On the Covering Number of $U_3(q)$

The covering number, $\sigma (G)$, of a finite, noncyclic group $G$ is the least positive integer $n$ such that $G$ is the union of $n$ proper subgroups. Here we investigate the covering numbers of the projective special unitary groups $U_3(q)$, give upper and lower bounds for $\sigma (U_3(q))$ when $q \geq 7$,andshowthat$\sigma(U_3(q))$isasymptoticto$q^6/3$as$q \rightarrow \infty$.