Designs, Codes and Cryptography, 37 (2005), 211-214.
(t,m,s)-nets were defined by Niederreiter, based on earlier work by Sobol, 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 GF(2)m 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-Klove-Levenshtein 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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