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Known switching classes of APN functions over $\mathbb {F} _{2^{5}}$, $\mathbb {F} _{2^{6}}$, $\mathbb {F} _{2^{7}}$ and $\mathbb {F} _{2^{8}}$

$n$ | $N^{\circ }$ | $F(x)$ |
---|---|---|

$5$ | $1,1$
$1,2$ $2,1$ |
$x^{3}$
$x^{5}$ $x^{-1}$ |

$6$ | $1,1$
$1,2$ $2.1$ |
$x^{3}$
$x^{3}+u^{11}x6+ux^{9}$ $ux^{5}+x^{9}+u^{4}x^{17}+ux^{18}+u^{4}x^{20}+ux^{24}+u^{4}x^{34}+ux^{40}$ |