It is shown that, apart from the smallest Ree group, a flag-transitive automorphism group G of a 2-k k λ ( , , ) 2 design , with λ k , is either an affine group or an almost simple classical group. Moreover, when G is the smallest Ree group, is isomorphic either to the 2-(6 , 6, 2) 2 design or to one of the three 2-(6 , 6, 6) 2 designs constructed in this paper. All the four 2-designs have the 36 secants of a non-degenerate conic of PG (8) 2 as a point set and 6-sets of secants in a remarkable configuration as a block set.
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