# Difference between revisions of "Lower bounds on APN-distance for all known APN functions in dimension 8"

 1 ${\displaystyle \{111^{85},135^{170},256\}}$ 2 ${\displaystyle \{111^{85},135^{170},256\}}$ 3 ${\displaystyle \{111^{85},135^{170},256\}}$ 4 ${\displaystyle \{111^{85},135^{170},256\}}$ 5 ${\displaystyle \{111^{85},135^{170},256\}}$ 6 ${\displaystyle \{111^{85},135^{170},256\}}$ 7 ${\displaystyle \{111^{85},135^{170},256\}}$ 8 ${\displaystyle \{111^{85},135^{170},256\}}$ 9 ${\displaystyle \{111^{85},135^{170},256\}}$ 10 ${\displaystyle \{99^{12},111^{10},117^{48},123^{40},129^{64},135^{44},141^{16},147^{20},159,256\}}$ 11 ${\displaystyle \{105^{8},111^{20},117^{48},123^{48},129^{48},135^{48},141^{16},147^{8},153^{8},159^{3},256\}}$ 12 ${\displaystyle \{105^{16},111^{18},117^{32},123^{56},129^{48},135^{36},141^{32},147^{16},159,256\}}$ 13 ${\displaystyle \{111^{85},135^{170},256\}}$ 14 ${\displaystyle \{99^{3},105^{8},111^{25},117^{36},123^{42},129^{52},135^{46},141^{28},147^{11},153^{4},256\}}$ 15 ${\displaystyle \{111^{85},135^{170},256\}}$ 16 ${\displaystyle \{111^{85},135^{170},256\}}$ 17 ${\displaystyle \{111^{85},135^{170},256\}}$ 18 ${\displaystyle \{111^{85},135^{170},256\}}$ 19 $\displaystyle \{ 111^{85}, 135^{170}, 256 \}$ 20 $\displaystyle \{ 111^{85}, 135^{170}, 256 \}$ 21 ${\displaystyle \{111^{85},135^{170},256\}}$ 22 $\displaystyle \{ 111^{85}, 135^{170}, 256 \}$ 23 ${\displaystyle \{111^{85},135^{170},256\}}$ 24 ${\displaystyle \{99,105^{11},111^{19},117^{42},123^{48},129^{48},135^{44},141^{22},147^{15},153^{5},256\}}$ 25 $\displaystyle \{ 93, 99^{6}, 105^{7}, 111^{16}, 117^{34}, 123^{50}, 129^{54}, 135^{46}, 141^{29}, 147^{8}, 153^{3}, 159, 256 \}$ 26 $\displaystyle \{ 99^{6}, 105^{5}, 111^{19}, 117^{38}, 123^{50}, 129^{56}, 135^{36}, 141^{26}, 147^{16}, 153^{3}, 256 \}$ 27 ${\displaystyle \{99^{4},111^{43},123^{98},135^{88},147^{18},159^{4},256\}}$ 28 $\displaystyle \{ 93, 99^{2}, 105^{7}, 111^{20}, 117^{39}, 123^{46}, 129^{62}, 135^{42}, 141^{15}, 147^{16}, 153^{3}, 159, 165, 256 \}$ 29 $\displaystyle \{ 93, 99^{2}, 105^{9}, 111^{21}, 117^{32}, 123^{54}, 129^{52}, 135^{40}, 141^{31}, 147^{8}, 153^{3}, 159^{2}, 256 \}$ 30 $\displaystyle \{ 87, 93^{2}, 99, 105^{7}, 111^{22}, 117^{32}, 123^{48}, 129^{54}, 135^{47}, 141^{30}, 147^{7}, 153^{3}, 159, 256 \}$ 31 $\displaystyle \{ 99^{4}, 105^{5}, 111^{22}, 117^{34}, 123^{54}, 129^{64}, 135^{30}, 141^{22}, 147^{14}, 153^{3}, 159^{3}, 256 \}$ 32 $\displaystyle \{ 93, 99^{4}, 105^{10}, 111^{11}, 117^{42}, 123^{54}, 129^{44}, 135^{44}, 141^{29}, 147^{14}, 153^{2}, 256 \}$ 33 $\displaystyle \{ 93, 99^{2}, 105^{7}, 111^{23}, 117^{36}, 123^{50}, 129^{52}, 135^{40}, 141^{27}, 147^{12}, 153^{5}, 256 \}$ 34 $\displaystyle \{ 93, 99^{3}, 105^{10}, 111^{19}, 117^{30}, 123^{52}, 129^{56}, 135^{44}, 141^{25}, 147^{9}, 153^{6}, 256 \}$ 35 ${\displaystyle \{99^{3},105^{7},111^{21},117^{38},123^{52},129^{52},135^{40},141^{26},147^{9},153^{5},159^{2},256\}}$ 