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1996-1997 | 78 | 4 | 377-399
Tytuł artykułu

Bounds for digital nets and sequences

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  • Institut für Mathematik, Universität Salzburg, Hellbrunnerstraße 34, A-5020 Salzburg, Austria
  • Institut für Mathematik, Universität Salzburg, Hellbrunnerstraße 34, A-5020 Salzburg, Austria
Bibliografia
  • [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.
  • [8] H. Niederreiter, Point sets and sequences with small discrepancy, Monatsh. Math. 104 (1987), 273-337.
  • [10] H. Niederreiter, 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] 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] 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.
  • [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] W. Ch. Schmid, (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.
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Bibliografia
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