Ree groups as automorphism groups of block designs

Abstract

A recent classification of flag-transitive 2-designs with parameters (v,k,λ) whose replication number r is coprime to λ 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=32n+1⩾27, there exist 2-designs with parameters (q3+1,qi,qi−1), for i=1,2, admitting the Ree group 2G2(q) as their automorphism groups.