Wolfgang.Schmid (University of Salzburg)

A highly interesting fact is the close relation to error-correcting codes and combinatorial objects. Corresponding combinatorial structures are so-called ordered orthogonal arrays (introduced in 1995) which are generalizations of orthogonal arrays.

The well-known duality between linear orthogonal arrays and linear codes carries over to the more general setting of linear ordered orthogonal arrays. This has been described by Rosenbloom and Tsfasman in 1997. They introduced the ** m**-metric, a generalization of the usual Hamming metric, and gave upper and lower bounds for the parameters of codes in this metric.

We will use this setting to deduce an improved Gilbert-Varshamov bound for linear ordered orthogonal arrays (equivalently for digital nets) and stress the basic problem of net-embeddability (``when can an
**[ s,s-m,k+1]**-code be completed to a digital

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