Bounds for digital nets and sequences

Wolfgang Ch. Schmid; Reinhard Wolf

Acta Arithmetica (1997)

  • Volume: 78, Issue: 4, page 377-399
  • ISSN: 0065-1036

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Wolfgang Ch. Schmid, and Reinhard Wolf. "Bounds for digital nets and sequences." Acta Arithmetica 78.4 (1997): 377-399. <http://eudml.org/doc/206957>.

@article{WolfgangCh1997,
author = {Wolfgang Ch. Schmid, Reinhard Wolf},
journal = {Acta Arithmetica},
keywords = {digital -sequences; low-discrepancy sequences; quasi-Monte Carlo methods; digital -nets; methods of linear combinations; low-discrepancy point sets; -dimensional unit cube; lower and upper bounds; quality parameter; propagation rules; dimension of digital nets; construction; linear codes},
language = {eng},
number = {4},
pages = {377-399},
title = {Bounds for digital nets and sequences},
url = {http://eudml.org/doc/206957},
volume = {78},
year = {1997},
}

TY - JOUR
AU - Wolfgang Ch. Schmid
AU - Reinhard Wolf
TI - Bounds for digital nets and sequences
JO - Acta Arithmetica
PY - 1997
VL - 78
IS - 4
SP - 377
EP - 399
LA - eng
KW - digital -sequences; low-discrepancy sequences; quasi-Monte Carlo methods; digital -nets; methods of linear combinations; low-discrepancy point sets; -dimensional unit cube; lower and upper bounds; quality parameter; propagation rules; dimension of digital nets; construction; linear codes
UR - http://eudml.org/doc/206957
ER -

References

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  1. [1] J. Bierbrauer, Bounds on orthogonal arrays and resilient functions, J. Combin. Designs 3 (1995), 179-183. Zbl0886.05034
  2. [2] A. E. Brouwer, Data base of bounds for the minimum distance for binary, ternary and quaternary codes, URL http://www.win.tue.nl/win/math/dw/voorlincod.html. 
  3. [3] R. Hill, A First Course in Coding Theory, Oxford Appl. Math. Comput. Sci. Ser., Oxford University Press, 1986. Zbl0616.94006
  4. [4] G. Larcher, H. Niederreiter, and W. Ch. Schmid, Digital nets and sequences constructed over finite rings and their application to quasi-Monte Carlo integration, Monatsh. Math. 121 (1996), 231-253. Zbl0876.11042
  5. [5] G. Larcher, W. Ch. Schmid, and R. Wolf, Digital (t,m,s)-nets, digital (T,s)-sequences, and numerical integration of multivariate Walsh series, in: P. Hellekalek, G. Larcher, and P. Zinterhof (eds.), Proc. 1st Salzburg Minisymposium on Pseudorandom Number Generation and Quasi-Monte Carlo Methods, Salzburg, 1994, Technical Report Ser. 95-4, Austrian Center for Parallel Computation, 1995, 75-107. 
  6. [6] M. Lawrence, Combinatorial bounds and constructions in the theory of uniform point distributions in unit cubes, connections with orthogonal arrays and a poset generalization of a related problem in coding theory, PhD thesis, University of Wisconsin, May 1995. 
  7. [7] M. Lawrence, A. Mahalanabis, G. L. Mullen, and W. Ch. Schmid, Construction of digital (t,m,s)-nets from linear codes, in: S. D. Cohen and H. Niederreiter (eds.), Finite Fields and Applications (Glasgow, 1995), London Math. Soc. Lecture Note Ser. 233, Cambridge University Press, Cambridge, 1996, 189-208. Zbl0869.11060
  8. [8] B. Nashier and W. Nichols, On Steinitz properties, Arch. Math. (Basel) 57 (1991), 247-253. Zbl0766.16005
  9. [8] H. Niederreiter, Point sets and sequences with small discrepancy, Monatsh. Math. 104 (1987), 273-337. Zbl0626.10045
  10. [10] H. Niederreiter, Random Number Generation and Quasi-Monte Carlo Methods, CBMS-NSF Ser. in Appl. Math. 63, SIAM, Philadelphia, 1992. 
  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, Finite Fields Appl. 2 (1996), 241-273. 
  13. [13] H. Niederreiter and C. P. Xing, Quasirandom points and global function fields, in: S. D. Cohen and H. Niederreiter (eds.), Finite Fields and Applications (Glasgow, 1995), London Math. Soc. Lecture Note Ser. 233, Cambridge University Press, Cambridge, 1996, 269-296. Zbl0932.11050
  14. [14] W. Ch. Schmid, Shift-nets: a new class of binary digital (t,m,s)-nets, submitted to Proceedings of the Second International Conference on Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing, 1996. 
  15. [15] W. Ch. Schmid, (t,m,s)-nets: digital construction and combinatorial aspects, PhD thesis, Institut für Mathematik, Universität Salzburg, May 1995. 
  16. [16] J. H. van Lint, Introduction to Coding Theory, Springer, Berlin, 1992. 

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