{"upper_bound_constraints": [{"parameter": "", "name": "all_subs", "value": 34718046121166753868579146371116506562228516029840080}, {"parameter": "", "name": "singleton", "value": 35303692060}, {"parameter": "1", "name": "ilp_2", "value": 31381591059}, {"parameter": "2", "name": "ilp_2", "value": 984937699705613035564}, {"parameter": "3", "name": "ilp_2", "value": 30950845243449212232351562291480}, {"parameter": "4", "name": "ilp_2", "value": 983411198527397133334817173541721249713068}, {"parameter": "6", "name": "ilp_3", "value": 522626014167796987333721908341359424390012284056}, {"parameter": "7", "name": "ilp_3", "value": 8741451151967514519582349843718116857817360}, {"parameter": "8", "name": "ilp_3", "value": 147834177345738550353103574121949107214}, {"parameter": "9", "name": "ilp_3", "value": 2503203195046424313822968098269459}, {"parameter": "", "name": "anticode", "value": 31381591059}, {"parameter": "", "name": "linear_programming_bound", "value": 31381591059}, {"parameter": "", "name": "sphere_packing", "value": 51137966719392366819551212}, {"parameter": "", "name": "DrakeFreeman", "value": 31381591055}, {"parameter": "", "name": "partial_spread_5", "value": 31381591058}, {"parameter": "", "name": "partial_spread_kurz16_28", "value": 31381591051}, {"parameter": "", "name": "spread_bound", "value": 31381591059}, {"parameter": "", "name": "XiaFuJohnson1", "value": 31381591059}, {"parameter": "10", "name": "ilp_4", "value": 2503203195046424313822968098269459}, {"parameter": "11", "name": "ilp_4", "value": 381521232109330440757112933358}, {"parameter": "12", "name": "ilp_4", "value": 58150139725461550118072387}, {"parameter": "13", "name": "ilp_4", "value": 8863013295616586199487}, {"parameter": "14", "name": "ilp_4", "value": 1350863492974377938}, {"parameter": "15", "name": "ilp_4", "value": 205894618944660}, {"parameter": "", "name": "johnson_1", "value": 31381591059}, {"parameter": "", "name": "johnson_2", "value": 205894618944660}, {"parameter": "0, 5", "name": "Ahlswede_Aydinian", "value": 34718046121166753868579146371116506562228516029840080}, {"parameter": "0, 6", "name": "Ahlswede_Aydinian", "value": 522626014167796987333721908341359424390012284056}, {"parameter": "0, 7", "name": "Ahlswede_Aydinian", "value": 8741451151967514519582349843718116857817360}, {"parameter": "0, 8", "name": "Ahlswede_Aydinian", "value": 147834177345738550353103574121949107214}, {"parameter": "0, 9", "name": "Ahlswede_Aydinian", "value": 2503203195046424313822968098269459}, {"parameter": "0, 10", "name": "Ahlswede_Aydinian", "value": 2503203195046424313822968098269459}, {"parameter": "0, 11", "name": "Ahlswede_Aydinian", "value": 381521232109330440757112933358}, {"parameter": "0, 12", "name": "Ahlswede_Aydinian", "value": 58150139725461550118072387}, {"parameter": "0, 13", "name": "Ahlswede_Aydinian", "value": 8863013295616586199487}, {"parameter": "0, 14", "name": "Ahlswede_Aydinian", "value": 1350863492974377938}, {"parameter": "0, 15", "name": "Ahlswede_Aydinian", "value": 205894618944660}, {"parameter": "1, 4", "name": "Ahlswede_Aydinian", "value": 983411198527397133334817173541721249713068}, {"parameter": "1, 5", "name": "Ahlswede_Aydinian", "value": 133235496349444400497609434609431273125}, {"parameter": "1, 6", "name": "Ahlswede_Aydinian", "value": 20056525121692855065359920109377433}, {"parameter": "1, 7", "name": "Ahlswede_Aydinian", "value": 3052738450704335021197659221467}, {"parameter": "1, 8", "name": "Ahlswede_Aydinian", "value": 3052738513733008291970038581437}, {"parameter": "1, 9", "name": "Ahlswede_Aydinian", "value": 4186932610782976088241174099}, {"parameter": "1, 10", "name": "Ahlswede_Aydinian", "value": 5743693180433643531490891}, {"parameter": "1, 