  A permutation array(permutation code, PA) of length $n$ and distance $d$,
denoted by $(n,d)$ PA, is a set of permutations $C$ from some fixed set of $n$
elements such that the Hamming distance between distinct members
$\mathbf{x},\mathbf{y}\in C$ is at least $d$. In this correspondence, we
present two constructions of PA from fractional polynomials over finite field,
and a construction of $(n,d)$ PA from permutation group with degree $n$ and
minimal degree $d$. All these new constructions produces some new lower bounds
for PA.
