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

Harald Niederreiter; Chaoping Xing

Acta Arithmetica (1995)

  • Volume: 72, Issue: 3, page 281-298
  • ISSN: 0065-1036

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Harald Niederreiter, and Chaoping Xing. "Low-discrepancy sequences obtained from algebraic function fields over finite fields." Acta Arithmetica 72.3 (1995): 281-298. <http://eudml.org/doc/206796>.

@article{HaraldNiederreiter1995,
author = {Harald Niederreiter, Chaoping Xing},
journal = {Acta Arithmetica},
keywords = {net-sequences; low-discrepancy sequences; algebraic function fields; -sequences},
language = {eng},
number = {3},
pages = {281-298},
title = {Low-discrepancy sequences obtained from algebraic function fields over finite fields},
url = {http://eudml.org/doc/206796},
volume = {72},
year = {1995},
}

TY - JOUR
AU - Harald Niederreiter
AU - Chaoping Xing
TI - Low-discrepancy sequences obtained from algebraic function fields over finite fields
JO - Acta Arithmetica
PY - 1995
VL - 72
IS - 3
SP - 281
EP - 298
LA - eng
KW - net-sequences; low-discrepancy sequences; algebraic function fields; -sequences
UR - http://eudml.org/doc/206796
ER -

References

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  1. [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. Zbl0846.11044
  2. [2] H. Faure, Discrépance de suites associées à un système de numération (en dimension s), Acta Arith. 41 (1982), 337-351. Zbl0442.10035
  3. [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. Zbl0876.11042
  4. [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. Zbl0831.65018
  5. [5] R. Lidl and H. Niederreiter, Introduction to Finite Fields and Their Applications, revised ed., Cambridge Univ. Press, Cambridge, 1994. Zbl0820.11072
  6. [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. Zbl0838.65004
  7. [7] H. Niederreiter, Point sets and sequences with small discrepancy, Monatsh. Math. 104 (1987), 273-337. Zbl0626.10045
  8. [8] H. Niederreiter, Low-discrepancy and low-dispersion sequences, J. Number Theory 30 (1988), 51-70. Zbl0651.10034
  9. [9] H. Niederreiter, A combinatorial problem for vector spaces over finite fields, Discrete Math. 96 (1991), 221-228. Zbl0747.11063
  10. [10] H. Niederreiter, Random Number Generation and Quasi-Monte Carlo Methods, SIAM, Philadelphia, Penn., 1992. Zbl0761.65002
  11. [11] H. Niederreiter, Pseudorandom numbers and quasirandom points, Z. Angew. Math. Mech. 73 (1993), T648-T652. Zbl0796.11028
  12. [12] H. Niederreiter, Factorization of polynomials and some linear-algebra problems over finite fields, Linear Algebra Appl. 192 (1993), 301-328. Zbl0845.11042
  13. [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. [14] H. Stichtenoth, Algebraic Function Fields and Codes, Springer, Berlin, 1993. 

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