11", "name": "Ahlswede_Aydinian", "value": 7879051941245424633049}, {"parameter": "1, 12", "name": "Ahlswede_Aydinian", "value": 10810291634078491371}, {"parameter": "1, 13", "name": "Ahlswede_Aydinian", "value": 14847035625813405}, {"parameter": "1, 14", "name": "Ahlswede_Aydinian", "value": 20592565397776}, {"parameter": "1, 15", "name": "Ahlswede_Aydinian", "value": 31385842953}, {"parameter": "2, 3", "name": "Ahlswede_Aydinian", "value": 30950845243449212232351562291480}, {"parameter": "2, 4", "name": "Ahlswede_Aydinian", "value": 37744933224905046947226628653}, {"parameter": "2, 5", "name": "Ahlswede_Aydinian", "value": 51137966719392366819551212}, {"parameter": "2, 6", "name": "Ahlswede_Aydinian", "value": 51137966849599833650542768}, {"parameter": "2, 7", "name": "Ahlswede_Aydinian", "value": 630468216063906092067430}, {"parameter": "2, 8", "name": "Ahlswede_Aydinian", "value": 7787645568336504196904}, {"parameter": "2, 9", "name": "Ahlswede_Aydinian", "value": 96209033969383824775}, {"parameter": "2, 10", "name": "Ahlswede_Aydinian", "value": 1187783462206529570}, {"parameter": "2, 11", "name": "Ahlswede_Aydinian", "value": 14666208982828984}, {"parameter": "2, 12", "name": "Ahlswede_Aydinian", "value": 181309820815903}, {"parameter": "2, 13", "name": "Ahlswede_Aydinian", "value": 2265993160429}, {"parameter": "2, 14", "name": "Ahlswede_Aydinian", "value": 31424165420}, {"parameter": "3, 2", "name": "Ahlswede_Aydinian", "value": 984937699705613035564}, {"parameter": "3, 3", "name": "Ahlswede_Aydinian", "value": 10823491205896834332}, {"parameter": "3, 4", "name": "Ahlswede_Aydinian", "value": 10823491208962658493}, {"parameter": "3, 5", "name": "Ahlswede_Aydinian", "value": 1187962043024697062}, {"parameter": "3, 6", "name": "Ahlswede_Aydinian", "value": 133442314743896813}, {"parameter": "3, 7", "name": "Ahlswede_Aydinian", "value": 14824694993197627}, {"parameter": "3, 8", "name": "Ahlswede_Aydinian", "value": 1647411831257356}, {"parameter": "3, 9", "name": "Ahlswede_Aydinian", "value": 183048480519227}, {"parameter": "3, 10", "name": "Ahlswede_Aydinian", "value": 20341815793619}, {"parameter": "3, 11", "name": "Ahlswede_Aydinian", "value": 2263267994999}, {"parameter": "3, 12", "name": "Ahlswede_Aydinian", "value": 254578373621}, {"parameter": "3, 13", "name": "Ahlswede_Aydinian", "value": 31773322846}, {"parameter": "4, 1", "name": "Ahlswede_Aydinian", "value": 31381591059}, {"parameter": "4, 2", "name": "Ahlswede_Aydinian", "value": 31381591059}, {"parameter": "4, 3", "name": "Ahlswede_Aydinian", "value": 31381591067}, {"parameter": "4, 4", "name": "Ahlswede_Aydinian", "value": 31381591140}, {"parameter": "4, 5", "name": "Ahlswede_Aydinian", "value": 31381591796}, {"parameter": "4, 6", "name": "Ahlswede_Aydinian", "value": 31381597701}, {"parameter": "4, 7", "name": "Ahlswede_Aydinian", "value": 31381650838}, {"parameter": "4, 8", "name": "Ahlswede_Aydinian", "value": 31382129078}, {"parameter": "4, 9", "name": "Ahlswede_Aydinian", "value": 31386433824}, {"parameter": "4, 10", "name": "Ahlswede_Aydinian", "value": 31425223899}, {"parameter": "4, 11", "name": "Ahlswede_Aydinian", "value": 31778213454}, {"parameter": "4, 12", "name": "Ahlswede_Aydinian", "value": 35303692060}, {"parameter": "0, 11, o", "name": "Ahlswede_Aydinian", "value": 34718046121166753868579146371116506562228516029840080}, {"parameter": "0, 12, o", "name": "Ahlswede_Aydinian", "value": 983411198527397133334817173541721249713068}, {"parameter": "0, 13, o", "name": "Ahlswede_Aydinian", "value": 30950845243449212232351562291480}, {"parameter": "0, 14, o", "name": "Ahlswede_Aydinian", "value": 984937699705613035564}, {"parameter": "0, 15, o", "name": "Ahlswede_Aydinian", "value": 31381591059}, {"parameter": "1, 