Strongly uniform extensions of dual 2-designs

Abstract

A strongly α-uniform partial line space of order (s, t) is called an α-partial geometry. If α = t+1, then the geometry is a dual 2-design. Locally triangular and locally Grassman graphs correspond to triangular extensions of certain dual 2-designs, and the class of strongly uniform quasi-biplanes coincides with the class of strongly uniform extensions of dual 2-designs. We study strongly uniform extensions of dual 2-designs.