Download PDF - Low-discrepancy sequences obtained from algebraic function fields over finite fieldsAll rights reserved. Copyright exceptions and limitations apply

ArticleOriginal scientific text

Title

Low-discrepancy sequences obtained from algebraic function fields over finite fields

Authors 1, 2

Affiliations

  1. Institut für Informationsverarbeitung, Österreichische Akademie, der Wissenschaften, Sonnenfelsgasse 19, A-1010 Wien, Austria
  2. Department of Mathematics, University of Science and Technology of China, Hefei, Anhui 230026, P.R. China

Bibliography

  1. P. Bratley, B. L. Fox and H. Niederreiter, Implementation and tests of low-discrepancy sequences, ACM Trans. Model. Comput. Simulation 2 (1992), 195-213.
  2. H. Faure, Discrépance de suites associées à un système de numération (en dimension s), Acta Arith. 41 (1982), 337-351.
  3. G. Larcher, H. Niederreiter and W. C. Schmid, Digital nets and sequences constructed over finite rings and their application to quasi-Monte Carlo integration, Monatsh. Math., to appear.
  4. G. Larcher and W. C. Schmid, Multivariate Walsh series, digital nets and quasi-Monte Carlo integration, in: Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing, H. Niederreiter and P. J.-S. Shiue (eds.), Lecture Notes in Statist., Springer, Berlin, to appear.
  5. R. Lidl and H. Niederreiter, Introduction to Finite Fields and Their Applications, revised ed., Cambridge Univ. Press, Cambridge, 1994.
  6. G. L. Mullen, A. Mahalanabis and H. Niederreiter, Tables of (t,m,s)-net and (t,s)-sequence parameters, in: Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing, H. Niederreiter and P. J.-S. Shiue (eds.), Lecture Notes in Statist., Springer, Berlin, to appear.
  7. H. Niederreiter, Point sets and sequences with small discrepancy, Monatsh. Math. 104 (1987), 273-337.
  8. H. Niederreiter, Low-discrepancy and low-dispersion sequences, J. Number Theory 30 (1988), 51-70.
  9. H. Niederreiter, A combinatorial problem for vector spaces over finite fields, Discrete Math. 96 (1991), 221-228.
  10. H. Niederreiter, Random Number Generation and Quasi-Monte Carlo Methods, SIAM, Philadelphia, Penn., 1992.
  11. H. Niederreiter, Pseudorandom numbers and quasirandom points, Z. Angew. Math. Mech. 73 (1993), T648-T652.
  12. H. Niederreiter, Factorization of polynomials and some linear-algebra problems over finite fields, Linear Algebra Appl. 192 (1993), 301-328.
  13. I. M. Sobol', The distribution of points in a cube and the approximate evaluation of integrals, Zh. Vychisl. Mat. i Mat. Fiz. 7 (1967), 784-802 (in Russian).
  14. H. Stichtenoth, Algebraic Function Fields and Codes, Springer, Berlin, 1993.
Acta Arithmetica
1995/72/3
Export to PBN, Opens in new tab
Pages:
281-298
Main language of publication
English
Received
1995-01-24
Published
1995
Exact and natural sciences