{"upper_bound_constraints": [{"parameter": "", "name": "trivial_3", "value": 1001235747932175990213632}, {"parameter": "", "name": "cdc_upper_bound", "value": 1001235747932175990213632}, {"parameter": "", "name": "relax_d", "value": 1001235747932175990213632}, {"parameter": "", "name": "improved_cdc_upper_bound", "value": 1001235747932175990213632}, {"parameter": "", "name": "special_improved_cdc_upper_bound", "value": 1001235747932175990213630}], "known_codes": [{"nrisotypes": "1", "details": "", "file": "", "size": 819240506883749877900800}], "upper_bound": 819240506883749877900800, "classified": true, "lower_bound": 819240506883749877900800, "lower_bound_constraints": [{"parameter": "", "name": "trivial_2", "value": 0}, {"parameter": "", "name": "gilbert_varshamov", "value": 40951689031089513510}, {"parameter": "", "name": "trivial_4", "value": 2}, {"parameter": "optimal [(0,), (0, 1, 2), (0, 1, 2, 3, 4), (0, 1, 2, 3, 4, 5, 6), (0, 1, 2, 3, 4, 5, 6, 7, 8), (0, 1, 2, 3, 4, 5, 6, 7, 9), (0, 1, 2, 3, 4, 5, 6, 8, 9), (0, 1, 2, 3, 4, 5, 7), (0, 1, 2, 3, 4, 5, 7, 8, 9), (0, 1, 2, 3, 4, 5, 8), (0, 1, 2, 3, 4, 5, 9), (0, 1, 2, 3, 4, 6, 7), (0, 1, 2, 3, 4, 6, 7, 8, 9), (0, 1, 2, 3, 4, 6, 8), (0, 1, 2, 3, 4, 6, 9), (0, 1, 2, 3, 4, 7, 8), (0, 1, 2, 3, 4, 7, 9), (0, 1, 2, 3, 4, 8, 9), (0, 1, 2, 3, 5), (0, 1, 2, 3, 5, 6, 7), (0, 1, 2, 3, 5, 6, 7, 8, 9), (0, 1, 2, 3, 5, 6, 8), (0, 1, 2, 3, 5, 6, 9), (0, 1, 2, 3, 5, 7, 8), (0, 1, 2, 3, 5, 7, 9), (0, 1, 2, 3, 5, 8, 9), (0, 1, 2, 3, 6), (0, 1, 2, 3, 6, 7, 8), (0, 1, 2, 3, 6, 7, 9), (0, 1, 2, 3, 6, 8, 9), (0, 1, 2, 3, 7), (0, 1, 2, 3, 7, 8, 9), (0, 1, 2, 3, 8), (0, 1, 2, 3, 9), (0, 1, 2, 4, 5), (0, 1, 2, 4, 5, 6, 7), (0, 1, 2, 4, 5, 6, 7, 8, 9), (0, 1, 2, 4, 5, 6, 8), (0, 1, 2, 4, 5, 6, 9), (0, 1, 2, 4, 5, 7, 8), (0, 1, 2, 4, 5, 7, 9), (0, 1, 2, 4, 5, 8, 9), (0, 1, 2, 4, 