  This article provides bounds on the size of a 3-uniform linear hypergraph
with restricted matching number and maximum degree. In particular, we show that
if a 3-uniform, linear family $\mathcal{F}$ has maximum matching size $\nu$ and
maximum degree $\Delta$ such that $\Delta\geq
\frac{23}{6}\nu(1+\frac{1}{\nu-1})$, then $|\mathcal{F}|\leq \Delta \nu$.
