Directed strongly regular graphs with rank 5

Preprint: Report R-2014-05.pdf

It is proved that a directed strongly regular with adjacency matrix of rank 5 has one the following parameter sets:
(where m is a positive integer)
or is the undirected strongly regular graph (5m,4m,4m,3m,4m).
For each of these families, a construction of directed strongly regular graphs is known for all values of m.

The result excludes existence of directed strongly regular graphs with the following previously open cases with n <=110.
(see Brouwer and Hobart: )