Known switching classes of APN functions over GF(2^n) for n = 5,6,7,8

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

$n$	$N^{\circ }$	$F(x)$
$5$	$1.1$ $1.2$ $2.1$	$x^{3}$ $x^{5}$ $x^{-1}$

$n$	$N^{\circ }$	$F(x)$
$6$	1.1	$x^{3}$
	1.2	$x^{3}+u^{11}x^{6}+ux^{9}$
	2.1	$ux^{5}+x^{9}+u^{4}x^{17}+ux^{18}+u^{4}x^{20}+ux^{24}+u^{4}x^{34}+ux^{40}$
	2.2	$u^{7}x^{3}+x^{5}+u^{3}x^{9}+u^{4}x^{10}+x^{17}+u^{6}x^{18}$
	2.3	$x^{3}+ux^{24}+x^{10}$
	2.4	$x^{3}+u^{17}(x^{17}+x^{18}+x^{20}+x^{24})$
	2.5	$x^{3}+u^{11}x^{5}+u^{13}x^{9}+x^{17}+u^{11}x^{33}+x^{48}$
	2.6	$u^{25}x^{5}+x^{9}+u^{38}x^{12}+u^{25}x^{18}+u^{25}x^{36}$
	2.7	$u^{40}x^{5}+u^{10}x^{6}+u^{62}x^{20}+u^{35}x^{33}+u^{15}x^{34}+u^{29}x^{48}$
	2.8	$u^{34}x^{6}+u^{52}x^{9}+u^{48}x^{12}+u^{6}x^{20}+u^{9}x^{33}+u^{23}x^{34}+u^{25}x^{40}$
	2.9	$x^{9}+u^{4}(x^{10}+x^{18})+u^{9}(x^{12}+x^{20}+x^{40})$
	2.10	$u^{52}x^{3}+u^{47}x^{5}+ux^{6}+u^{9}x^{9}+u^{44}x^{12}+u^{47}x^{33}+u^{10}x^{34}+u^{33}x^{40}$
	2.11	$u(x^{6}+x^{10}+x^{24}+x^{33})+x^{9}+u^{4}x^{17}$
	2.12	$x^{3}+$ $u^{17}(x^{17}+$ $x^{18}+$ $x^{20}+$ $x^{24})+$ $u^{14}((u^{52}x^{3}+$ $u^{6}x^{5}+$ $u^{19}x^{7}+$ $u^{28}x^{11}+$ $u^{2}x^{13})+(u^{52}x^{3}+$ $u^{6}x^{5}+$ $u^{19}x^{7}+$ $u^{28}x^{11}+$ $u^{2}x^{13})^{2}+$ $(u^{52}x^{3}+$ $u^{6}x^{5}+$ $u^{19}x^{7}+$ $u^{28}x^{11}+$ $u^{2}x^{13})^{4}+(u^{52}x^{3}+$ $u^{6}x^{5}+$ $u^{19}x^{7}+$ $u^{28}x^{11}+$ $u^{2}x^{13})^{8}+(u^{52}x^{3}+$ $u^{6}x^{5}+$ $u^{19}x^{7}+$ $u^{28}x^{11}+$ $u^{2}x^{13})^{16}+(u^{52}x^{3}+$ $u^{6}x^{5}+$ $u^{19}x^{7}+$ $u^{28}x^{11}+$ $u^{2}x^{13})^{32}+(u^{2}x)^{9}+(u^{2}x)^{19}+(u^{2}x)^{36}+$ $x^{21}+x^{42}$

$n$	$N^{\circ }$	$F(x)$
$7$	1.1	$x^{3}$
	1.2	$x^{3}+{\rm {Tr}}(x^{9})$
	2.1	$x^{34}+x^{18}+x^{5}$
	2.2	$x^{3}+x^{17}+x^{33}+x^{34}$
	3.1	$x^{5}$
	4.1	$x^{9}$
	5.1	$x^{13}$
	6.1	$x^{57}$
	7.1	$x^{-1}$
	8.1	$x^{65}+x^{10}+x^{3}$
	9.1	$x^{3}+x^{9}+x^{18}+x^{66}$
	10.1	$x^{3}+x^{12}+x^{17}+x^{33}$
	10.2	$x^{3}+x^{17}+x^{20}+x^{34}+x^{66}$
	11.1	$x^{3}+x^{20}+x^{34}+x^{66}$
	12.1	$x^{3}+x^{12}+x^{40}+x^{72}$
	13.1	$x^{3}+x^{5}+x^{10}+x^{33}+x^{34}$
	14.1	$x^{3}+x^{6}+x^{34}+x^{40}+x^{72}$
	14.2	$x^{3}+x^{5}+x^{6}+x^{12}+x^{33}+x^{34}$
	14.3	$u^{2}x^{96}+$ $u^{78}x^{80}+$ $u^{121}x^{72}+$ $u^{49}x^{68}+$ $u^{77}x^{66}+$ $u^{29}x^{65}+$ $u^{119}x^{48}+$ $u^{117}x^{40}+$ $u^{28}x^{36}+$ $u^{107}x^{34}+u^{62}x^{33}+u^{125}x^{24}+u^{76}x^{20}+u^{84}x^{18}+u^{110}x^{17}+u^{49}x^{12}+u^{102}x^{10}+u^{69}x^{9}+$ $u^{14}x^{6}+$ $x^{5}+$ $x^{3}$