6), (0, 1, 2, 4, 6, 7, 8), (0, 1, 2, 4, 6, 7, 9), (0, 1, 2, 4, 6, 8, 9), (0, 1, 2, 4, 7), (0, 1, 2, 4, 7, 8, 9), (0, 1, 2, 4, 8), (0, 1, 2, 4, 9), (0, 1, 2, 5, 6), (0, 1, 2, 5, 6, 7, 8), (0, 1, 2, 5, 6, 7, 9), (0, 1, 2, 5, 6, 8, 9), (0, 1, 2, 5, 7), (0, 1, 2, 5, 7, 8, 9), (0, 1, 2, 5, 8), (0, 1, 2, 5, 9), (0, 1, 2, 6, 7), (0, 1, 2, 6, 7, 8, 9), (0, 1, 2, 6, 8), (0, 1, 2, 6, 9), (0, 1, 2, 7, 8), (0, 1, 2, 7, 9), (0, 1, 2, 8, 9), (0, 1, 3), (0, 1, 3, 4, 5), (0, 1, 3, 4, 5, 6, 7), (0, 1, 3, 4, 5, 6, 7, 8, 9), (0, 1, 3, 4, 5, 6, 8), (0, 1, 3, 4, 5, 6, 9), (0, 1, 3, 4, 5, 7, 8), (0, 1, 3, 4, 5, 7, 9), (0, 1, 3, 4, 5, 8, 9), (0, 1, 3, 4, 6), (0, 1, 3, 4, 6, 7, 8), (0, 1, 3, 4, 6, 7, 9), (0, 1, 3, 4, 6, 8, 9), (0, 1, 3, 4, 7), (0, 1, 3, 4, 7, 8, 9), (0, 1, 3, 4, 8), (0, 1, 3, 4, 9), (0, 1, 3, 5, 6), (0, 1, 3, 5, 6, 7, 8), (0, 1, 3, 5, 6, 7, 9), (0, 1, 3, 5, 6, 8, 9), (0, 1, 3, 5, 7), (0, 1, 3, 5, 7, 8, 9), (0, 1, 3, 5, 8), (0, 1, 3, 5, 9), (0, 1, 3, 6, 7), (0, 1, 3, 6, 7, 8, 9), (0, 1, 3, 6, 8), (0, 1, 3, 6, 9), (0, 1, 3, 7, 8), (0, 1, 3, 7, 9), (0, 1, 3, 8, 9), (0, 1, 4), (0, 1, 4, 5, 6), (0, 1, 4, 5, 6, 7, 8), (0, 1, 4, 5, 6, 7, 9), (0, 1, 4, 5, 6, 8, 9), (0, 1, 4, 5, 7), (0, 1, 4, 5, 7, 8, 9), (0, 1, 4, 5, 8), (0, 1, 4, 5, 9), (0, 1, 4, 6, 7), (0, 1, 4, 6, 7, 8, 9), (0, 1, 4, 6, 8), (0, 1, 4, 6, 9), (0, 1, 4, 7, 8), (0, 1, 4, 7, 9), (0, 1, 4, 8, 9), (0, 1, 5), (0, 1, 5, 6, 7), (0, 1, 5, 6, 7, 8, 9), (0, 1, 5, 6, 8), (0, 1, 5, 6, 9), (0, 1, 5, 7, 8), (0, 1, 5, 7, 9), (0, 1, 5, 8, 9), (0, 1, 6), (0, 1, 6, 7, 8), (0, 1, 6, 7, 9), (0, 1, 6, 8, 9), (0, 1, 7), (0, 1, 7, 8, 9), (0, 1, 8), (0, 1, 9), (0, 2, 3), (0, 2, 3, 4, 5), (0, 2, 3, 4, 5, 6, 7), (0, 2, 3, 4, 5, 6, 7, 8, 9), (0, 2, 3, 4, 5, 6, 8), (0, 2, 3, 4, 5, 6, 9), (0, 2, 3, 4, 5, 7, 8), (0, 2, 3, 4, 5, 7, 9), (0, 2, 3, 4, 5, 8, 9), (0, 2, 3, 4, 6), (0, 2, 3, 4, 6, 