Yves Edel: New families of $(t,m,s)$-nets related to BCH codes

$(t,m,s)-$nets are point sets in Euclidian $s$-space satisfying certain uniformity conditions, for use in numerical integration. They can equivalently be described in terms of ordered orthogonal arrays, a class of finite geometrical structures generalizing orthogonal arrays. This establishes a link between quasi-Monte Carlo methods and coding theory. We construct several new families of $(t,m,s)-$nets improving the known bounds on the size of $(t,m,s)-$nets. These constructions use coding-theoretic construction techniques, exploiting some of the nice properties of BCH-codes.

Bibliography

1

Jürgen Bierbrauer, Yves Edel, and Wolfgang Ch. Schmid.
Coding-theoretic constructions for $(t,m,s)$-nets and ordered orthogonal arrays.
J. Combin. Des., 10(6):403-418, 2002.

2

Harald Niederreiter.
Point sets and sequences with small discrepancy.
Monatsh. Math., 104(4):273-337, 1987.

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