Key points are not available for this paper at this time.
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.
Delcourt et al. (Tue,) studied this question.