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In this note, we prove that there exists a universal constant$c=\frac{43}{50}$ such that for every $k\in \mathbb{N}$ and every $d<k/2$,every $k$-uniform hypergraph on $n$ vertices and with minimum $d$-degree atleast $(c+o_n(1))\binom{n-d}{k-d}$ contains a perfect matching. This is thefirst such bound which is independent of $k$, and therefore, improves allpreviously known bounds when $k$ is large. Our approach is based on combiningthe seminal work of Alon et al. with known bounds on a conjecturedprobabilistic inequality due to Feige.

Uniformity-independent minimum degree conditions for perfect matchings in hypergraphs