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

Known switching classes of APN functions over GF(2⁵), GF(2⁶), GF(2⁷) and GF(2⁸).

Also available is Magma code generating representatives from the switching classes.

n	N	F(x)	Γ-rank	Δ-rank	Aut(dev(GF))/22n	Aut(dev(GF))/22n	Multiplier group
5	1.1	x3	330	42	4960	4960	4960
	1.2	x5	330	42	4960	158720	4960
	2.1	x-1	496	232	310	310	310
6	1.1	x3	1102	94	24192	48384	24192
	1.2	x3 + u11x6 + ux9	1146	94	4032	8064	4032
	2.1	ux5 + x9 + u4x17 + ux18 + u4x20 + ux24 + u4x34 + ux40	1158	96	320	320	320
	2.2	u7x3 + x5 + u3x9 + u4x10 + x17 + u6x18	1166	94	448	896	448
	2.3	x3 + ux24 + x10	1166	96	896	896	896
	2.4	x3 + u17(x17 + x18 + x20 + x24)	1168	96	64	64	64
	2.5	x3 + u11x5 + u13x9 + x17 + u11x33 + x48	1170	96	320	320	320
	2.6	u25x5 + x9 + u38x12 + u25x18 + u25x36	1170	96	64	64	64
	2.7	u40x5 + u10x6 + u62x20 + u35x33 + u15x34 + u29x48	1170	96	64	64	64
	2.8	u34x6 + u52x9 + u48x12 + u6x20 + u9x33 + u23x34 + u25x40	1170	96	64	64	64
	2.9	x9 + u4(x10 + x18) + u9(x12 + x20 + x40)	1172	96	64	64	64
	2.10	u52x3 + u47x5 + ux6 + u9x9 + u44x12 + u47x33 + u10x34 + u33x40	1172	96	64	64	64
	2.11	u(x6 + x10 + x24 + x33) + x9 + u4x17	1174	96	64	64	64
	2.12	x3 + u17(x17 + x18 + x20 + x24) + u14(u52x3 + u6x5 + u19x7 + u28x11 + u2x13)+ (u52x3 + u6x5 + u19x7 + u28x11 + u2x13)2 + (u52x3 + u6x5 + u19x7 + u28x11 + u2x13)4+ (u52x3 + u6x5 + u19x7 + u28x11 + u2x13)8+ (u52x3 + u6x5 + u19x7 + u28x11 + u2x13)16+ (u52x3 + u6x5 + u19x7 + u28x11 + u2x13)32+ (u2x)9 +(u2x)19 +(u2x)36 + x21+x42	1300	152	8	8	8
7	1.1	x3	3610	198	113792	113792	113792
	1.2	x3 + Tr(x9)	4026	212	896	896	896
	2.1	x34 + x18 + x5	4034	210	896	896	896
	2.2	x3 + x17 + x33 + x34	4040	212	896	896	896
	3.1	x5	3708	198	113792	113792	113792
	4.1	x9	3610	198	113792	14565376	113792
	5.1	x13	4270	338	889	889	889
	6.1	x57	4704	436	889	889	889
	7.1	x-1	8128	4928	1778	1778	1778
	8.1	x65 + x10 + x3	4038	212	896	896	896
	9.1	x3 + x9 + x18 + x66	4044	212	896	896	896
	10.1	x3 + x12 + x17 + x33	4048	210	896	896	896
	10.2	x3 + x17 + x20 + x34 + x66	4040	210	896	896	896
	11.1	x3 + x20 + x34 + x66	4048	210	896	896	896
	12.1	x3 + x12 + x40 + x72	4048	210	896	896	896
	13.1	x3 + x5 + x10 + x33 + x34	4040	212	896	896	896
	14.1	x3 + x6 + x34 + x40 + x72	4048	212	896	896	896
	14.2	x3 + x5 + x6 + x12 + x33 + x34	4050	210	896	896	896
	14.3	u2x96 + u78x80 + u121x72 + u49x68 + u77x66 + u29x65 + u119x48 + u117x40 + u28x36 + u107x34 +u62x33 +u125x24 +u76x20 +u84x18 +u110x17 +u49x12 +u102x10 +u69x9 + u14x6 + x5 + x3	4046	212	128	128	128
