The notion of globally irreducible representations of finite groups was int
roduced by B. H. Gross, in order to explain new series of Euclidean lattice
s discovered by N. Elkies and T. Shioda using Mordell-Well lattices of elli
ptic curves. In this paper we classify all globally irreducible representat
ions coming from projective complex representations of the finite simple gr
oups PSL3(q) and PSU3(q). The main result is that these representations are
essentially those discovered by Gross.