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Let $H$ be a random $k$-uniform $n$-vertex hypergraph where every $k$-tuplebelongs to $H$ independently with probability $p$. We show that for some$\varepsilon_k > 0$, if $p \geq n^{-\varepsilon_k}$, then asymptotically almostsurely $H$ contains an $\left( n , k , k - 1 \right)$-Steiner System. Our maintool is Keevash's method of Randomized Algebraic Constructions.

$\left( n , k , k - 1 \right)$-Steiner Systems in Random Hypergraphs