  We use finite incident structures to construct new infinite families of
directed strongly regular graphs with parameters \[(l(q-1)q^l,\ l(q-1)q^{l-1},\
(lq-l+1)q^{l-2},\ (l-1)(q-1)q^{l-2},\ (lq-l+1)q^{l-2})\] for integers $q$ and
$l$ ($q, l\ge 2$), and \[(lq^2(q-1),\ lq(q-1),\ lq-l+1,\ (l-1)(q-1),\ lq-l+1)\]
for all prime powers $q$ and $l\in \{1, 2,..., q\}$. The new graphs given by
these constructions have parameters $(36, 12, 5, 2, 5)$, $(54, 18, 7, 4, 7)$,
$(72, 24, 10, 4, 10)$, $(96, 24, 7, 3, 7)$, $(108, 36, 14, 8, 14)$ and $(108,
36, 15, 6, 15)$ listed as feasible parameters on "Parameters of directed
strongly regular graphs," at ${http://homepages.cwi.nl/^\sim
aeb/math/dsrg/dsrg.html}$ by S. Hobart and A. E. Brouwer. We review these
constructions and show how our methods may be used to construct other infinite
families of directed strongly regular graphs.
