Sporadic groups as block-transitive automorphism groups of \( t\)-designs with \(\lambda\le5\)

This paper studies the classi cation problem of block-transitivet-designs. LetD= (P,B) be a non-trivalt-(v, k, λ)design withλ≤5, and letGbe a block-transitive, point- primitive automorphism group ofD. We prove that if Soc(G)is a sporadic simple group, then up to isomorphism, there are exactly 15 such designsD.