Strongly regular designs and coherent configurations of type \([{32\atop\;3}]\)
Strongly regular designs arise in the study of coherent configurations. They may, however, be defined in purely design-theoretic terms as follows: A strongly regular design is a finite incidence structure satisfying the following three axioms and their duals: (1) Each block has \(s_ 1\) points. (2) Two distinct blocks intersect in either \(a_ 1\) or \(b_ 1\) points (where \(a_ 1>b_ 1)\), and both cases occur. (3) The number of blocks through a point \(x\) intersecting a given block \(y\) in \(a_ 1\) points is either \(N_ 2\) or \(P_ 2\), depending only on whether x and y are incident or not. As a consequence, both the point and the block graph of an SRD are strongly regular graphs. SRD's are \(1\)-designs in the sense of \textit{A. Neumaier} [``\(t\)-designs'', J. Comb. Theory, Ser. A 28, 226-248 (1980; Zbl 0433.05012)]. They include those partial geometries which are neither 2-designs nor dual 2-designs. In the present paper, the author gives a systematic study of strongly regular designs.
scientific article; zbMATH DE number 4077239