A construction of low-discrepancy sequences using global function fields

Chaoping Xing; Harald Niederreiter

Acta Arithmetica (1995)

  • Volume: 73, Issue: 1, page 87-102
  • ISSN: 0065-1036

How to cite

top

Chaoping Xing, and Harald Niederreiter. "A construction of low-discrepancy sequences using global function fields." Acta Arithmetica 73.1 (1995): 87-102. <http://eudml.org/doc/206812>.

@article{ChaopingXing1995,
author = {Chaoping Xing, Harald Niederreiter},
journal = {Acta Arithmetica},
keywords = {construction of low-discrepancy sequences; digital -sequence; global function fields},
language = {eng},
number = {1},
pages = {87-102},
title = {A construction of low-discrepancy sequences using global function fields},
url = {http://eudml.org/doc/206812},
volume = {73},
year = {1995},
}

TY - JOUR
AU - Chaoping Xing
AU - Harald Niederreiter
TI - A construction of low-discrepancy sequences using global function fields
JO - Acta Arithmetica
PY - 1995
VL - 73
IS - 1
SP - 87
EP - 102
LA - eng
KW - construction of low-discrepancy sequences; digital -sequence; global function fields
UR - http://eudml.org/doc/206812
ER -

References

top
  1. [1] H. Faure, Discrépance de suites associées à un système de numération (en dimension s ), Acta Arith. 41 (1982), 337-351. Zbl0442.10035
  2. [2] A. Garcia and H. Stichtenoth, A tower of Artin-Schreier extensions of function fields attaining the Drinfeld-Vladut bound, Invent. Math., to appear. Zbl0822.11078
  3. [3] G. Larcher and H. Niederreiter, Generalized (t,s)-sequences, Kronecker-type sequences, and diophantine approximations of formal Laurent series, Trans. Amer. Math. Soc. 347 (1995), 2051-2073. Zbl0829.11039
  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] 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, Berli, to appear. Zbl0838.65004
  6. [6] H. Niederreiter, Point sets and sequences with small discrepancy, Monatsh. Math. 104 (1987), 273-337. Zbl0626.10045
  7. [7] H. Niederreiter, Low-discrepancy and low-dispersion sequences, J. Number Theory 30 (1988), 51-70. Zbl0651.10034
  8. [8] H. Niederreiter, Random Number Generation and Quasi-Monte Carlo Methods, SIAM, Philadelphia, Penn., 1992. 
  9. [9] H. Niederreiter, Pseudorandom numbers and quasirandom points, Z. Angew. Math. Mech. 73 (1993), T648-T652. Zbl0796.11028
  10. [10] H. Niederreiter, Factorization of polynomials and some linear-algebra problems over finite fields, Linear Algebra Appl. 192 (1993), 301-328. Zbl0845.11042
  11. [11] 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
  12. [12] H. Niederreiter and C. P. Xing, Low-discrepancy sequences and global function fields with many rational places, preprint, 1995. 
  13. [13] J.-P. Serre, Sur le nombre des points rationnels d'une courbe algébrique sur un corps fini, C. R. Acad. Sci. Paris Sér. I Math. 296 (1983), 397-402. Zbl0538.14015
  14. [14] 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). 
  15. [15] H. Stichtenoth, Algebraic Function Fields and Codes, Springer, Berlin, 1993. 
  16. [16] S. Tezuka, Polynomial arithmetic analogue of Halton sequences, ACM Trans. Model. Comput. Simulation 3 (1993), 99-107. Zbl0846.11045

Citations in EuDML Documents

top
  1. Harald Niederreiter, Chaoping Xing, Explicit global function fields over the binary field with many rational places
  2. Harald Niederreiter, Chaoping Xing, Global function fields with many rational places over the ternary field
  3. Harald Niederreiter, Chaoping Xing, Cyclotomic function fields, Hilbert class fields, and global function fields with many rational places
  4. Harald Niederreiter, Chaoping Xing, Drinfeld modules of rank 1 and algebraic curves with many rational points. II

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.