ring: F3[X]/(X^2) ring elements: #0: 0 #1: 1 #2: 2 #3: X #4: X+1 #5: X+2 #6: 2X #7: 2X+1 #8: 2X+2 == (9,2)-arc == 1 1 1 0 1 1 1 3 0 7 6 8 6 4 5 6 1 1 2 0 0 1 7 5 7 8 6 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 = 54 == (18,3)-arc == 0 1 3 1 1 1 6 1 1 1 1 1 3 1 1 1 0 6 0 2 3 8 2 5 6 0 6 3 6 5 1 8 0 3 1 1 1 8 1 0 6 3 1 0 3 6 7 8 4 8 7 7 7 1 intersection numbers: {* 0^^36, 2^^27, 3^^54 *} quotient point multiplicities: {* 0^^7, 3^^6 *} quotient intersection numbers: {* 3^^6, 6^^3, 9^^4 *} point neighborhood spectrum: {{ [line segment]^^6, [empty neighborhood class]^^7 }} line spectrum: {* {* 0^^9, 1^^6, 2^^3 *}^^36, {* 0^^12, 1^^4, 2^^2 *}^^27, {* 0^^15, 1^^3 *}^^36, {* 0^^15, 2^^3 *}^^18 *} Gray map gives a [54,6,27]-code over F_3. #Aut = 1296 == (30,4)-arc == 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 6 1 1 6 1 1 1 1 6 1 1 1 1 1 1 3 7 1 5 0 8 1 3 1 6 6 1 7 3 5 1 3 5 1 6 6 2 5 1 8 8 7 4 7 8 0 1 1 2 0 2 7 6 2 7 4 5 5 7 6 4 5 0 7 2 5 0 1 1 7 1 3 6 6 8 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 = 108 == (38,5)-arc == 0 1 1 1 0 1 1 6 1 1 3 0 1 0 1 3 3 0 1 6 1 1 1 1 6 1 1 1 1 1 1 1 1 1 1 1 1 1 0 7 4 7 6 7 1 1 1 1 1 1 1 1 7 1 1 1 5 1 5 2 5 8 1 8 3 0 8 3 5 8 6 6 3 3 6 6 1 3 6 6 1 1 1 0 7 2 1 4 5 1 5 4 7 7 6 2 0 0 1 7 5 1 0 0 8 6 2 2 7 4 7 5 2 5 intersection numbers: {* 0^^2, 1^^12, 2^^15, 4^^26, 5^^62 *} quotient point multiplicities: {* 1, 2^^2, 3^^9, 6 *} quotient intersection numbers: {* 10^^3, 11^^7, 15^^3 *} point neighborhood spectrum: {{ [triangle]^^9, [two points]^^2, [single point]^^1, [complement of a line segment]^^1 }} line spectrum: {* {* 0^^23, 1^^10, 2^^5 *}^^27, {* 0^^27, 1^^6, 2^^5 *}^^29, {* 0^^27, 1^^7, 2^^4 *}^^14, {* 0^^27, 1^^9, 2^^2 *}^^12, {* 0^^27, 1^^10, 2 *}^^6, {* 0^^27, 1^^11 *}^^2, {* 0^^28, 1^^5, 2^^5 *}^^6, {* 0^^28, 1^^6, 2^^4 *}^^12, {* 0^^28, 1^^8, 2^^2 *}^^3, {* 0^^28, 1^^9, 2 *}^^6 *} Gray map gives a [114,6,69]-code over F_3. #Aut = 4 == (50,6)-arc == 0 1 1 3 1 1 0 1 6 0 6 1 1 1 0 1 3 3 6 1 6 1 3 1 1 0 6 0 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 8 0 2 5 6 5 6 1 1 5 8 8 1 2 1 1 1 5 1 8 1 5 8 1 1 1 1 3 6 0 0 3 0 3 3 6 0 1 4 4 7 7 7 1 4 1 7 4 1 8 0 1 6 6 1 0 1 0 0 1 7 4 6 1 6 1 4 2 7 2 7 5 5 8 8 2 2 0 0 3 1 1 7 7 8 5 8 3 3 6 6 1 4 7 7 2 2 8 intersection numbers: {* 0^^4, 2^^3, 3^^14, 4^^4, 5^^16, 6^^76 *} quotient point multiplicities: {* 3^^2, 4^^11 *} quotient intersection numbers: {* 14, 15^^6, 16^^6 *} point neighborhood spectrum: {{ {{ {{ 0^^1, 2^^2 }}^^2, {{ 1^^2, 2^^1 }}^^2 }}^^11, [triangle]^^2 }} line spectrum: {* {* 0^^34, 1^^10, 2^^6 *}^^42, {* 0^^34, 1^^13, 2^^3 *}^^12, {* 0^^35, 1^^9, 2^^6 *}^^30, {* 0^^35, 1^^10, 2^^5 *}^^16, {* 0^^35, 1^^12, 2^^3 *}^^2, {* 0^^35, 1^^13, 2^^2 *}^^2, {* 0^^35, 1^^15 *}^^4, {* 0^^36, 1^^8, 2^^6 *}^^4, {* 0^^36, 1^^10, 2^^4 *}^^4, {* 0^^36, 1^^12, 2^^2 *} *} Gray map gives a [150,6,96]-code over F_3. #Aut = 4 == (60,7)-arc == 1 0 3 6 1 1 0 3 1 0 1 6 1 0 1 3 1 6 1 1 3 1 0 1 6 1 3 1 1 6 0 1 1 6 3 0 1 3 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 7 4 6 6 7 1 4 1 7 1 1 1 1 1 4 7 1 4 1 1 1 8 1 2 2 1 1 8 8 1 1 1 8 1 8 2 6 0 2 2 0 3 3 0 3 6 6 3 