APN functions obtained via polynomial expansion in small dimensions

ID	Representative	Equivalent to	Orthoderivative diff. spec.
8.1	<math>\alpha^{170}x^{192} + \alpha^{85}x^{132} + x^6 + x^3</math>	SW 19	<math>0^{37872}, 2^{22788}, 4^{4068}, 6^{492}, 8^{60}</math>
8.2	<math>x^{66} + \alpha^{85}x^{33} + x^{18} + x^9 + x^3</math>	SW 11	<math>0^{38040}, 2^{22461}, 4^{4218}, 6^{513}, 8^{36}, 10^{12}</math>
8.3	<math>x^{66} + \alpha^{85}x^{33} + \alpha^{17}x^9 + \alpha^{102}x^6 + x^3</math>	SW 13	<math>0^{38076}, 2^{22311}, 4^{4374}, 6^{495}, 8^{24}</math>
8.4	<math>\alpha^{85}x^{132} + \alpha^{85}x^{72} + x^9 + x^6 + x^3</math>	SW 12	<math>0^{38160}, 2^{22104}, 4^{4536}, 6^{456}, 8^{24}</math>
8.5	<math>x^{66} + x^{12} + \alpha^{85}x^6 + x^3</math>	SW 6	<math>0^{38160}, 2^{22164}, 4^{4428}, 6^{492}, 8^{36}</math>
8.6	<math>x^{129} + \alpha^{85}x^{24} + x^{12} + x^9 + x^3</math>	SW 8	<math>0^{38184}, 2^{22179}, 4^{4338}, 6^{531}, 8^{48}</math>
8.7	<math>\alpha^{170}x^{132} + \alpha^{85}x^{66} + \alpha^{85}x^{18} + x^3</math>	new	<math>0^{38196}, 2^{22008}, 4^{4608}, 6^{456}, 8^{12}</math>
8.8	<math>\alpha^{85}x^{132} + \alpha^{85}x^{72} + x^{36} + x^{24} + x^3</math>	SW 9	<math>0^{38256}, 2^{22116}, 4^{4230}, 6^{648}, 8^{30}</math>
8.9	<math>\alpha^{85}x^{192} + x^{72} + x^{33} + x^{24} + x^9 + \alpha^{153}x^6</math>	SW 17	<math>0^{38388}, 2^{21723}, 4^{4626}, 6^{507}, 8^{36}</math>
8.10	<math>\alpha^{221}x^{96} + \alpha^{221}x^{33} + x^{12} + x^9 + x^6 + \alpha^{187}*x^3</math>	SW 10	<math>0^{38439}, 2^{21618}, 4^{4671}, 6^{528}, 8^{24}</math>
8.11	<math>\alpha^{238}x^{144} + x^{132} + \alpha^{51}x^{96} + \alpha^{119}x^{48} + x^{33} + x^9</math>	SW 16	<math>0^{38457}, 2^{21552}, 4^{4743}, 6^{510}, 8^{18}</math>
8.12	<math>\alpha^{204}x^{160} + \alpha^{51}x^{48} + \alpha^{102}x^{12} + \alpha^{204}x^{10} + x^9</math>	SW 22	<math>0^{38844}, 2^{20974}, 4^{4764}, 6^{654}, 8^{44}</math>
8.13	<math>\alpha^{160}x^{132} + \alpha^{10}x^{72} + x^{48} + \alpha x^{34} + \alpha^3x^{33} + \alpha^{48}x^{18} + x^{17} + x^3</math>	B 31	<math>0^{39150}, 2^{20463}, 4^{4920}, 6^{675}, 8^{54}, 10^{12}, 12^6</math>
8.14	<math>x^{144} + \alpha^{85}x^{96} + \alpha^{170}x^{80} + \alpha^{85}x^{65} + \alpha^{85}x^{17} + x^9 + x^5</math>	B 12668	<math>0^{39408}, 2^{20072}, 4^{4922}, 6^{798}, 8^{70}, 10^{10}</math>
8.15	<math>x^{66} + \alpha^{170}x^{40} + x^{18} + \alpha^{85}x^5 + x^3</math>	Y 4346	<math>0^{39408}, 2^{20218}, 4^{4692}, 6^{838}, 8^{104}, 10^{12}, 12^8</math>
8.16	<math>x^{160} + x^{132} + x^{80} + x^{68} + x^6 + x^3</math>	SW 20	<math>0^{39692}, 2^{19752}, 4^{4756}, 6^{978}, 8^{72}, 10^{26}, 12^4</math>

ID	Representative	Equivalent to	Orthoderivative diff. spec.
