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

Known switching classes of APN functions over [math]\displaystyle{ \mathbb{F}_{2^5} }[/math], [math]\displaystyle{ \mathbb{F}_{2^6} }[/math], [math]\displaystyle{ \mathbb{F}_{2^7} }[/math] and [math]\displaystyle{ \mathbb{F}_{2^8} }[/math]

[math]\displaystyle{ n }[/math]	[math]\displaystyle{ N^\circ }[/math]	[math]\displaystyle{ F(x) }[/math]
[math]\displaystyle{ 5 }[/math]	[math]\displaystyle{ 1.1 }[/math] [math]\displaystyle{ 1.2 }[/math] [math]\displaystyle{ 2.1 }[/math]	[math]\displaystyle{ x^3 }[/math] [math]\displaystyle{ x^5 }[/math] [math]\displaystyle{ x^{-1} }[/math]

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

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