Quasi-symmetric designs and biplanes of characteristic three (Q1186113)

A 2-\((v,k,\lambda)\) design is quasi-symmetric if any pair of blocks intersect in \(x\) or \(y\) points, with \(x<y\). The authors generalize classification results obtained by \textit{V. C. Mavron} and the second author [Arch. Math. 52, 407-412 (1989; Zbl 0636.05015)] for \((x,y)=(0,2)\) to \((x,y)=(0,y)\), \(y\geq 2\). The additional condition that any triple of points is contained in 0 or a positive constant number of blocks is frequently imposed on these designs. The structure of biplanes of characteristic three is also investigated.