Ree groups as automorphism groups of block designs

A recent classification of flag-transitive 2-designs with parameters ( v, k, ) ) whose replication number r is coprime to ) gives rise to eight possible infinite families of 2-designs, some of which are with new parameters. In this note, we give explicit constructions for two of these families of 2-designs, and show that for a given positive integer q = 3 2 n +1 >= 27, there exist 2-designs with parameters ( q 3 + 1 , qi, i , qi i - 1), for i = 1,2, , 2, admitting the Ree group 2 G 2 ( q ) as their automorphism groups.