Minimum codegree threshold for -factors

Given hypergraphs H and F, an F-factor in H is a spanning subgraph consisting of vertex-disjoint copies of F. Let denote the 3-uniform hypergraph on 4 vertices with 3 edges. We show that for any γ>0 there exists an integer n0 such that every 3-uniform hypergraph H of order n>n0 with minimum codegree at least (1/2+γ)n and 4|n contains a -factor. Moreover, this bound is asymptotically the best possible and we further give a conjecture on the exact value of the threshold for the existence of a -factor. Thereby, all minimum codegree thresholds for the existence of F-factors are known asymptotically for 3-uniform hypergraphs F on 4 vertices.