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