The theory of digital \((t, m, s)\)-nets provides powerful tools for the construction of low-discrepancy point sets in the \(s\)-dimensional unit cube. In this paper the duality theory for digital nets developed recently by \textit{H. Niederreiter} and \textit{G. Pirsic} [Acta Arith. 97, 173-182 (2001; Zbl 0972.11066)] is applied to establish a new propagation rule for digital nets. Furthermore, the authors construct families of digital \((t, m, s)\)-nets with the property that if \(m-t\) is fixed and the dimension \(s\) tends to \(\infty\), then the quality parameter \(t\) grows at the minimal rate.