The existence and construction of a family of block-transitive 2-(v,6,1) designs

Let G be a block-transitive automorphism group of a 2-(v,k,1) design D. It has been shown that the pairs (G,D) fall into three classes: those where G is unsolvable and is flag-transitive, those where G is a subgroup of AΓL(1,q), and those where G is solvable and is of small order. Not much is known about the latter two classes.In this paper, we investigate the existence of 2-(v,6,1) designs admitting a block-transitive automorphism group G