Strongly regular designs of the second kind
The author introduces a new type of combinatorial design, called a strongly regular design of the second kind, satisfying a rather involved set of axioms. The motivation for this is a connection to the theory of coherent configurations having two fibers of rank 2 or 3; there are 4 types of such configurations, three of which are equivalent to symmetric designs, quasi-symmetric designs and strongly regular designs (of the first kind). In the paper under review, the author shows that the new class of designs is equivalent to coherent configurations of type \(\left[\begin{smallmatrix} 3\\ \phantom 3\end{smallmatrix} \begin{smallmatrix} 3\\ 3\end{smallmatrix}\right]\). He also discusses the known examples (one of them being provided by the lines and colines of \(\text{PG}(m, q)\) for \(m\geq 4\)), parametric restrictions and polarities.
strongly regular design of the second kind
scientific article; zbMATH DE number 798913