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We report about the results of the application of modern computer algebratools for construction of directed strongly regular graphs. The suggestedtechniques are based on the investigation of non-commutative associationschemes and Cayley graphs over non-Abelian groups. We demonstrate examples ofdirected strongly regular graphs for 28 different parameter sets, for which theexistence of a corresponding digraph has not been known before.

Sporadic Examples of Directed Strongly Regular Graphs Obtained by Computer Algebra Experimentation (Extended version)