6 0 3 6 0 7 1 4 6 1 1 1 6 1 1 1 4 0 4 3 7 3 7 0 2 6 2 8 1 8 1 8 7 0 7 3 6 1 8 3 6 8 5 2 7 2 1 4 0 0 1 7 3 3 6 1 4 4 1 7 8 2 2 2 8 0 3 0 intersection numbers: {* 2^^12, 4^^9, 6^^12, 7^^84 *} quotient point multiplicities: {* 0, 5^^12 *} quotient intersection numbers: {* 15^^4, 20^^9 *} point neighborhood spectrum: {{ {{ {{ 0^^1, 2^^1, 3^^1 }}^^1, {{ 1^^1, 2^^2 }}^^3 }}^^12, [empty neighborhood class]^^1 }} line spectrum: {* {* 0^^40, 1^^13, 2^^7 *}^^72, {* 0^^40, 1^^16, 2^^4 *}^^9, {* 0^^45, 1^^8, 2^^7 *}^^12, {* 0^^45, 1^^9, 2^^6 *}^^12, {* 0^^45, 1^^13, 2^^2 *}^^12 *} Gray map gives a [180,6,114]-code over F_3. #Aut = 432 == (69,8)-arc == 0 3 3 6 1 0 6 1 0 1 6 1 6 1 0 1 3 0 6 1 3 1 3 1 3 0 1 1 1 1 6 1 1 1 1 6 1 0 3 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 0 3 0 3 5 6 6 8 1 2 1 5 1 8 1 8 1 1 1 5 1 2 1 2 1 1 5 8 2 5 1 8 2 5 8 1 2 1 1 1 1 1 3 6 0 6 0 0 3 3 6 0 6 3 6 0 3 3 6 0 4 1 7 1 7 4 7 1 4 1 1 1 1 3 1 1 6 0 0 0 1 3 7 3 4 0 6 6 4 3 1 6 7 1 4 8 8 2 2 7 2 5 5 5 2 8 8 8 5 2 5 0 0 0 3 6 3 3 6 6 1 7 4 1 4 7 5 2 8 3 0 6 1 4 7 2 5 8 intersection numbers: {* 1^^6, 3^^3, 4^^6, 6^^6, 7^^15, 8^^81 *} quotient point multiplicities: {* 3^^6, 6^^4, 9^^3 *} quotient intersection numbers: {* 15^^4, 24^^9 *} point neighborhood spectrum: {{ [line segment]^^6, [complement of a line segment]^^4, [full neighborhood class]^^3 }} line spectrum: {* {* 0^^45, 1^^16, 2^^8 *}^^81, {* 0^^54, 1^^8, 2^^7 *}^^15, {* 0^^54, 1^^9, 2^^6 *}^^6, {* 0^^54, 1^^11, 2^^4 *}^^6, {* 0^^54, 1^^12, 2^^3 *}^^3, {* 0^^54, 1^^14, 2 *}^^6 *} Gray map gives a [207,6,132]-code over F_3. #Aut = 18 == (81,9)-arc == 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 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 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 7 1 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 0 0 3 3 0 6 6 3 6 1 4 4 1 4 7 7 7 1 2 8 5 8 8 5 2 2 5 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 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^^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 = 5668704 == (93,10)-arc == 0 3 3 6 6 0 0 3 6 0 6 6 0 3 0 6 3 3 3 0 6 0 3 6 3 0 6 6 3 0 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 3 6 0 6 0 0 3 3 6 0 6 3 6 0 3 0 3 3 6 6 0 1 4 7 4 7 1 7 1 4 7 1 4 1 4 7 4 7 1 4 7 1 8 2 2 5 5 8 5 8 2 5 8 8 8 2 5 2 2 5 8 5 2 1 1 1 1 1 1 1 1 1 0 0 3 3 0 6 6 3 6 1 4 4 1 4 7 7 7 1 8 5 2 0 0 0 3 6 3 3 6 6 1 4 7 8 2 8 5 5 2 2 5 8 3 0 6 1 1 1 4 4 4 7 7 7 2 2 8 5 2 5 8 5 8 0 3 6 6 3 3 0 6 0 1 7 4 1 4 4 1 7 7 8 2 5 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 = 78732 == (105,11)-arc == 3 6 6 0 0 3 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 1 1 1 1 1 1 1 1 1 0 0 3 3 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 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 1 7 1 7 7 1 7 1 7 1 1 7 7 1 7 1 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 1 1 1 0 0 3 3 0 6 6 3 6 1 4 4 1 4 7 7 7 1 2 8 5 8 8 5 2 2 5 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 3 0 6 1 1 4 4 7 7 2 8 2 5 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, 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 = 629856