  A mixed graph is said to be dense if its order is close to the Moore bound
and it is optimal if there is not a mixed graph with the same parameters and
bigger order.
  We present a construction that provides dense mixed graphs of undirected
degree $q$, directed degree $\frac{q-1}{2}$ and order $2q^2$, for $q$ being an
odd prime power. Since the Moore bound for a mixed graph with these parameters
is equal to $\frac{9q^2-4q+3}{4}$ the defect of these mixed graphs is
$({\frac{q-2}{2}})^2-\frac{1}{4}$.
  In particular we obtain a known mixed Moore graph of order $18$, undirected
degree $3$ and directed degree $1$ called Bos\'ak's graph and a new mixed graph
of order $50$, undirected degree $5$ and directed degree $2$, which is proved
to be optimal.
