For flag-transitive non-symmetric 2-(v,k,λ) designs with (r,λ)=1 and exceptional socle T of Lie type, T must be a Ree or Suzuki group and exactly five isomorphism classes of designs exist.
Saxl, On finite linear spaces with almost simple flag-transitive au tomorphism groups, J
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Flag-transitive non-symmetric $2$-designs with $(r,\lambda)=1$ and exceptional groups of Lie type
For flag-transitive non-symmetric 2-(v,k,λ) designs with (r,λ)=1 and exceptional socle T of Lie type, T must be a Ree or Suzuki group and exactly five isomorphism classes of designs exist.