On the existence of directed strongly regular graphs with parameters (22, 9, 6, 3, 4)

The paper shows the existence of a family of directed strongly regular graphs with parameters (22, 9, 6, 3, 4). The adjacency matrices of the found digraphs are composed of $3\times 3$ circulant blocks. The automorphism group of all the digraphs found is the group ${\mathbb{Z}}_3$. The structure of the resulting digraphs is described using concepts of skeleton and rigging.