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A Family of Binary (t, m,s)-Nets of Strength 5

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Abstract

(t,m,s)-Nets were defined by Niederreiter [Monatshefte fur Mathematik, Vol. 104 (1987) pp. 273–337], based on earlier work by Sobol’ [Zh. Vychisl Mat. i mat. Fiz, Vol. 7 (1967) pp. 784–802], in the context of quasi-Monte Carlo methods of numerical integration. Formulated in combinatorial/coding theoretic terms a binary linear (m−k,m,s)2-net is a family of ks vectors in F m2 satisfying certain linear independence conditions (s is the length, m the dimension and k the strength: certain subsets of k vectors must be linearly independent). Helleseth et al. [5] recently constructed (2r−3,2r+2,2r−1)2-nets for every r. In this paper, we give a direct and elementary construction for (2r−3,2r+2,2r+1)2-nets based on a family of binary linear codes of minimum distance 6.

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References

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Authors and Affiliations

  1. Department of Mathematical Sciences, Michigan Technological University, Houghton, MI, 49931, USA

    Jürgen Bierbrauer

  2. Mathematisches Institut der Universität, Im Neuenheimer Feld 288, 69120, Heidelberg, Germany

    Yves Edel

Authors
  1. Jürgen Bierbrauer
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  2. Yves Edel
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Correspondence to Jürgen Bierbrauer.

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Communicated by: T. Helleseth

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Bierbrauer, J., Edel, Y. A Family of Binary (t, m,s)-Nets of Strength 5. Des Codes Crypt 37, 211–214 (2005). https://doi.org/10.1007/s10623-004-3986-0

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  • DOI: https://doi.org/10.1007/s10623-004-3986-0

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