9.1	<math>\alpha^{365}x^{257} + x^{96} + x^{68} + \alpha^{219}x^{33} + x^5</math>	I 4	<math>0^{158529}, 2^{80829}, 4^{18144}, 6^{3283}, 8^{469}, 10^{294}, 12^{84}</math>
9.2	<math>\alpha^{438}x^{129} + x^{66} + \alpha^{219}x^{10} + x^3</math>	I 8	<math>0^{159418}, 2^{79275}, 4^{18690}, 6^{3213}, 8^{742}, 10^{252}, 12^{21}, 16^{21}</math>
9.3	<math>x^{136} + x^{24} + x^{17} + \alpha^{73}x^{10} + x^3</math>	I 3	<math>0^{159684}, 2^{78687}, 4^{19089}, 6^{3136}, 8^{777}, 10^{147}, 12^{84}, 14^{28}</math>
9.4	<math>x^{68} + \alpha^{73}x^{40} + x^{33} + x^5</math>	I 10	<math>0^{159684}, 2^{79590}, 4^{17871}, 6^{3283}, 8^{700}, 10^{273}, 12^{147}, 14^{84}</math>
9.5	<math>\alpha^{73}x^{136} + \alpha^{146}x^{66} + \alpha^{219}x^{10} + x^3</math>	I 16	<math>0^{159908}, 2^{79086}, 4^{18081}, 6^{3353}, 8^{721}, 10^{336}, 12^{105}, 14^{21}, 16^{21}</math>
9.6	<math>x^{264} + \alpha^{73}x^{96} + \alpha^{219}x^{68} + x^5</math>	I 11	<math>0^{160020}, 2^{79023}, 4^{17997}, 6^{3213}, 8^{868}, 10^{378}, 12^{133}</math>
9.7	<math>\alpha^{219}x^{136} + x^{10} + x^3</math>	I 12	<math>0^{160657}, 2^{77910}, 4^{18312}, 6^{3360}, 8^{952}, 10^{273}, 12^{147}, 14^{21}</math>
9.8	<math>x^{192} + x^{66} + x^{17} + \alpha^{73}x^{10} + x^3</math>	I 14	<math>0^{162183}, 2^{76482}, 4^{17388}, 6^{3871}, 8^{1162}, 10^{252}, 12^{126}, 14^{126}, 16^{21}, 22^{21}</math>
9.9	<math>\alpha^{73}x^{192} + x^{136} + \alpha^{365}x^{129} + x^{17} + x^3</math>	I 5	<math>0^{162708}, 2^{77175}, 4^{15498}, 6^{4270}, 8^{1260}, 10^{252}, 12^{168}, 14^{84}, 16^{126}, 18^{42}, 22^{42}, 26^7</math>
9.10	<math>\alpha^{73}x^{129} + \alpha^{292}x^{66} + x^{10} + x^3</math>	I 9	<math>0^{163009}, 2^{75537}, 4^{17283}, 6^{4116}, 8^{1071}, 10^{168}, 12^{231}, 14^{28}, 16^{84}, 18^{63}, 20^{42}</math>
9.11	<math>x^{80} + \alpha^{146}x^{66} + \alpha^{73}x^{24} + x^{17}</math>	I 13	<math>0^{163366}, 2^{75117}, 4^{17010}, 6^{4536}, 8^{966}, 10^{252}, 12^{63}, 14^{154}, 16^{63}, 18^{84}, 22^{21}</math>
9.12	<math>x^{129} + \alpha^{73}x^{66} + x^{17} + x^{10} + \alpha^{365}x^3</math>	I 6	<math>0^{163996}, 2^{74802}, 4^{16380}, 6^{4368}, 8^{1449}, 10^{231}, 12^{126}, 14^{84}, 16^{42}, 18^{84}, 20^{42}, 22^{21}, 32^7</math>
9.13	<math>\alpha^{73}x^{136} + \alpha^{219}x^{66} + \alpha^{438}x^{10} + x^3</math>	I 15	<math>0^{168994}, 2^{68712}, 4^{15141}, 6^{6279}, 8^{1659}, 10^{336}, 12^{21}, 14^{21}, 16^{105}, 18^{147}, 20^{189}, 24^{21}, 26^7</math>
9.14	<math>\alpha^{438}x^{129} + x^{66} + \alpha^{219}x^{17} + x^3</math>	I 2	<math>0^{169428}, 2^{68040}, 4^{15561}, 6^{6034}, 8^{1533}, 10^{420}, 12^{126}, 14^{21}, 16^{84}, 18^{189}, 20^{126}, 22^{63}, 26^7</math>
9.15	<math>\alpha^{365}x^{80} + \alpha^{292}x^{24} + \alpha^{219}x^{17} + x^3</math>	I 17	<math>0^{170079}, 2^{66297}, 4^{16737}, 6^{6160}, 8^{1407}, 10^{420}, 12^{21}, 14^{42}, 16^{63}, 18^{210}, 20^{133}, 22^{63}</math>
9.16	<math>x^{257} + \alpha^{438}x^{68} + \alpha^{219}x^{12} + x^5</math>	I 7	<math>0^{171430}, 2^{64617}, 4^{16842}, 6^{5733}, 8^{1932}, 10^{483}, 12^{105}, 14^{21}, 16^{147}, 18^{105}, 20^{154}, 22^{21}, 24^{42}</math>
9.17	<math>x^{80} + \alpha^{73}x^{66} + x^{17} + \alpha^{73}x^{10} + x^3</math>	B 31	<math>0^{160440}, 2^{78834}, 4^{17514}, 6^{3388}, 8^{777}, 10^{483}, 12^{126}, 14^{49}, 16^{21}</math>
9.18	<math>\alpha^{365}x^{136} + x^{129} + \alpha^{73}x^{80} + x^{24} + x^{17} + x^3</math>	B 34	<math>0^{164199}, 2^{76734}, 4^{13524}, 6^{4312}, 8^{2205}, 12^{147}, 16^{294}, 18^{147}, 20^{49}, 22^{21}</math>
9.19	<math>\alpha^{73}x^{320} + x^{96} + \alpha^{219}x^{68} + x^{40} + x^{33} + x^5</math>	B 35	<math>0^{172557}, 2^{68355}, 4^{12201}, 6^{3871}, 8^{1638}, 10^{735}, 12^{1470}, 14^{49}, 16^{147}, 18^{441}, 20^{147}, 42^{21}</math>