ring: Z9 ring elements: #0: 0 #1: 1 #2: 2 #3: 3 #4: 4 #5: 5 #6: 6 #7: 7 #8: 8 == (9,2)-arc == 1 0 1 1 1 1 1 0 6 4 0 2 0 7 8 6 1 1 3 1 1 0 4 8 2 0 2 intersection numbers: {* 0^^45, 1^^36, 2^^36 *} quotient point multiplicities: {* 0^^4, 1^^9 *} quotient intersection numbers: {* 0, 3^^12 *} point neighborhood spectrum: {{ [single point]^^9, [empty neighborhood class]^^4 }} line spectrum: {* {* 0^^6, 1, 2^^2 *}^^36, {* 0^^6, 1^^2, 2 *}^^36, {* 0^^6, 1^^3 *}^^36, {* 0^^9 *}^^9 *} Gray map gives a [27,6,15]-code over F_3. #Aut = 3 == (19,3)-arc == 1 3 1 1 3 1 1 1 1 1 3 1 1 1 0 1 1 1 6 4 3 8 2 6 3 4 1 0 7 1 5 1 6 1 5 6 8 1 8 1 0 3 1 0 3 0 3 4 6 4 4 7 4 2 8 2 5 intersection numbers: {* 0^^16, 1^^30, 2^^15, 3^^56 *} quotient point multiplicities: {* 1^^7, 2^^6 *} quotient intersection numbers: {* 5^^6, 6^^3, 7^^4 *} point neighborhood spectrum: {{ [two points]^^6, [single point]^^7 }} line spectrum: {* {* 0^^12, 1^^4, 2^^3 *}^^20, {* 0^^12, 1^^5, 2^^2 *}^^12, {* 0^^12, 1^^7 *}^^4, {* 0^^13, 1^^3, 2^^3 *}^^12, {* 0^^13, 1^^4, 2^^2 *}^^3, {* 0^^13, 1^^5, 2 *}^^12, {* 0^^14, 1^^2, 2^^3 *}^^24, {* 0^^14, 1^^4, 2 *}^^18, {* 0^^14, 1^^5 *}^^12 *} Gray map gives a [57,6,34]-code over F_3. #Aut = 12 == (30,4)-arc == 0 1 3 1 1 1 1 1 6 1 0 1 1 1 6 1 1 3 0 3 6 1 6 1 1 1 3 1 0 1 0 5 0 6 0 5 0 8 6 4 1 6 3 4 1 1 3 1 1 1 1 5 1 8 8 1 1 7 1 7 1 2 1 3 6 5 3 5 1 2 0 7 4 8 6 8 7 6 4 4 7 1 5 4 1 6 8 3 2 6 intersection numbers: {* 0^^6, 1^^27, 3^^3, 4^^81 *} quotient point multiplicities: {* 0^^3, 3^^10 *} quotient intersection numbers: {* 3, 9^^9, 12^^3 *} point neighborhood spectrum: {{ [triangle]^^9, [line segment]^^1, [empty neighborhood class]^^3 }} line spectrum: {* {* 0^^18, 1^^8, 2^^4 *}^^27, {* 0^^21, 1^^5, 2^^4 *}^^54, {* 0^^21, 1^^8, 2 *}^^27, {* 0^^27, 1^^3 *}^^6, {* 0^^27, 2^^3 *}^^3 *} Gray map gives a [90,6,54]-code over F_3. #Aut = 2 == (39,5)-arc == 0 3 1 0 1 1 1 6 6 1 3 3 1 0 1 6 1 1 0 0 1 1 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 7 3 7 7 4 1 1 4 1 1 1 1 4 1 8 8 1 1 2 5 1 8 3 2 6 8 2 6 0 2 6 3 0 0 3 7 4 1 1 6 1 1 4 4 3 6 2 6 1 5 4 8 4 0 3 8 5 0 1 2 4 0 4 3 8 2 6 1 8 