An effective upper bound for anti-canonical volumes of singular Fano threefolds

For a real number $0<\epsilon <1\mathrm{/}3$, we show that the anti-canonical volume of an $\epsilon$-klt Fano $3$-fold is at most $3200\mathrm{/}{\epsilon }^4$ and the order $O(1\mathrm{/}{\epsilon }^4)$ is sharp.