Packing perfect matchings in random hypergraphs

We introduce a new procedure for generating the binomial random graph/hypergraph models, referred to as \emph{online sprinkling}. As an illustrative application of this method, we show that for any fixed integer $k\ge 3$, the binomial $k$-uniform random hypergraph $H_{n,p}^k$ contains $N:=(1-o(1))\left(\genfrac{}{}{0px}{}{n-1}{k-1}\right)p$ edge-disjoint perfect matchings, provided $p\geq \frac{\log^{C}n}{n^{k-1}}$,where$C:=C(k)$isanintegerdependingonlyon$k$\mathrm{.}Ourresultfor$N$isasymptoticallybestoptimalandfor$p$ is optimal up to the $polylog(n)$ factor.