Families of nets of low and medium strength,

Integers: Electronic Journal of Combinatorial Number Theory , 5(3) (2005).

Abstract:

The theory of primitive BCH-codes is used to construct linear tms-nets. The codes provide explicit descriptions of ordered orthogonal arrays of low depth. In most cases a Gilbert-Varshamov theorem guarantees the existence of the net. In certain favorable circumstances we obtain explicit descriptions of the nets. Among others the following binary nets are constructed

• (3r-5,3r+1,2^r-1)₂
• (3r-5,3r+2,2^r-1)₂
• (5r-8,5r,2^r-1)₂
• (5r-8,5r+1,2^r-1)₂ for r <= 8 and (5r-7,5r+2,2^r-1)₂ for all r.

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