Block-transitive 2-(v,k,1) designs and the twisted simple groups 2E6(q)

This article is a contribution to the study of block-transitive automorphism groups of 2-(v,k,1) block designs. Let D be a 2-(v,k,1) design admitting a block-transitive, point-primitive but not flag-transitive group G of automorphisms. Let kr=(k,v-1) and q=pf for prime p. In this paper we prove that if G and D are as above and q> (3(krk-kr+1)f)1/3 then G does not admit a twisted simple group 2E6(q) as its socle.