The Chevalley groups G2(q) with q odd and 2−(v,k,1) designs

Let D be a 2−(v,k,1) design, and let G be an automorphism group of D. Delandtsheer proved that if D is not a projective plane and G is line-primitive then G is almost simple, that is, T≤G≤Aut(T), where T is a non-Abelian simple group. In this paper, we prove that T is not isomorphic to G2(q), where q is odd.