An Asymptotic Gilber-Varshamov Bound for (t,m,s)-nets

(t, m, s)-nets are point sets in Euclidean s-space satisfying certain uniformity conditions, for use in numerical integration. They can be equivalently 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. In the present paper we prove an asymptotic Gilbert-Varshamov bound for linear nets and compare it to the algebraic-geometric net construction.