7, 8), (0, 2, 3, 4, 6, 7, 9), (0, 2, 3, 4, 6, 8, 9), (0, 2, 3, 4, 7), (0, 2, 3, 4, 7, 8, 9), (0, 2, 3, 4, 8), (0, 2, 3, 4, 9), (0, 2, 3, 5, 6), (0, 2, 3, 5, 6, 7, 8), (0, 2, 3, 5, 6, 7, 9), (0, 2, 3, 5, 6, 8, 9), (0, 2, 3, 5, 7), (0, 2, 3, 5, 7, 8, 9), (0, 2, 3, 5, 8), (0, 2, 3, 5, 9), (0, 2, 3, 6, 7), (0, 2, 3, 6, 7, 8, 9), (0, 2, 3, 6, 8), (0, 2, 3, 6, 9), (0, 2, 3, 7, 8), (0, 2, 3, 7, 9), (0, 2, 3, 8, 9), (0, 2, 4), (0, 2, 4, 5, 6), (0, 2, 4, 5, 6, 7, 8), (0, 2, 4, 5, 6, 7, 9), (0, 2, 4, 5, 6, 8, 9), (0, 2, 4, 5, 7), (0, 2, 4, 5, 7, 8, 9), (0, 2, 4, 5, 8), (0, 2, 4, 5, 9), (0, 2, 4, 6, 7), (0, 2, 4, 6, 7, 8, 9), (0, 2, 4, 6, 8), (0, 2, 4, 6, 9), (0, 2, 4, 7, 8), (0, 2, 4, 7, 9), (0, 2, 4, 8, 9), (0, 2, 5), (0, 2, 5, 6, 7), (0, 2, 5, 6, 7, 8, 9), (0, 2, 5, 6, 8), (0, 2, 5, 6, 9), (0, 2, 5, 7, 8), (0, 2, 5, 7, 9), (0, 2, 5, 8, 9), (0, 2, 6), (0, 2, 6, 7, 8), (0, 2, 6, 7, 9), (0, 2, 6, 8, 9), (0, 2, 7), (0, 2, 7, 8, 9), (0, 2, 8), (0, 2, 9), (0, 3, 4), (0, 3, 4, 5, 6), (0, 3, 4, 5, 6, 7, 8), (0, 3, 4, 5, 6, 7, 9), (0, 3, 4, 5, 6, 8, 9), (0, 3, 4, 5, 7), (0, 3, 4, 5, 7, 8, 9), (0, 3, 4, 5, 8), (0, 3, 4, 5, 9), (0, 3, 4, 6, 7), (0, 3, 4, 6, 7, 8, 9), (0, 3, 4, 6, 8), (0, 3, 4, 6, 9), (0, 3, 4, 7, 8), (0, 3, 4, 7, 9), (0, 3, 4, 8, 9), (0, 3, 5), (0, 3, 5, 6, 7), (0, 3, 5, 6, 7, 8, 9), (0, 3, 5, 6, 8), (0, 3, 5, 6, 9), (0, 3, 5, 7, 8), (0, 3, 5, 7, 9), (0, 3, 5, 8, 9), (0, 3, 6), (0, 3, 6, 7, 8), (0, 3, 6, 7, 9), (0, 3, 6, 8, 9), (0, 3, 7), (0, 3, 7, 8, 9), (0, 3, 8), (0, 3, 9), (0, 4, 5), (0, 4, 5, 6, 7), (0, 4, 5, 6, 7, 8, 9), (0, 4, 5, 6, 8), (0, 4, 5, 6, 9), (0, 4, 5, 7, 8), (0, 4, 5, 7, 9), (0, 4, 5, 8, 9), (0, 4, 6), (0, 4, 6, 7, 8), (0, 4, 6, 7, 9), (0, 4, 6, 8, 9), (0, 4, 7), (0, 4, 7, 8, 9), (0, 4, 8), (0, 4, 9), (0, 5, 6), (0, 5, 6, 7, 8), (0, 5, 6, 7, 9), (0, 5, 6, 8, 9), (0, 5, 7), (0, 5, 7, 8, 9), (0, 