This classification reveals block size 5 3-designs with transitive automorphisms, indicating relationships with sporadic and alternating groups.
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).
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Huang et al. (2025) studied this question.
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