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 ${𝔽}_{2^n}$
$x^{-1}+\mathrm{T}\mathrm{r}(x+(x^{-1}+1{)}^{-1})$	$n=2t$ is even
$x^{-1}+\mathrm{T}\mathrm{r}(x^{-3(2^k+1)}+(x^{-1}+1{)}^{3(2^k+1)})$	$n=2t$ and $2\le k\le t-1$
$L_u(F^{-1}(x)){|}_{H_u}$	$n=2t,F(x)$ is a quadratic APN permutation on ${𝔽}_{2^{n+1}},u\in {{𝔽}^{\ast }}_{2^{n+1}}$
$\sum _{i=0}^{2^n-3}{x}^i$	$n=2t,$ t is odd