5, 8), (0, 5, 9), (0, 6, 7), (0, 6, 7, 8, 9), (0, 6, 8), (0, 6, 9), (0, 7, 8), (0, 7, 9), (0, 8, 9), (1,), (1, 2, 3), (1, 2, 3, 4, 5), (1, 2, 3, 4, 5, 6, 7), (1, 2, 3, 4, 5, 6, 7, 8, 9), (1, 2, 3, 4, 5, 6, 8), (1, 2, 3, 4, 5, 6, 9), (1, 2, 3, 4, 5, 7, 8), (1, 2, 3, 4, 5, 7, 9), (1, 2, 3, 4, 5, 8, 9), (1, 2, 3, 4, 6), (1, 2, 3, 4, 6, 7, 8), (1, 2, 3, 4, 6, 7, 9), (1, 2, 3, 4, 6, 8, 9), (1, 2, 3, 4, 7), (1, 2, 3, 4, 7, 8, 9), (1, 2, 3, 4, 8), (1, 2, 3, 4, 9), (1, 2, 3, 5, 6), (1, 2, 3, 5, 6, 7, 8), (1, 2, 3, 5, 6, 7, 9), (1, 2, 3, 5, 6, 8, 9), (1, 2, 3, 5, 7), (1, 2, 3, 5, 7, 8, 9), (1, 2, 3, 5, 8), (1, 2, 3, 5, 9), (1, 2, 3, 6, 7), (1, 2, 3, 6, 7, 8, 9), (1, 2, 3, 6, 8), (1, 2, 3, 6, 9), (1, 2, 3, 7, 8), (1, 2, 3, 7, 9), (1, 2, 3, 8, 9), (1, 2, 4), (1, 2, 4, 5, 6), (1, 2, 4, 5, 6, 7, 8), (1, 2, 4, 5, 6, 7, 9), (1, 2, 4, 5, 6, 8, 9), (1, 2, 4, 5, 7), (1, 2, 4, 5, 7, 8, 9), (1, 2, 4, 5, 8), (1, 2, 4, 5, 9), (1, 2, 4, 6, 7), (1, 2, 4, 6, 7, 8, 9), (1, 2, 4, 6, 8), (1, 2, 4, 6, 9), (1, 2, 4, 7, 8), (1, 2, 4, 7, 9), (1, 2, 4, 8, 9), (1, 2, 5), (1, 2, 5, 6, 7), (1, 2, 5, 6, 7, 8, 9), (1, 2, 5, 6, 8), (1, 2, 5, 6, 9), (1, 2, 5, 7, 8), (1, 2, 5, 7, 9), (1, 2, 5, 8, 9), (1, 2, 6), (1, 2, 6, 7, 8), (1, 2, 6, 7, 9), (1, 2, 6, 8, 9), (1, 2, 7), (1, 2, 7, 8, 9), (1, 2, 8), (1, 2, 9), (1, 3, 4), (1, 3, 4, 5, 6), (1, 3, 4, 5, 6, 7, 8), (1, 3, 4, 5, 6, 7, 9), (1, 3, 4, 5, 6, 8, 9), (1, 3, 4, 5, 7), (1, 3, 4, 5, 7, 8, 9), (1, 3, 4, 5, 8), (1, 3, 4, 5, 9), (1, 3, 4, 6, 7), (1, 3, 4, 6, 7, 8, 9), (1, 3, 4, 6, 8), (1, 3, 4, 6, 9), (1, 3, 4, 7, 8), (1, 3, 4, 7, 9), (1, 3, 4, 8, 9), (1, 3, 5), (1, 3, 5, 6, 7), (1, 3, 5, 6, 7, 8, 9), (1, 3, 5, 6, 8), (1, 3, 5, 6, 9), (1, 3, 5, 7, 8), (1, 3, 5, 7, 9), (1, 3, 5, 8, 9), (1, 3, 6), (1, 3, 6, 7, 8), (1, 3, 6, 7, 9), (1, 3, 6, 8, 9), (1, 3, 7), (1, 3, 7, 8, 9), (1, 3, 8), (1, 3, 9), (1, 4, 