Quasi-symmetric designs and biplanes of characteristic three

Abstract

Quasi-symmetric 2-designs with block intersection numbers 0 and y≥ 2 are studied using an additional property that any triple of points is contained in 0 or p blocks for some positive constant p. Some characterization results including the extremal cases k = y² + y, λ = y² + y - 1 and λ = y² are given. The paper also contains some structural investigations of biplanes of characteristic three.