The dichromatic number $\vec{\chi }(D)$ of a digraph $D$ is the least integer $k$ such that $D$ can be partitioned into $k$ directed acyclic digraphs. A digraph is $k$-dicritical if $\vec{\chi }(D) = k$ and each proper subgraph $D^{\prime }$ of $D$ satisfies $\vec{\chi }(D^{\prime }) \leq k-1$. An oriented graph is a digraph with no directed cycle of length 2. For integers $k$ and $n$, we denote by $o_k(n)$ the minimum number of edges of a $k$-dicritical oriented graph on $n$ vertices. The main result of this paper is a proof that $o_3(n) \geq \frac{7n+2}{3}$ together with a construction witnessing that $o_3(n) \leq \lceil \frac{5n}{2} \rceil$ for all $n \geq 12$. We also give a construction showing that for all sufficiently large $n$ and all $k\geq 3$, $o_k(n) \lt (2k-3)n$, disproving a conjecture of Hoshino and Kawarabayashi.