Differentially 4-uniform permutations

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 ${𝔽}_{2^n}$
$x^{-1}+{\mathrm{T}\mathrm{r}}_1^n(x+(x^{-1}+1{)}^{-1})$	$n=2t$ is even
$x^{-1}+{\mathrm{T}\mathrm{r}}_1^n(x^{-3(2^k+1)}+(x^{-1}+1{)}^{3(2^k+1)})$	$n=2t$ and $2\le k\le t-1$
$L_u(F^{-1}(x)){|}_{H_u}$	$n=2t,F(x)$ is a quadratic APN permutation on ${𝔽}_{2^{n+1}},u\in {𝔽}_{2^{n+1}}^{\ast },$ $L_u(x)=F(x)+F(x+u)+F(u),$ $H_u=\{L_u(x)|x\in {𝔽}_{2^{n+1}}\}$
$\sum _{i=0}^{2^n-3}{x}^i$	$n=2t,$ t is odd
$x^{-1}+t(x^{2^s}+x{)}^{2^{sn}-1}$	$s$ is even $,t\in {𝔽}_{2^s}^{\ast },$ or $s,n$ are odd, $t\in {𝔽}_{2^s}^{\ast }$
$x^{2^k+1}+t(x^{2^s}+x{)}^{2^{sn}-1}$	$n,s$ are odd, $t\in {𝔽}_{2^s}^{\ast },gcd(k,sn)=1$
$(x,x_n)\mapsto$ $((1+x_n)x^{-1}+x_n\alpha x^{-1},f(x,x_n))$	$n$ is even $x,\alpha \in {𝔽}_{2^{n-1}},x_n\in {𝔽}_2,{\mathrm{T}\mathrm{r}}_1^{n-1}(\alpha )={\mathrm{T}\mathrm{r}}_1^{n-1}\left(\frac{1}{\alpha }\right)=1,$ $f(x,x_n)$ is $(n,1)-$function