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

Abstract

We prove that if $p\ge n^{-(q-6)/2}$, 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.

17 pages