Number of unitary representations of a Kazhdan group

Question

It was proved by de la Harpe, Robertson, and Valette that for a discrete group $\Gamma$ with Kazhdan's property (T), there is a constant $c$ so that the number of irreducible unitary representations of dimension $n$ is bounded by $c^{n^2}$. Lubotzky and Zuk later proved the same holds if $\Gamma$ is just assumed to have property $(\tau)$ in place of property $(T)$. My question is: Are there examples which show that this bound of $c^{n^2}$ is the best-possible upper bound?