Bounds for digital nets and sequences

Acta Arithmetica

Volumn 78, Issue 4, 1997, Pages 377-399

  Schmid, Wolfgang Ch ^a   Wolf, Reinhard ^a  

^a UNIVERSITY OF SALZBURG   (Austria)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0031537177     PISSN: 00651036     EISSN: None     Source Type: Journal    
DOI: 10.4064/aa-78-4-377-399     Document Type: Article

References (16)

1. J. Bierbrauer, Bounds on orthogonal arrays and resilient functions, J. Combin. Designs 3 (1995), 179-183.
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. R. Hill, A First Course in Coding Theory, Oxford Appl. Math. Comput. Sci. Ser., Oxford University Press, 1986.
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.
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. 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. 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.
8. B. Nashier and W. Nichols, On Steinitz properties, Arch. Math. (Basel) 57 (1991), 247-253.
9. H. Niederreiter, Point sets and sequences with small discrepancy, Monatsh. Math. 104 (1987), 273-337.
10. -, Random Number Generation and Quasi-Monte Carlo Methods, CBMS-NSF Ser. in Appl. Math. 63, SIAM, Philadelphia, 1992.
11. H. Niederreiter and C. P. Xing, Low-discrepancy sequences obtained from algebraic function fields over finite fields, Acta Arith. 72 (1995), 281-298.
12. -, -, Low-discrepancy sequences and global function fields with many rational places, Finite Fields Appl. 2 (1996), 241-273.
13. -, -, 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.
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. -, (t, m, s)-nets: digital construction and combinatorial aspects, PhD thesis, Institut für Mathematik, Universität Salzburg, May 1995.
16. J. H. van Lint, Introduction to Coding Theory, Springer, Berlin, 1992.