The main aim of this talk is to present a classification of 2-designs with gcd(r,λ) = 1. In 1988, Zieschang [11] proved that if an automorphism group of a 2-design with gcd(r, λ) = 1 is flag-transitive, then it is point-primitive of almost simple or affine type. Such designs admitting an almost simple automorphism group have been studied in [1–3,7–10]. The case where a 2-design with gcd(r,λ) = 1 admits an affine type automorphism group has been studied in [4–6]. In conclusion, all 2-designs with gcd(r, λ) = 1 admitting flag-transitive automorphism groups are known except for those admitting one dimensional affine type automorphism groups.