36 $\displaystyle \{ 99^{2}, 105^{7}, 111^{23}, 117^{38}, 123^{52}, 129^{52}, 135^{38}, 141^{26}, 147^{10}, 153^{5}, 159^{2}, 256 \}$ 37 $\displaystyle \{ 93^{3}, 99^{5}, 105^{17}, 111^{18}, 117^{28}, 123^{42}, 129^{48}, 135^{44}, 141^{25}, 147^{17}, 153^{7}, 159, 256 \}$ 38 $\displaystyle \{ 99^{3}, 105^{3}, 111^{24}, 117^{42}, 123^{50}, 129^{56}, 135^{36}, 141^{22}, 147^{11}, 153^{5}, 159^{3}, 256 \}$ 39 $\displaystyle \{ 99, 105^{11}, 111^{17}, 117^{42}, 123^{52}, 129^{48}, 135^{44}, 141^{22}, 147^{11}, 153^{5}, 159^{2}, 256 \}$ 40 $\displaystyle \{ 93^{2}, 99^{2}, 105^{8}, 111^{23}, 117^{28}, 123^{48}, 129^{60}, 135^{46}, 141^{26}, 147^{6}, 153^{4}, 159^{2}, 256 \}$ 41 $\displaystyle \{ 93^{2}, 99^{3}, 105^{9}, 111^{12}, 117^{38}, 123^{56}, 129^{52}, 135^{42}, 141^{24}, 147^{13}, 153^{3}, 159, 256 \}$ 42 $\displaystyle \{ 93, 99^{4}, 105^{8}, 111^{16}, 117^{34}, 123^{58}, 129^{52}, 135^{38}, 141^{29}, 147^{10}, 153^{4}, 159, 256 \}$ 43 $\displaystyle \{ 105^{10}, 111^{28}, 117^{34}, 123^{46}, 129^{50}, 135^{42}, 141^{30}, 147^{10}, 153^{4}, 159, 256 \}$ 44 $\displaystyle \{ 93^{3}, 99, 105^{6}, 111^{21}, 117^{38}, 123^{46}, 129^{56}, 135^{42}, 141^{23}, 147^{17}, 153^{2}, 256 \}$ 45 $\displaystyle \{ 93, 99^{3}, 105^{7}, 111^{25}, 117^{34}, 123^{42}, 129^{54}, 135^{46}, 141^{29}, 147^{11}, 153^{3}, 256 \}$ 46 $\displaystyle \{ 99, 105^{9}, 111^{27}, 117^{34}, 123^{48}, 129^{52}, 135^{36}, 141^{30}, 147^{15}, 153^{3}, 256 \}$ 47 $\displaystyle \{ 99^{2}, 105^{11}, 111^{24}, 117^{28}, 123^{50}, 129^{58}, 135^{38}, 141^{28}, 147^{12}, 153^{3}, 159, 256 \}$ 48 $\displaystyle \{ 93^{2}, 99^{6}, 105^{13}, 111^{22}, 117^{32}, 123^{44}, 129^{42}, 135^{40}, 141^{30}, 147^{14}, 153^{9}, 159, 256 \}$ 49 $\displaystyle \{ 93, 99^{4}, 105^{6}, 111^{19}, 117^{34}, 123^{56}, 129^{56}, 135^{34}, 141^{29}, 147^{12}, 153^{2}, 159^{2}, 256 \}$ 50 $\displaystyle \{ 93^{2}, 99, 105^{9}, 111^{21}, 117^{32}, 123^{54}, 129^{50}, 135^{42}, 141^{30}, 147^{9}, 153^{5}, 256 \}$ 51 ${\displaystyle \{93,105^{10},111^{20},117^{38},123^{50},129^{56},135^{42},141^{17},147^{14},153^{6},159,256\}}$ 52 ${\displaystyle \{93^{2},99^{7},105^{12},111^{19},117^{38},123^{38},129^{46},135^{42},141^{24},147^{19},153^{6},159^{2},256\}}$ 53 ${\displaystyle \{99^{5},105^{8},111^{21},117^{34},123^{42},129^{58},135^{50},141^{22},147^{9},153^{6},256\}}$ 54 ${\displaystyle \{99,105^{12},111^{25},117^{28},123^{50},129^{56},135^{38},141^{28},147^{13},153^{4},256\}}$ 55 ${\displaystyle \{93^{2},99^{4},105^{5},111^{16},117^{36},123^{58},129^{54},135^{38},141^{26},147^{10},153^{5},159,256\}}$ 56 ${\displaystyle \{93^{2},99^{2},105^{9},111^{19},117^{38},123^{42},129^{52},135^{52},141^{24},147^{12},153^{3},256\}}$ 57 ${\displaystyle \{87,93,99^{3},105^{14},111^{26},117^{30},123^{44},129^{48},135^{35},141^{25},147^{17},153^{10},159,256\}}$ 58 ${\displaystyle \{99,105^{13},111^{23},117^{34},123^{48},129^{40},135^{48},141^{38},147^{7},153^{3},256\}}$ 59 ${\displaystyle \{93,99^{3},105^{9},111^{19},117^{36},123^{52},129^{44},135^{44},141^{35},147^{9},153^{3},256\}}$ 60 ${\displaystyle \{99^{4},105^{5},111^{17},117^{42},123^{60},129^{52},135^{30},141^{22},147^{16},153^{7},256\}}$ 61 ${\displaystyle \{99^{3},105^{10},111^{19},117^{38},123^{42},129^{58},135^{50},141^{18},147^{11},153^{4},159^{2},256\}}$ 62 ${\displaystyle \{99^{4},105^{7},111^{24},117^{38},123^{42},129^{48},135^{46},141^{34},147^{10},153,159,256\}}$ 63 ${\displaystyle \{93,99^{2},105^{9},111^{19},117^{40},123^{44},129^{52},135^{50},141^{23},147^{10},153^{3},159^{2},256\}}$ 64 ${\displaystyle \{93,99^{4},105^{7},111^{16},117^{44},123^{46},129^{48},135^{46},141^{27},147^{14},153,159,256\}}$ 65 ${\displaystyle \{99^{2},105^{8},111^{22},117^{38},123^{52},129^{50},135^{40},141^{26},147^{10},153^{6},159,256\}}$ 66 ${\displaystyle \{93,99^{2},105^{9},111^{20},117^{30},123^{58},129^{58},135^{34},141^{25},147^{12},153^{5},159,256\}}$ 67 ${\displaystyle \{93,99^{4},105^{7},111^{21},117^{34},123^{48},129^{54},135^{42},141^{29},147^{12},153^{3},256\}}$ 68 ${\displaystyle \{93,99^{2},105^{10},111^{19},117^{34},123^{54},129^{48},135^{44},141^{29},147^{8},153^{6},256\}}$ 69 ${\displaystyle \{93,99^{4},105^{9},111^{20},117^{28},123^{50},129^{60},135^{42},141^{27},147^{10},153^{3},159,256\}}$ 70 ${\displaystyle \{99^{6},111^{36},123^{105},135^{88},147^{16},159^{3},171,256\}}$ 71 ${\displaystyle \{93^{2},99^{4},105^{9},111^{17},117^{26},123^{56},129^{60},135^{38},141^{28},147^{12},153^{3},256\}}$ 72 ${\displaystyle \{87,99^{3},105^{5},111^{18},117^{42},123^{52},129^{52},135^{43},141^{22},147^{9},153^{7},159,256\}}$ 73 ${\displaystyle \{93,99^{2},105^{8},111^{24},117^{32},123^{46},129^{58},135^{46},141^{23},147^{8},153^{6},159,256\}}$ 74 ${\displaystyle \{93,99^{2},105^{10},111^{19},117^{32},123^{54},129^{54},135^{44},141^{23},147^{8},153^{8},256\}}$ 75 ${\displaystyle \{93,99^{3},105^{9},111^{23},117^{32},123^{44},129^{52},135^{48},141^{31},147^{9},153^{3},256\}}$ 76 ${\displaystyle \{99,105^{11},111^{17},117^{42},123^{52},129^{48},135^{44},141^{22},147^{11},153^{5},159^{2},256\}}$ 77 ${\displaystyle \{93^{2},99^{4},105^{4},111^{15},117^{42},123^{58},129^{46},135^{40},141^{28},147^{10},153^{6},256\}}$ 78 ${\displaystyle \{93^{2},99,105^{5},111^{18},117^{49},123^{50},129^{42},135^{44},141^{28},147^{13},153,159,165,256\}}$ 79 ${\displaystyle \{99,105^{9},111^{22},117^{38},123^{54},129^{48},135^{40},141^{26},147^{9},153^{7},159,256\}}$ 80 ${\displaystyle \{99^{3},105^{5},111^{26},117^{42},123^{38},129^{52},135^{52},141^{22},147^{7},153^{7},159,256\}}$ 81 ${\displaystyle \{93,99,105^{11},111^{15},117^{40},123^{56},129^{48},135^{40},141^{23},147^{15},153^{5},256\}}$ 82 ${\displaystyle \{87,99^{4},105^{5},111^{15},117^{41},123^{58},129^{50},135^{37},141^{30},147^{10},153,159^{2},165,256\}}$