10, o", "name": "Ahlswede_Aydinian", "value": 522626014167796987333721908341359424390012284056}, {"parameter": "1, 11, o", "name": "Ahlswede_Aydinian", "value": 133235496349444400497609434609431273125}, {"parameter": "1, 12, o", "name": "Ahlswede_Aydinian", "value": 37744933224905046947226628653}, {"parameter": "1, 13, o", "name": "Ahlswede_Aydinian", "value": 10823491205896834332}, {"parameter": "1, 14, o", "name": "Ahlswede_Aydinian", "value": 10943752081147375739}, {"parameter": "1, 15, o", "name": "Ahlswede_Aydinian", "value": 12159724534259458429}, {"parameter": "2, 9, o", "name": "Ahlswede_Aydinian", "value": 8741451151967514519582349843718116857817360}, {"parameter": "2, 10, o", "name": "Ahlswede_Aydinian", "value": 20056525121692855065359920109377433}, {"parameter": "2, 11, o", "name": "Ahlswede_Aydinian", "value": 51137966719392366819551212}, {"parameter": "2, 12, o", "name": "Ahlswede_Aydinian", "value": 51207343963459502480142583}, {"parameter": "2, 13, o", "name": "Ahlswede_Aydinian", "value": 51839533393636747965871247}, {"parameter": "2, 14, o", "name": "Ahlswede_Aydinian", "value": 58239475771210002588197674}, {"parameter": "3, 8, o", "name": "Ahlswede_Aydinian", "value": 147834177345738550353103574121949107214}, {"parameter": "3, 9, o", "name": "Ahlswede_Aydinian", "value": 3052738450704335021197659221467}, {"parameter": "3, 10, o", "name": "Ahlswede_Aydinian", "value": 3053203168816812435193622899237}, {"parameter": "3, 11, o", "name": "Ahlswede_Aydinian", "value": 3057391376094815879649313101839}, {"parameter": "3, 12, o", "name": "Ahlswede_Aydinian", "value": 3095556343090673740181220243578}, {"parameter": "3, 13, o", "name": "Ahlswede_Aydinian", "value": 3481970088764917078588839478708}, {"parameter": "4, 7, o", "name": "Ahlswede_Aydinian", "value": 2503203195046424313822968098269459}, {"parameter": "4, 8, o", "name": "Ahlswede_Aydinian", "value": 2503245581261066799415431636778875}, {"parameter": "4, 9, o", "name": "Ahlswede_Aydinian", "value": 2503627115343671358093104267225921}, {"parameter": "4, 10, o", "name": "Ahlswede_Aydinian", "value": 2507065638773773861999180536825965}, {"parameter": "4, 11, o", "name": "Ahlswede_Aydinian", "value": 2538399176899527592081716448864301}, {"parameter": "4, 12, o", "name": "Ahlswede_Aydinian", "value": 2855650645340126913932218722028600}, {"parameter": "", "name": "improved_johnson", "value": 31381591051}, {"parameter": "", "name": "HKK_lemma_2_4_upper_bound", "value": 1350877136766525645}], "known_codes": [], "upper_bound": 31381591051, "classified": false, "lower_bound": 31381591051, "lower_bound_constraints": [{"parameter": "", "name": "trivial_1", "value": 0}, {"parameter": "", "name": "LMRD", "value": 31381059609}, {"parameter": "", "name": "sphere_covering", "value": 4251673}, {"parameter": "", "name": "graham_sloane", "value": 1}, {"parameter": "", "name": "partial_spread_3", "value": 31381591051}, {"parameter": "", "name": "multicomponent", "value": 31381591051}, {"parameter": "[(0, 1, 2, 3, 4), (5, 6, 7, 8, 9), (11, 12, 13, 14, 15)]", "name": "ef_computation", "value": 31381591051}, {"parameter": "", "name": "LiuChangFeng2019_Theo_2_6", "value": 31381059609}, {"parameter": "(5, 11)", "name": "CKMP2019_Lem_41", "value": 31381591051}, {"parameter": "(6, 10)", "name": "CKMP2019_Lem_41", "value": 3486843451}, {"parameter": "(7, 9)", "name": "CKMP2019_Lem_41", "value": 387420490}, {"parameter": "(8, 8)", "name": "CKMP2019_Lem_41", "value": 43046722}, {"parameter": "(9, 7)", "name": "CKMP2019_Lem_41", "value": 4782970}, {"parameter": "(10, 6)", "name": "CKMP2019_Lem_41", "value": 31381591051}, {"parameter": "(11, 5)", "name": "CKMP2019_Lem_41", "value": 31381118659}, {"parameter": "(5, 5, 6)", "name": "CKMP2019_Lem_41", "value": 