  Given two $k$-graphs $F$ and $H$, a perfect $F$-tiling (also called an
$F$-factor) in $H$ is a set of vertex disjoint copies of $F$ that together
cover the vertex set of $H$. Let $t_{k-1}(n, F)$ be the smallest integer $t$
such that every $k$-graph $H$ on $n$ vertices with minimum codegree at least
$t$ contains a perfect $F$-tiling. Mycroft (JCTA, 2016) determined the
asymptotic values of $t_{k-1}(n, F)$ for $k$-partite $k$-graphs $F$. Mycroft
also conjectured that the error terms $o(n)$ in $t_{k-1}(n, F)$ can be replaced
by a constant that depends only on $F$. In this paper, we improve the error
term of Mycroft's result to a sub-linear term when $F=K^3(m)$, the complete
$3$-partite $3$-graph with each part of size $m$. We also show that the
sub-linear term is tight for $K^3(2)$, {the result also provides another family
of counterexamples of Mycroft's conjecture (Gao, Han, Zhao (arXiv, 2016) gave a
family of counterexamples when $H$ is a $k$-partite $k$-graph with some
restrictions.)} Finally, we show that Mycroft's conjecture holds for
generalized 4-cycle $C_4^3$ (the 3-graph on six vertices and four distinct
edges $A, B, C, D$ with $A\cup B= C\cup D$ and $A\cap B=C\cap D=\emptyset$),
i.e. we determine the exact value of $t_2(n, C_4^3)$.
