Let \({\mathcal{F}}\) be a (0, 1) matrix. A (0, 1) matrix \({\mathcal{M}}\) is said to have \({\mathcal{F}}\) as a configuration if there is a submatrix of \({\mathcal{M}}\) which is a row and column permutation of \({\mathcal{F}}\). We say that a matrix \({\mathcal{M}}\) is simple if it has no repeated columns. For a given \({v \in \mathbb{N}}\), we shall denote by forb\({(v, \mathcal{F})}\) the maximum number of columns in a simple (0, 1) matrix with v rows for which \({\mathcal{F}}\)
does not occur as a configuration. We say that a matrix \({\mathcal{M}}\) is maximal for
\({\mathcal{F}}\) if \({\mathcal{M}}\) has forb\({(v, \mathcal{F})}\) columns. In this paper we show that for certain natural choices of \({\mathcal{F}}\), forb\({(v, \mathcal{F})\leq\frac{\binom{v}{t}}{t+1}}\). In particular this gives an extremal characterization for Steiner t-designs as maximal (0, 1) matrices in terms of certain forbidden configurations.