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"improved_johnson", "value": 12326959735315999300}], "known_codes": [], "upper_bound": 12326959735315999300, "classified": false, "lower_bound": 12159772591358508651, "lower_bound_constraints": [{"parameter": "", "name": "trivial_1", "value": 0}, {"parameter": "", "name": "LMRD", "value": 12157665459056928801}, {"parameter": "", "name": "sphere_covering", "value": 1670344887941592}, {"parameter": "", "name": "graham_sloane", "value": 1879074357110506}, {"parameter": "optimal [(0, 1, 2, 3, 4), (0, 1, 2, 5, 6), (0, 1, 2, 7, 8), (0, 1, 3, 5, 7), (0, 1, 3, 6, 8), (0, 1, 4, 5, 8), (0, 1, 4, 6, 7), (0, 2, 3, 5, 8), (0, 2, 3, 6, 7), (0, 2, 4, 5, 7), (0, 2, 4, 6, 8), (0, 3, 4, 5, 6), (0, 3, 4, 7, 8), (0, 5, 6, 7, 8), (1, 2, 3, 5, 9), (1, 2, 4, 6, 9), (1, 3, 4, 7, 9), (1, 5, 6, 7, 9), (2, 3, 4, 8, 9), (2, 5, 6, 8, 9), (3, 5, 7, 8, 9), (4, 6, 7, 8, 9)] (if conjecture about Ferrers Diagram Rank-Metric Codes is true: 12159543650778161152 with optimal [(0, 1, 2, 3, 4), (0, 1, 2, 5, 6), (0, 1, 2, 7, 8), (0, 1, 3, 5, 7), (0, 1, 3, 6, 8), (0, 1, 4, 5, 8), (0, 1, 4, 6, 7), (0, 2, 3, 5, 8), (0, 2, 3, 6, 7), (0, 2, 4, 5, 7), (0, 2, 4, 6, 8), (0, 3, 4, 5, 6), (0, 3, 4, 7, 8), (0, 5, 6, 7, 8), (1, 2, 3, 5, 9), (1, 2, 4, 6, 9), (1, 3, 4, 7, 9), (1, 5, 6, 7, 9), (2, 3, 4, 8, 9), (2, 5, 6, 8, 9), (3, 5, 7, 8, 9), (4, 6, 7, 8, 9)])", "name": "pending_dots", "value": 12159543650778161152}, {"parameter": "optimal [(0, 1, 2, 3, 4), (0, 1, 2, 5, 6), (0, 1, 2, 7, 8), (0, 1, 3, 5, 7), (0, 1, 3, 6, 8), (0, 1, 4, 5, 8), (0, 1, 4, 6, 7), (0, 2, 3, 5, 8), (0, 2, 3, 6, 7), (0, 2, 4, 5, 7), (0, 2, 4, 6, 8), (0, 3, 4, 5, 6), (0, 3, 4, 7, 8), (0, 5, 6, 7, 8), (1, 2, 3, 5, 9), (1, 2, 4, 6, 9), (1, 3, 4, 7, 9), (1, 5, 6, 7, 9), (2, 3, 4, 8, 9), (2, 5, 6, 8, 9), (3, 5, 7, 8, 9), (4, 6, 7, 8, 9)] (if conjecture about Ferrers Diagram Rank-Metric Codes is true: 12159543650778159104 with optimal [(0, 1, 2, 3, 4), (0, 1, 2, 5, 6), (0, 1, 2, 7, 8), (0, 1, 3, 5, 7), (0, 1, 3, 6, 8), (0, 1, 4, 5, 8), (0, 1, 4, 6, 7), (0, 2, 3, 5, 8), (0, 2, 3, 6, 7), (0, 2, 4, 5, 7), (0, 2, 4, 6, 8), (0, 3, 4, 5, 6), (0, 3, 4, 7, 8), (0, 5, 6, 7, 8), (1, 2, 3, 5, 9), (1, 2, 4, 6, 9), (1, 3, 4, 7, 9), (1, 5, 6, 7, 9), (2, 3, 4, 8, 9), (2, 5, 6, 8, 9), (3, 5, 7, 8, 9), (4, 6, 7, 8, 9)])", "name": "echelon_ferrers", "value": 12159543650778159104}, {"parameter": "", "name": "multicomponent", "value": 12157665462543713203}, {"parameter": "[(0, 1, 2, 3, 4), (0, 1, 2, 5, 6), (0, 1, 3, 5, 7), (0, 1, 3, 6, 8), (0, 3, 4, 5, 6), (0, 2, 4, 5, 7), (0, 1, 4, 6, 7), (0, 1, 4, 5, 8), (0, 1, 2, 7, 8), (0, 2, 3, 6, 7), (0, 2, 3, 5, 8), (1, 2, 3, 5, 9), (0, 2, 4, 6, 8), (1, 2, 4, 6, 9), (0, 3, 4, 7, 8), (2, 3, 4, 7, 9), (1, 3, 4, 8, 9), (1, 3, 6, 7, 9), (1, 4, 5, 7, 9), (2, 4, 5, 8, 9), (2, 3, 6, 8, 9), (0, 5, 6, 7, 8), (1, 5, 6, 8, 9), (2, 5, 6, 7, 9), (3, 5, 7, 8, 9), (4, 6, 7, 8, 9)]", "name": "ef_computation", "value": 12159543650774039506}, {"parameter": "", "name": "CossidentePavese14_theorem311", "value": 12159772590972225574}, {"parameter": "", "name": "XuChen2018", "value": 12159772590971088161}, {"parameter": "", "name": "ChenHeWengXu2019_T41", "value": 12159772590971088161}, {"parameter": "", "name": "LiuChangFeng2019_Theo_2_6", "value": 12159772590971088162}, {"parameter": "", "name": "two_pivot_block_construction", "value": 