A classification of the flag-transitive 2-(v,k,2) designs

In this paper, we provide a complete classification of 2-$(v,k,2)$ designs admitting a flag-transitive automorphism group of affine type with the only exception of the semilinear 1-dimensional group. Alongside this analysis, we provide a construction of seven new families of such flag-transitive 2-designs, one of them infinite, and some of them involving remarkable objects such as t-spreads, translation planes, quadrics and Segre varieties.

Our result together with those of Alavi et al. [1], [2], Praeger et al. [17], Zhou and the first author [39], [40] provides a complete classification of 2-$(v,k,2)$ design admitting a flag-transitive automorphism group with the only exception of the semilinear 1-dimensional case.