Differentially 4-uniform permutation

Functions	Conditions	References
$x^{2^{i}+1}$	$gcd(i,n)=2,n=2t$ and t is odd
$x^{2^{2i}-2^{i}+1}$	$gcd(i,n)=2,n=2t$ and t is odd
$x^{2^{n}-2}$	$n=2t$ (inverse)
$x^{2^{2t}-2^{t}+1}$	$n=4t$ and t is odd
$\alpha x^{2^{s}+1}+\alpha ^{2^{t}}x^{{2-t}+2^{t+s}}$	$n=3t,t/2$ is odd, $gcd(n,s)=2,3|t+s$ and $\alpha$ is a primitive element in $\mathbb {F} _{2^{n}}$
$x^{-1}+\mathrm {Tr} (x+(x^{-1}+1)^{-1})$	$n=2t$ is even
$x^{-1}+\mathrm {Tr} (x^{-3(2^{k}+1)}+(x^{-1}+1)^{3(2^{k}+1)})$	$n=2t$ and $2\leq k\leq t-1$
$a^{2}x^{2^{2m+1}+1}+b^{2}x^{2^{m+1}+1}+ax^{2^{2m}+2}+bx^{2^{m}+2}+(c^{2}+c)x^{3}$	$n=3m,m\ {\text{odd}},L(x)=ax^{2^{2m}}+bx^{2^{m}}+cx$ satisfies the conditions in Lemma 8 of [7]