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

(t, m, s)-nets were defined by Niederreiter [6], based on earlier work by Sobol' [7], 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 Fm 2 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-Kl?ve-Levenshtein [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)2nets based on a family of binary linear codes of minimum distance 6.

• Type: Conference
• Year: 2005
• Where: DCC
• Authors: Jürgen Bierbrauer, Yves Edel
• Keywords: Binary Linear Codes, Certain Linear Independence, Computer Graphics, DCC 2005, Quasi-monte Carlo Methods