8	1.1	x3	11818	420			522240
	1.2	x9	12370	420			522240
	1.3	x3+Tr(x9)	13800	432			6144
	1.4	x9+Tr(x3)	13804	434			6144
	1.5	x3+u245x33+u183x66+u21x144	13842	436			3072
	1.6	x3 + u65x18+u120x66+u135x144	13848	438			3072
	1.7	u188x192 + u129x144 + u172x132 + u138x129 + u74x96 + u244x72 + u22x66 + u178x48 + u150x36 + u146x33 + u6x24 + u60x18 + u80x12 + u140x9 + u221x6 + u19x3	14034	438			768
	1.8	u37x192 + u110x144 + u40x132 + u53x129 + u239x96 + u235x72 + u126x66 + u215x48 + u96x36 + u29x33 + u19x24 + u14x18 + u139x12 + u230x9 + u234x6 + u228x3	14032	438			3072
	1.9	u242x192 + u100x144 + u66x132 + u230x129 + u202x96 + u156x72 + u254x66 + u18x48 + u44x36 + u95x33 + u100x24 + u245x18 + u174x12 + u175x9 + u247x6 + u166x3	14036	438			3072
	1.10	u100x192 + u83x144 + u153x132 + u65x129 + u174x96 + u136x72 + u46x66+ u55x48+ u224x36+ u180x33+ u179x24+u226x18+ u54x12+ u168x9+ u89x6+ u56x3	14036	438			1536
	1.11	u77x192 + u133x144 + u47x132 + u229x129 + u23x96 + u242x72 + u242x66 + u245x48 + u212x36 + u231x33 + u174x24 + u216x18 + u96x12 + u253x9 + u154x6 + u71x3	14032	438			3072
	1.12	u220x192 + u94x144 + u70x132 + u159x129 + u145x96 + u160x72 + u74x66 + u184x48 + u119x36 + u106x33 + u253x24 + wx18 + u90x12 + u169x9 + u118x6 + u187x3	14034	438			3072
	1.13	u98x192 + u225x144 + u111x132 + u238x129 + u182x96 + u125x72 + u196x66 + u219x48 + u189x36 + u199x33 + u181x24 + u110x18 + u19x12 + u175x9 + u133x6 + u47x3	14030	438			1536
	1.14	u236x192 + u212x160 + u153x144 + u185x136 + u3x132 + u89x130 + u189x129 + u182x96 + u105x80 + u232x72 + u219x68 + u145x66 + u171x65 + u107x48 + u179x40 + u227x36 + u236x34 + u189x33 + u162x24 + u216x20 + u162x18 + u117x17 + u56x12 + u107x10 + u236x9 + u253x6 + u180x5 + u18x3	14046	454			512
	1.15	u27x192 + u167x144 + u26x132 + u231x129 + u139x96 + u30x72 + u139x66 + u203x48 + u36x36 + u210x33 + u195x24 + u12x18 + u43x12 + u97x9 + u61x6 + u39x3	14036	454			768
	1.16	u6x192 + u85x144 + u251x132 + u215x129 + u229x96 + u195x72 + u152x66 + u173x48 + u209x36 + u165x33 + u213x24 + u214x18 + u158x12 + u146x9 + x6 + u50x3	14032	438			1536
	1.17	u164x192 + u224x144 + u59x132 + u124x129 + u207x96 + u211x72 + u5x66 + u26x48 + u20x36 + u101x33 + u175x24 + u241x18 + x12 + u15x9 + u217x6 + u212x3	14028	438			1536
	2.1	x3+ x17+u16(x18+x33)+u15x48	13200	414			46080
	3.1	x3+ u24x6+u182x132+u67x192	14024	438			3072
	4.1	x3+x6+x68+x80+x132+x160	14040	454			2048
	5.1	x3+x5+x18+x40+x66	14044	446			2048
	6.1	x3+x12+x40+x66+x130	14046	438			2048
	7.1	x57	15358	960			2040