(untitled) (Contemporary Mathematics, 2025)
This paper presents a systematic classification of 3-designs with block size 5. Let be a nontrivial 3-(v, 5, λ) design, and let G ≤ Aut act transitively on blocks. We classify all such pairs (, G) where the socle of G is either: one of the 26 sporadic simple groups, or an alternating group An (n ≥ 5).