Block-transitive \(t\)-designs. I: Point-imprimitive designs
The authors study block-transitive, point-imprimitive \(t\)- \((v,k,\lambda)\)-designs and give bounds on the size of \(v\) in terms of \(k\). In particular, they give a proof for the bound obtained by \textit{A. Delandtsheer} and \textit{J. Doyen} [``Most block-transitive \(t\)-designs are point-primitive'', Geom. Dedicata 29, No. 3, 307-310 (1989; Zbl 0673.05010)] in the case \(t=2\) and study the case of equality in this bound. They obtain stronger bounds than Delandtsheer and Doyen provided that either \(t\geq 3\) or the design is flag-transitive.
scientific article; zbMATH DE number 417461