Block-Transitive 3-(v, 5, λ) Designs with Sporadic or Alternating Socle (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).
Keywords: 3-design; block-transitive; automorphism; sporadic group; alternating group