.
- S. Tezuka, The -dimensional distribution of combined GFSR sequences, Math. Comp. 62 (1994), no. 206, 809-817. MR 94i:65014
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Additional Information:
Raymond
Couture
Affiliation:
Département d'Informatique et de Recherche Opérationnelle, Université de Montréal, C.P. 6128, Succ. Centre-Ville, Montréal, H3C 3J7, Canada
Email:
couture@iro.umontreal.ca
Pierre
L'Ecuyer
Affiliation:
Département d'Informatique et de Recherche Opérationnelle, Université de Montréal, C.P. 6128, Succ. Centre-Ville, Montréal, H3C 3J7, Canada
Email:
lecuyer@iro.umontreal.ca
DOI:
10.1090/S0025-5718-99-01112-6
PII:
S 0025-5718(99)01112-6
Keywords:
Random number generation,
lattice structure
Received by editor(s):
April 7, 1998
Received by editor(s) in revised form:
July 24, 1998
Posted:
February 24, 1999
Additional Notes:
This work has been supported by NSERC-Canada grants no. OGP0110050 and SMF0169893 to the second author.
Copyright of article:
Copyright
2000,
American Mathematical Society
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