Fix integers $k \ge 2$ and $\lambda \ge 1$. For all sufficiently large integers $v$ satisfying the necessary divisibility conditions \begin{align*} \lambda(v-1) \equiv 0 \pmod{k-1}, \end{align*} and \begin{align*} \lambda v(v-1) \equiv 0 \pmod{k(k-1)}, \end{align*} there exists a balanced incomplete block design with parameters $(v,b,r,k,\lambda)$, where \begin{align*} r=\frac{\lambda(v-1)}{k-1}, \qquad b=\frac{\lambda v(v-1)}{k(k-1)}. \end{align*}