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ArticleOriginal scientific text

Title

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

Authors 1

Affiliations

  1. Institut für Mathematik, Universität Salzburg, Hellbrunnerstr. 34, A-5020 Salzburg, Austria

Bibliography

  1. T. G. Lewis and W. H. Payne, Generalized feedback shift register pseudorandom number algorithm, J. Assoc. Comput. Mach. 20 (1973), 456-468.
  2. H. Niederreiter, Point sets and sequences with small discrepancy, Monatsh. Math. 104 (1987), 273-337.
  3. H. Niederreiter, The serial test for digital k-step pseudorandom numbers, Math. J. Okayama Univ. 30 (1988), 93-119.
  4. H. Niederreiter, Random Number Generation and Quasi-Monte Carlo Methods, CBMS-NSF Regional Conf. Ser. in Appl. Math. 63, SIAM, Philadelphia, 1992.
  5. H. Niederreiter, Factorization of polynomials and some linear-algebra problems over finite fields, Linear Algebra Appl. 192 (1993), 301-328.
  6. H. Niederreiter, The multiple recursive matrix method for pseudorandom number generation, Finite Fields Appl. 1 (1995), 3-30.
  7. H. Niederreiter, Improved bounds in the multiple-recursive matrix method for pseudorandom number and vector generation, Finite Fields Appl. 2 (1996), 225-240.
  8. H. Niederreiter and C. P. Xing, Low-discrepancy sequences obtained from algebraic function fields over finite fields, Acta Arith. 72 (1995), 281-298.
  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. 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.
  11. K. F. Roth, On irregularities of distribution, Mathematika 1 (1954), 73-79.
  12. W. M. Schmidt, Irregularities of distribution, VII, Acta Arith. 21 (1972), 45-50.
  13. R. C. Tausworthe, Random numbers generated by linear recurrence modulo two, Math. Comp. 19 (1965), 201-209.
Acta Arithmetica
1998/83/1
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Pages:
1-15
Main language of publication
English
Received
1996-10-08
Accepted
1997-04-04
Published
1998
Exact and natural sciences