A bound for the discrepancy of digital nets and its application to the analysis of certain pseudo-random number generators

Gerhard Larcher

Acta Arithmetica (1998)

  • Volume: 83, Issue: 1, page 1-15
  • ISSN: 0065-1036

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Gerhard Larcher. "A bound for the discrepancy of digital nets and its application to the analysis of certain pseudo-random number generators." Acta Arithmetica 83.1 (1998): 1-15. <http://eudml.org/doc/207103>.

@article{GerhardLarcher1998,
author = {Gerhard Larcher},
journal = {Acta Arithmetica},
keywords = {low-discrepancy sequences; discrepancy estimate for digital nets; pseudo-random number generators},
language = {eng},
number = {1},
pages = {1-15},
title = {A bound for the discrepancy of digital nets and its application to the analysis of certain pseudo-random number generators},
url = {http://eudml.org/doc/207103},
volume = {83},
year = {1998},
}

TY - JOUR
AU - Gerhard Larcher
TI - A bound for the discrepancy of digital nets and its application to the analysis of certain pseudo-random number generators
JO - Acta Arithmetica
PY - 1998
VL - 83
IS - 1
SP - 1
EP - 15
LA - eng
KW - low-discrepancy sequences; discrepancy estimate for digital nets; pseudo-random number generators
UR - http://eudml.org/doc/207103
ER -

References

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  1. [1] T. G. Lewis and W. H. Payne, Generalized feedback shift register pseudorandom number algorithm, J. Assoc. Comput. Mach. 20 (1973), 456-468. Zbl0266.65009
  2. [2] H. Niederreiter, Point sets and sequences with small discrepancy, Monatsh. Math. 104 (1987), 273-337. Zbl0626.10045
  3. [3] H. Niederreiter, The serial test for digital k-step pseudorandom numbers, Math. J. Okayama Univ. 30 (1988), 93-119. Zbl0666.65003
  4. [4] H. Niederreiter, Random Number Generation and Quasi-Monte Carlo Methods, CBMS-NSF Regional Conf. Ser. in Appl. Math. 63, SIAM, Philadelphia, 1992. 
  5. [5] H. Niederreiter, Factorization of polynomials and some linear-algebra problems over finite fields, Linear Algebra Appl. 192 (1993), 301-328. Zbl0845.11042
  6. [6] H. Niederreiter, The multiple recursive matrix method for pseudorandom number generation, Finite Fields Appl. 1 (1995), 3-30. Zbl0823.11041
  7. [7] H. Niederreiter, Improved bounds in the multiple-recursive matrix method for pseudorandom number and vector generation, Finite Fields Appl. 2 (1996), 225-240. Zbl0893.11031
  8. [8] H. Niederreiter and C. P. Xing, Low-discrepancy sequences obtained from algebraic function fields over finite fields, Acta Arith. 72 (1995), 281-298. Zbl0833.11035
  9. [9] H. Niederreiter and C. P. Xing, Low-discrepancy sequences and global function fields with many rational places, Finite Fields Appl. 2 (1996), 241-273. 
  10. [10] H. Niederreiter and C. P. Xing, Quasirandom points and global function fields, in: S. Cohen and H. Niederreiter (eds.), Finite Fields and Applications (Glasgow, 1995), London Math. Soc. Lecture Note Ser. 233, Cambridge Univ. Press, Cambridge, 1996, 269-296. Zbl0932.11050
  11. [11] K. F. Roth, On irregularities of distribution, Mathematika 1 (1954), 73-79. Zbl0057.28604
  12. [12] W. M. Schmidt, Irregularities of distribution, VII, Acta Arith. 21 (1972), 45-50. Zbl0244.10035
  13. [13] R. C. Tausworthe, Random numbers generated by linear recurrence modulo two, Math. Comp. 19 (1965), 201-209. Zbl0137.34804

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