5), (1, 4, 5, 6, 7), (1, 4, 5, 6, 7, 8, 9), (1, 4, 5, 6, 8), (1, 4, 5, 6, 9), (1, 4, 5, 7, 8), (1, 4, 5, 7, 9), (1, 4, 5, 8, 9), (1, 4, 6), (1, 4, 6, 7, 8), (1, 4, 6, 7, 9), (1, 4, 6, 8, 9), (1, 4, 7), (1, 4, 7, 8, 9), (1, 4, 8), (1, 4, 9), (1, 5, 6), (1, 5, 6, 7, 8), (1, 5, 6, 7, 9), (1, 5, 6, 8, 9), (1, 5, 7), (1, 5, 7, 8, 9), (1, 5, 8), (1, 5, 9), (1, 6, 7), (1, 6, 7, 8, 9), (1, 6, 8), (1, 6, 9), (1, 7, 8), (1, 7, 9), (1, 8, 9), (2,), (2, 3, 4), (2, 3, 4, 5, 6), (2, 3, 4, 5, 6, 7, 8), (2, 3, 4, 5, 6, 7, 9), (2, 3, 4, 5, 6, 8, 9), (2, 3, 4, 5, 7), (2, 3, 4, 5, 7, 8, 9), (2, 3, 4, 5, 8), (2, 3, 4, 5, 9), (2, 3, 4, 6, 7), (2, 3, 4, 6, 7, 8, 9), (2, 3, 4, 6, 8), (2, 3, 4, 6, 9), (2, 3, 4, 7, 8), (2, 3, 4, 7, 9), (2, 3, 4, 8, 9), (2, 3, 5), (2, 3, 5, 6, 7), (2, 3, 5, 6, 7, 8, 9), (2, 3, 5, 6, 8), (2, 3, 5, 6, 9), (2, 3, 5, 7, 8), (2, 3, 5, 7, 9), (2, 3, 5, 8, 9), (2, 3, 6), (2, 3, 6, 7, 8), (2, 3, 6, 7, 9), (2, 3, 6, 8, 9), (2, 3, 7), (2, 3, 7, 8, 9), (2, 3, 8), (2, 3, 9), (2, 4, 5), (2, 4, 5, 6, 7), (2, 4, 5, 6, 7, 8, 9), (2, 4, 5, 6, 8), (2, 4, 5, 6, 9), (2, 4, 5, 7, 8), (2, 4, 5, 7, 9), (2, 4, 5, 8, 9), (2, 4, 6), (2, 4, 6, 7, 8), (2, 4, 6, 7, 9), (2, 4, 6, 8, 9), (2, 4, 7), (2, 4, 7, 8, 9), (2, 4, 8), (2, 4, 9), (2, 5, 6), (2, 5, 6, 7, 8), (2, 5, 6, 7, 9), (2, 5, 6, 8, 9), (2, 5, 7), (2, 5, 7, 8, 9), (2, 5, 8), (2, 5, 9), (2, 6, 7), (2, 6, 7, 8, 9), (2, 6, 8), (2, 6, 9), (2, 7, 8), (2, 7, 9), (2, 8, 9), (3,), (3, 4, 5), (3, 4, 5, 6, 7), (3, 4, 5, 6, 7, 8, 9), (3, 4, 5, 6, 8), (3, 4, 5, 6, 9), (3, 4, 5, 7, 8), (3, 4, 5, 7, 9), (3, 4, 5, 8, 9), (3, 4, 6), (3, 4, 6, 7, 8), (3, 4, 6, 7, 9), (3, 4, 6, 8, 9), (3, 4, 7), (3, 4, 7, 8, 9), (3, 4, 8), (3, 4, 9), (3, 5, 6), (3, 5, 6, 7, 8), (3, 5, 6, 7, 9), (3, 5, 6, 8, 9), (3, 5, 7), (3, 5, 7, 8, 9), (3, 5, 8), (3, 5, 9), (3, 6, 7), (3, 6, 7, 8, 9), (3, 6, 8), (3, 6, 