31381591051}, {"parameter": "(5, 6, 5)", "name": "CKMP2019_Lem_41", "value": 31381118659}, {"parameter": "(6, 5, 5)", "name": "CKMP2019_Lem_41", "value": 3486843451}, {"parameter": "(5, 11)", "name": "CKMP2019_Cor_42", "value": 31381591051}, {"parameter": "(6, 10)", "name": "CKMP2019_Cor_42", "value": 3486843451}, {"parameter": "(7, 9)", "name": "CKMP2019_Cor_42", "value": 387420490}, {"parameter": "(8, 8)", "name": "CKMP2019_Cor_42", "value": 43046722}, {"parameter": "(9, 7)", "name": "CKMP2019_Cor_42", "value": 4782970}, {"parameter": "(10, 6)", "name": "CKMP2019_Cor_42", "value": 31381591051}, {"parameter": "(11, 5)", "name": "CKMP2019_Cor_42", "value": 31381118659}, {"parameter": "(5, 5, 6)", "name": "CKMP2019_Cor_42", "value": 31381591051}, {"parameter": "(5, 6, 5)", "name": "CKMP2019_Cor_42", "value": 31381118659}, {"parameter": "(6, 5, 5)", "name": "CKMP2019_Cor_42", "value": 3486843451}, {"parameter": "5", "name": "linkage_GLT", "value": 31381591051}, {"parameter": "6", "name": "linkage_GLT", "value": 3486843451}, {"parameter": "7", "name": "linkage_GLT", "value": 387420490}, {"parameter": "8", "name": "linkage_GLT", "value": 43046722}, {"parameter": "9", "name": "linkage_GLT", "value": 4782970}, {"parameter": "10", "name": "linkage_GLT", "value": 31381591051}, {"parameter": "11", "name": "linkage_GLT", "value": 31381118659}, {"parameter": "5", "name": "improved_linkage", "value": 31381591051}, {"parameter": "6", "name": "improved_linkage", "value": 3486843451}, {"parameter": "7", "name": "improved_linkage", "value": 387420490}, {"parameter": "8", "name": "improved_linkage", "value": 43046722}, {"parameter": "9", "name": "improved_linkage", "value": 4782970}, {"parameter": "10", "name": "improved_linkage", "value": 31381591051}, {"parameter": "11", "name": "improved_linkage", "value": 31381118659}, {"parameter": "5,0", "name": "generalized_linkage", "value": 31381591051}, {"parameter": "6,0", "name": "generalized_linkage", "value": 3486843451}, {"parameter": "7,0", "name": "generalized_linkage", "value": 387420490}, {"parameter": "8,0", "name": "generalized_linkage", "value": 43046722}, {"parameter": "9,0", "name": "generalized_linkage", "value": 4782970}, {"parameter": "10,0", "name": "generalized_linkage", "value": 31381591051}, {"parameter": "11,0", "name": "generalized_linkage", "value": 31381118659}, {"parameter": "[5, 11],[0, 0]", "name": "generalized_linkage_multipleblocks", "value": 31381591051}, {"parameter": "[6, 10],[0, 0]", "name": "generalized_linkage_multipleblocks", "value": 3486843451}, {"parameter": "[7, 9],[0, 0]", "name": "generalized_linkage_multipleblocks", "value": 387420490}, {"parameter": "[8, 8],[0, 0]", "name": "generalized_linkage_multipleblocks", "value": 43046722}, {"parameter": "[9, 7],[0, 0]", "name": "generalized_linkage_multipleblocks", "value": 4782970}, {"parameter": "[10, 6],[0, 0]", "name": "generalized_linkage_multipleblocks", "value": 31381591051}, {"parameter": "[11, 5],[0, 0]", "name": "generalized_linkage_multipleblocks", "value": 31381118659}, {"parameter": "[5, 5, 6],[0, 0, 0]", "name": "generalized_linkage_multipleblocks", "value": 31381591051}, {"parameter": "[5, 6, 5],[0, 0, 0]", "name": "generalized_linkage_multipleblocks", "value": 31381118659}, {"parameter": "[6, 5, 5],[0, 0, 0]", "name": "generalized_linkage_multipleblocks", "value": 3486843451}, {"parameter": "", "name": "JohnsonLB", "value": 31381000569}, {"parameter": "", "name": "HKK_lemma_2_4_lower_bound", "value": 9}], "request": [9, 16, 10, 5], "liftedmrdsizebound": 31381591051, "comments": "", "equal_bound_constraints": [{"parameter": "", "name": "partial_spread_2", "value": 31381591051}, {"parameter": "", "name": "partial_spread_NS", "value": 31381591051}]}