A note on geometric structures of linear ordered orthogonal arrays and \((t,m,s)\)-nets of low strength
Ordered orthogonal arrays are a large family of combinatorial objects, which contain orthogonal arrays and \((t,m,s)\)-nets as subclasses. A \(q\)-ary ordered orthogonal array is linear if it forms a vector space over the field with \(q\) elements. Each \((t,m,s)\)-net projects to an ordinary orthogonal array. The embedding problem asks if a given orthogonal array can be embedded in a \((t,m,s)\)-net. In the present paper well-known embedding theorems for linear orthogonal arrays (these are just the duals of linear error-correcting codes) in the case of strenghts 3 and 4 are reproved using geometric language.
scientific article; zbMATH DE number 1785713