Finite linear spaces admitting a projective group PSU(3,q) with q even

This article is a contribution to the study of the automorphism groups of finite linear spaces. In particular we look at simple groups and prove the following theorem: Let G=PSU(3,q) with q even and G acts line-transitively on a finite linear space . Then is one of the following cases: (i)A projective plane;(ii)A regular linear space with parameters (b,v,r,k)=(q2(q2−q+1),q3+1,q2−q+1,q+1). This is called the Hermitian unitary design.