9), (3, 7, 8), (3, 7, 9), (3, 8, 9), (4,), (4, 5, 6), (4, 5, 6, 7, 8), (4, 5, 6, 7, 9), (4, 5, 6, 8, 9), (4, 5, 7), (4, 5, 7, 8, 9), (4, 5, 8), (4, 5, 9), (4, 6, 7), (4, 6, 7, 8, 9), (4, 6, 8), (4, 6, 9), (4, 7, 8), (4, 7, 9), (4, 8, 9), (5,), (5, 6, 7), (5, 6, 7, 8, 9), (5, 6, 8), (5, 6, 9), (5, 7, 8), (5, 7, 9), (5, 8, 9), (6,), (6, 7, 8), (6, 7, 9), (6, 8, 9), (7,), (7, 8, 9), (8,), (9,)] (if conjecture about Ferrers Diagram Rank-Metric Codes is true: 819240506883748980064256 with optimal [(0,), (0, 1, 2), (0, 1, 2, 3, 4), (0, 1, 2, 3, 4, 5, 6), (0, 1, 2, 3, 4, 5, 6, 7, 8), (0, 1, 2, 3, 4, 5, 6, 7, 9), (0, 1, 2, 3, 4, 5, 6, 8, 9), (0, 1, 2, 3, 4, 5, 7), (0, 1, 2, 3, 4, 5, 7, 8, 9), (0, 1, 2, 3, 4, 5, 8), (0, 1, 2, 3, 4, 5, 9), (0, 1, 2, 3, 4, 6, 7), (0, 1, 2, 3, 4, 6, 7, 8, 9), (0, 1, 2, 3, 4, 6, 8), (0, 1, 2, 3, 4, 6, 9), (0, 1, 2, 3, 4, 7, 8), (0, 1, 2, 3, 4, 7, 9), (0, 1, 2, 3, 4, 8, 9), (0, 1, 2, 3, 5), (0, 1, 2, 3, 5, 6, 7), (0, 1, 2, 3, 5, 6, 7, 8, 9), (0, 1, 2, 3, 5, 6, 8), (0, 1, 2, 3, 5, 6, 9), (0, 1, 2, 3, 5, 7, 8), (0, 1, 2, 3, 5, 7, 9), (0, 1, 2, 3, 5, 8, 9), (0, 1, 2, 3, 6), (0, 1, 2, 3, 6, 7, 8), (0, 1, 2, 3, 6, 7, 9), (0, 1, 2, 3, 6, 8, 9), (0, 1, 2, 3, 7), (0, 1, 2, 3, 7, 8, 9), (0, 1, 2, 3, 8), (0, 1, 2, 3, 9), (0, 1, 2, 4, 5), (0, 1, 2, 4, 5, 6, 7), (0, 1, 2, 4, 5, 6, 7, 8, 9), (0, 1, 2, 4, 5, 6, 8), (0, 1, 2, 4, 5, 6, 9), (0, 1, 2, 4, 5, 7, 8), (0, 1, 2, 4, 5, 7, 9), (0, 1, 2, 4, 5, 8, 9), (0, 1, 2, 4, 6), (0, 1, 2, 4, 6, 7, 8), (0, 1, 2, 4, 6, 7, 9), (0, 1, 2, 4, 6, 8, 9), (0, 1, 2, 4, 7), (0, 1, 2, 4, 7, 8, 9), (0, 1, 2, 4, 8), (0, 1, 2, 4, 9), (0, 1, 2, 5, 6), (0, 1, 2, 5, 6, 7, 8), (0, 1, 2, 5, 6, 7, 9), (0, 1, 2, 5, 6, 8, 9), (0, 1, 2, 5, 7), (0, 1, 2, 5, 7, 8, 9), (0, 1, 2, 5, 8), (0, 1, 2, 5, 9), (0, 1, 2, 6, 7), (0, 1, 2, 6, 7, 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