1 7 2 5 5 0 0 intersection numbers: {* 2^^39, 5^^78 *} quotient point multiplicities: {* 3^^13 *} quotient intersection numbers: {* 12^^13 *} point neighborhood spectrum: {{ [triangle]^^13 }} line spectrum: {* {* 0^^27, 1^^7, 2^^5 *}^^78, {* 0^^27, 1^^10, 2^^2 *}^^39 *} Gray map gives a [117,6,75]-code over F_3. #Aut = 13 == (49,6)-arc == 1 0 1 1 6 0 6 0 1 1 1 0 1 3 1 3 1 1 3 1 6 1 6 0 6 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 7 0 8 2 3 6 6 1 2 5 8 1 2 1 5 1 5 5 1 2 1 8 1 1 1 1 3 0 3 6 0 3 6 0 0 3 0 3 1 7 1 7 1 1 4 4 4 7 4 5 1 0 3 1 1 1 0 0 1 7 3 1 3 7 1 8 2 7 5 1 5 5 5 2 2 0 6 3 6 1 4 4 7 2 8 5 5 3 3 0 6 1 4 4 7 2 8 8 intersection numbers: {* 0^^4, 1^^2, 2^^2, 3^^10, 4^^7, 5^^28, 6^^64 *} quotient point multiplicities: {* 3^^3, 4^^10 *} quotient intersection numbers: {* 14^^3, 15^^6, 16^^4 *} point neighborhood spectrum: {{ {{ {{ 0^^1, 2^^2 }}^^2, {{ 1^^2, 2^^1 }}^^2 }}^^10, [triangle]^^3 }} line spectrum: {* {* 0^^33, 1^^10, 2^^6 *}^^31, {* 0^^33, 1^^13, 2^^3 *}^^2, {* 0^^33, 1^^16 *}^^3, {* 0^^34, 1^^9, 2^^6 *}^^24, {* 0^^34, 1^^10, 2^^5 *}^^17, {* 0^^34, 1^^11, 2^^4 *}^^6, {* 0^^34, 1^^12, 2^^3 *}^^5, {* 0^^34, 1^^13, 2^^2 *}, {* 0^^34, 1^^15 *}, {* 0^^35, 1^^8, 2^^6 *}^^9, {* 0^^35, 1^^9, 2^^5 *}^^11, {* 0^^35, 1^^10, 2^^4 *}, {* 0^^35, 1^^11, 2^^3 *}^^3, {* 0^^35, 1^^12, 2^^2 *}, {* 0^^35, 1^^13, 2 *}^^2 *} Gray map gives a [147,6,94]-code over F_3. #Aut = 1 == (60,7)-arc == 1 0 1 3 6 6 0 3 1 1 1 6 1 0 1 1 1 1 3 1 3 1 1 6 0 1 3 6 0 1 1 0 3 1 6 3 1 0 6 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 4 3 0 3 6 6 7 1 4 1 7 1 1 4 1 4 1 4 1 7 1 1 1 7 1 1 1 2 5 1 1 8 1 1 5 1 1 8 2 6 0 0 3 8 3 6 5 0 3 2 6 6 0 3 3 6 0 7 6 1 3 1 1 1 1 1 4 4 4 3 7 3 7 7 2 2 3 5 1 2 5 4 1 5 4 7 7 6 6 5 8 6 2 5 1 2 8 1 1 3 6 3 3 8 6 6 2 1 1 5 1 8 2 5 2 5 8 0 intersection numbers: {* 1^^6, 3^^3, 4^^15, 6^^6, 7^^87 *} quotient point multiplicities: {* 3^^6, 6^^7 *} quotient intersection numbers: {* 15^^4, 18^^3, 21^^6 *} point neighborhood spectrum: {{ [line segment]^^6, [complement of a line segment]^^7 }} line spectrum: {* {* 0^^39, 1^^14, 2^^7 *}^^54, {* 0^^42, 1^^11, 2^^7 *}^^18, {* 0^^42, 1^^14, 2^^4 *}^^9, {* 0^^45, 1^^8, 2^^7 *}^^15, {* 0^^45, 1^^9, 2^^6 *}^^6, {* 0^^45, 1^^11, 2^^4 *}^^6, {* 0^^45, 1^^12, 2^^3 *}^^3, {* 0^^45, 1^^14, 2 *}^^6 *} Gray map gives a [180,6,114]-code over F_3. #Aut = 3 == (69,8)-arc == 1 1 3 1 3 1 6 1 1 1 3 1 6 0 1 6 1 1 0 6 1 3 1 1 0 1 1 3 6 1 1 6 1 1 0 3 6 3 0 6 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 7 1 3 8 0 2 0 2 5 8 6 5 6 1 5 1 8 8 1 1 5 1 2 2 1 5 2 1 1 8 5 1 8 2 1 1 1 1 1 1 3 6 0 3 3 6 0 3 6 6 3 0 3 6 6 0 4 7 1 7 4 7 4 7 4 4 7 1 4 5 8 1 0 1 3 1 6 6 3 1 0 1 0 1 3 7 4 6 6 4 3 1 7 4 8 2 4 7 2 5 1 5 8 5 8 2 5 2 8 0 0 0 3 6 6 1 1 7 4 8 5 2 2 5 8 0 3 0 6 1 4 4 7 7 2 2 5 8 intersection numbers: {* 0^^3, 4^^3, 5^^6, 6^^12, 7^^30, 8^^63 *} quotient point multiplicities: {* 4^^3, 5^^3, 6^^7 *} quotient intersection numbers: {* 20^^6, 21^^3, 23^^3, 24 *} point neighborhood spectrum: {{ {{ {{ 0^^1, 2^^2 }}^^2, {{ 1^^2, 2^^1 }}^^2 }}^^3, {{ {{ 0^^1, 2^^1, 3^^1 }}^^1, {{ 1^^1, 2^^2 }}^^3 }}^^3, [complement of a triangle]^^1, [complement of a line segment]^^6 }} line spectrum: {* {* 0^^45, 1^^16, 2^^8 *}^^9, {* 0^^46, 1^^15, 2^^8 *}^^18, {* 0^^46, 1^^16, 2^^7 *}^^9, {* 0^^48, 1^^13, 2^^8 *}^^12, {* 0^^48, 1^^14, 2^^7 *}^^6, {* 0^^48, 1^^15, 2^^6 *}^^6, {* 0^^48, 1^^16, 2^^5 *}^^3, {* 0^^49, 1^^12, 2^^8 *}^^24, {* 0^^49, 1^^13, 2^^7 *}^^15, {* 0^^49, 1^^14, 2^^6 *}^^6, {* 0^^49, 1^^15, 2^^5 *}^^3, {* 0^^49, 1^^16, 2^^4 *}^^3, {* 0^^49, 1^^20 *}^^3 *} Gray map gives a [207,6,134]-code over F_3. #Aut = 3 == (81,9)-arc == 1 1 0 6 6 0 3 0 6 3 3 3 0 6 0 3 6 3 0 6 6 0 0 3 6 3 0 3 6 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 7 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 6 0 6 0 0 3 3 6 0 3 6 3 6 6 0 0 3 6 0 3 0 3 3 6 6 0 7 1 4 1 4 7 1 4 7 4 7 1 7 1 4 7 1 4 1 4 7 4 7 1 4 5 8 0 0 3 3 0 6 6 3 6 1 4 4 1 4 7 7 7 1 5 8 5 8 2 5 2 2 8 0 0 0 3 6 3 3 6 6 1 1 7 4 4 1 4 7 7 8 2 8 5 5 2 2 5 8 0 3 0 6 3 3 0 6 6 1 1 1 4 4 4 7 7 7 2 2 8 5 2 5 8 intersection numbers: {* 0^^9, 9^^108 *} quotient point multiplicities: {* 0^^4, 9^^9 *} quotient intersection numbers: {* 0, 27^^12 *} point neighborhood