12159518761675317248}, {"parameter": "", "name": "ChenHeWengXu2019_T31", "value": 12159772590971088161}, {"parameter": "(5,),(3,),(2,)", "name": "CKMP2019_Cor_45", "value": 12159772591358508651}, {"parameter": "(5,),(2,),(1,)", "name": "CKMP2019_Cor_45", "value": 12159772591358508651}, {"parameter": "(5, 5)", "name": "CKMP2019_Lem_41", "value": 12159772590971088162}, {"parameter": "(5, 5)", "name": "CKMP2019_Cor_42", "value": 12159772590971088162}, {"parameter": "5", "name": "linkage_GLT", "value": 12157665459056928802}, {"parameter": "5", "name": "improved_linkage", "value": 12157665462544318444}, {"parameter": "6", "name": "improved_linkage", "value": 205891132154428}, {"parameter": "7", "name": "improved_linkage", "value": 208436484707380}, {"parameter": "8", "name": "improved_linkage", "value": 205926871029508}, {"parameter": "5,0", "name": "generalized_linkage", "value": 12159772590971088162}, {"parameter": "5,1", "name": "generalized_linkage", "value": 12157665459497544978}, {"parameter": "5,2", "name": "generalized_linkage", "value": 12157665459062368690}, {"parameter": "5,3", "name": "generalized_linkage", "value": 12157665462544318444}, {"parameter": "6,1", "name": "generalized_linkage", "value": 205926870424266}, {"parameter": "6,2", "name": "generalized_linkage", "value": 205891132095469}, {"parameter": "6,3", "name": "generalized_linkage", "value": 205891132154428}, {"parameter": "7,2", "name": "generalized_linkage", "value": 208436484714760}, {"parameter": "7,3", "name": "generalized_linkage", "value": 208436484707380}, {"parameter": "8,3", "name": "generalized_linkage", "value": 205926871029508}, {"parameter": "[5, 5],[0, 0]", "name": "generalized_linkage_multipleblocks", "value": 12159772590971088162}, {"parameter": "[5, 5],[0, 1]", "name": "generalized_linkage_multipleblocks", "value": 12157665459497544978}, {"parameter": "[5, 5],[0, 2]", "name": "generalized_linkage_multipleblocks", "value": 12157665459062368690}, {"parameter": "[5, 5],[0, 3]", "name": "generalized_linkage_multipleblocks", "value": 12157665462544318444}, {"parameter": "[6, 4],[0, 1]", "name": "generalized_linkage_multipleblocks", "value": 205926870424266}, {"parameter": "[6, 4],[0, 2]", "name": "generalized_linkage_multipleblocks", "value": 205891132095469}, {"parameter": "[6, 4],[0, 3]", "name": "generalized_linkage_multipleblocks", "value": 205891132154428}, {"parameter": "[7, 3],[0, 2]", "name": "generalized_linkage_multipleblocks", "value": 208436484714760}, {"parameter": "[7, 3],[0, 3]", "name": "generalized_linkage_multipleblocks", "value": 208436484707380}, {"parameter": "[8, 2],[0, 3]", "name": "generalized_linkage_multipleblocks", "value": 205926871029508}, {"parameter": "[5, 2, 3],[0, 3, 2]", "name": "generalized_linkage_multipleblocks", "value": 2313026533038411}, {"parameter": "[5, 3, 2],[0, 2, 3]", "name": "generalized_linkage_multipleblocks", "value": 2313023051627469}, {"parameter": "[5, 3, 2],[0, 3, 3]", "name": "generalized_linkage_multipleblocks", "value": 2313023046313059}, {"parameter": "", "name": "JohnsonLB", "value": 1351080793742922656}, {"parameter": "", "name": "HKK_lemma_2_4_lower_bound", "value": 1351063712808578880}], "request": [9, 10, 4, 5], "liftedmrdsizebound": 12159804759493221135, "comments": "", "equal_bound_constraints": []}