Thresholds for $(n,q,2)$-Steiner Systems via Refined Absorption

We prove that if p≥n−(q−6)/2, then asymptotically almost surely the binomial random q-uniform hypergraph G(q)(n,p) contains an (n,q,2)-Steiner system, provided n satisfies the necessary divisibility conditions.

Submitted 27 February, 2024; originally announced February 2024.