spectrum: {{ [full neighborhood class]^^9, [empty neighborhood class]^^4 }} line spectrum: {* {* 0^^54, 1^^18, 2^^9 *}^^108, {* 0^^81 *}^^9 *} Gray map gives a [243,6,162]-code over F_3. #Aut = 2834352 == (93,10)-arc == 3 6 0 0 6 6 0 3 0 6 3 3 3 0 6 0 3 6 3 0 6 6 0 0 3 6 3 0 3 6 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 3 6 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 6 0 6 0 0 3 3 6 0 3 6 3 6 6 0 0 3 6 0 3 0 3 3 6 6 0 4 4 4 1 1 1 4 4 4 8 2 2 5 5 8 5 8 2 5 8 8 8 2 5 2 2 5 5 8 2 5 8 2 5 8 2 1 1 1 0 0 3 3 0 6 6 3 6 1 4 4 1 4 7 7 7 1 5 8 5 8 2 5 2 2 8 0 0 0 3 6 3 3 6 6 1 1 7 4 4 1 4 7 7 8 2 8 5 5 2 2 5 8 0 3 6 1 4 7 2 5 8 0 3 6 6 3 3 0 6 0 1 7 4 1 4 4 1 7 7 8 8 2 2 2 5 5 5 8 intersection numbers: {* 0^^2, 3^^3, 6^^3, 9, 10^^108 *} quotient point multiplicities: {* 3^^4, 9^^9 *} quotient intersection numbers: {* 12, 30^^12 *} point neighborhood spectrum: {{ [line segment]^^4, [full neighborhood class]^^9 }} line spectrum: {* {* 0^^63, 1^^20, 2^^10 *}^^108, {* 0^^81, 1^^3, 2^^9 *}, {* 0^^81, 1^^6, 2^^6 *}^^3, {* 0^^81, 1^^9, 2^^3 *}^^3, {* 0^^81, 1^^12 *}^^2 *} Gray map gives a [279,6,171]-code over F_3. #Aut = 39366 == (105,11)-arc == 0 3 3 6 6 0 0 3 6 0 6 6 0 3 0 6 3 3 3 0 6 3 0 6 6 0 0 3 6 3 0 3 6 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 3 0 0 3 3 6 6 6 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 6 0 6 0 0 3 3 6 0 3 6 3 6 0 6 0 3 0 3 3 6 6 0 7 1 4 1 4 7 1 4 7 4 7 1 7 1 4 7 1 4 1 4 7 4 7 1 8 2 5 5 8 2 5 8 8 8 2 5 2 2 5 5 8 2 5 8 2 5 8 2 1 1 1 1 1 1 1 1 1 0 0 3 3 0 6 6 3 6 1 4 4 7 7 1 5 8 5 8 2 5 2 2 8 0 0 0 3 6 3 3 6 6 1 1 7 4 4 7 8 2 8 5 5 2 2 5 8 0 3 0 6 3 3 0 6 6 1 1 1 4 4 4 7 7 7 2 2 8 5 5 8 0 3 6 3 6 0 1 7 4 1 4 4 1 7 7 8 8 2 2 2 5 5 5 8 intersection numbers: {* 0, 9^^8, 11^^108 *} quotient point multiplicities: {* 6^^4, 9^^9 *} quotient intersection numbers: {* 24, 33^^12 *} point neighborhood spectrum: {{ [complement of a line segment]^^4, [full neighborhood class]^^9 }} line spectrum: {* {* 0^^72, 1^^22, 2^^11 *}^^108, {* 0^^81, 1^^15, 2^^9 *}^^8, {* 0^^81, 1^^24 *} *} Gray map gives a [315,6,207]-code over F_3. #Aut = 314928