2-(v,k,λ) designs with gcd(r,λ)=2 admitting a flag-transitive automorphism group with socle PSL(2,q)

In this paper, we completely classify the non-trivial 2- ( v , k , λ ) designs with gcd ⁡ ( r , λ ) = 2 , admitting an almost simple, flag-transitive automorphism group with the socle PSL ( 2 , q ) .