\] Let $M$ be a $q$-PMD induced by a $q$-Steiner system with blocks $\mathcal{B}$. Let $\mathcal{C}_{t+0}$ be the collection of all circuits of $M$ of dimension $(t+0)$. Then $\mathcal{C}_{t+0}$ are the blocks of a $t$-$(n,t+0,\lambda_{\mathcal{C}_{t+0}})$ design where $$\lambda_{\mathcal{C}_{t+0}}=q^{k-t}{\left[\begin{matrix} n-k \\ 0 \end{matrix} \right]_{q}}\left( {\left[\begin{matrix} n-t-0 \\ 0 \end{matrix} \right]_{q}}-\frac{0}{q}{\left[\begin{matrix} k-t \\ 0 \end{matrix} \right]_{q}}{\left[\begin{matrix} t+0 \\ 0 \end{matrix} \right]_{q}}\right)\frac{0}{q+0}.$$  