Details for entry \(A_2(16,8;6)\)

Lower bounds

• greedy_multicomponent ( show
  q^30 + q^18 + q^14 + q^12 + q^7 + q^5 + 2*q^4 + 1
  ) : 1074024641
• ef_computation ( show
  [(0, 1, 2, 3, 4, 5), (2, 5, 6, 7, 8, 9), (0, 4, 6, 7, 10, 11), (1, 3, 8, 9, 10, 11), (1, 3, 6, 7, 12, 13), (0, 4, 8, 9, 12, 13), (0, 3, 7, 8, 14, 15), (2, 5, 10, 11, 12, 13), (1, 4, 6, 9, 14, 15)] (if conjecture about Ferrers Diagram Rank-Metric Codes is true: 1074025792)
  ) : 1074022528
• generalized_linkage ( 6,2 ) : 1074003989
• generalized_linkage_multipleblocks ( show
  [6, 10],[0, 2]
  ) : 1074003989
• improved_linkage ( 6 ) : 1074003989
• multicomponent ( ) : 1074003969
• generalized_linkage ( 6,1 ) : 1073745921
• generalized_linkage_multipleblocks ( show
  [6, 10],[0, 1]
  ) : 1073745921
• generalized_linkage ( 6,0 ) : 1073743189
• generalized_linkage_multipleblocks ( show
  [6, 10],[0, 0]
  ) : 1073743189
• CKMP2019_Cor_42 ( (6, 10) ) : 1073741889
• CKMP2019_Lem_41 ( (6, 10) ) : 1073741889
• linkage_GLT ( 6 ) : 1073741889
• LiuChangFeng2019_Theo_2_6 ( ) : 1073741825
• LMRD ( ) : 1073741824
• JohnsonLB ( ) : 1065386111
• generalized_linkage ( 7,2 ) : 134221825
• generalized_linkage_multipleblocks ( show
  [7, 9],[0, 2]
  ) : 134221825
• improved_linkage ( 7 ) : 134221825
• generalized_linkage ( 7,1 ) : 134217793
• generalized_linkage_multipleblocks ( show
  [7, 9],[0, 1]
  ) : 134217793
• generalized_linkage ( 7,0 ) : 134217749
• generalized_linkage_multipleblocks ( show
  [7, 9],[0, 0]
  ) : 134217749
• CKMP2019_Cor_42 ( (7, 9) ) : 134217729
• CKMP2019_Lem_41 ( (7, 9) ) : 134217729
• linkage_GLT ( 7 ) : 134217729
• generalized_linkage_multipleblocks ( show
  [6, 4, 6],[0, 2, 0]
  ) : 17039465
• generalized_linkage ( 10,0 ) : 17039381
• generalized_linkage_multipleblocks ( show
  [10, 6],[0, 0]
  ) : 17039381
• generalized_linkage_multipleblocks ( show
  [6, 4, 6],[0, 2, 1]
  ) : 17039381
• generalized_linkage_multipleblocks ( show
  [6, 4, 6],[0, 2, 2]
  ) : 17039381
• CKMP2019_Cor_42 ( (10, 6) ) : 17039361
• CKMP2019_Lem_41 ( (10, 6) ) : 17039361
• generalized_linkage ( 10,1 ) : 17039361
• generalized_linkage ( 10,2 ) : 17039361
• generalized_linkage_multipleblocks ( show
  [10, 6],[0, 1]
  ) : 17039361
• generalized_linkage_multipleblocks ( show
  [10, 6],[0, 2]
  ) : 17039361
• improved_linkage ( 10 ) : 17039361
• linkage_GLT ( 10 ) : 17039361
• generalized_linkage_multipleblocks ( show
  [6, 5, 5],[0, 1, 1]
  ) : 16781333
• generalized_linkage_multipleblocks ( show
  [6, 5, 5],[0, 1, 2]
  ) : 16781333
• generalized_linkage_multipleblocks ( show
  [6, 5, 5],[0, 2, 1]
  ) : 16781333
• generalized_linkage_multipleblocks ( show
  [6, 5, 5],[0, 2, 2]
  ) : 16781333
• generalized_linkage ( 11,1 ) : 16781313
• generalized_linkage ( 11,2 ) : 16781313
• generalized_linkage_multipleblocks ( show
  [11, 5],[0, 1]
  ) : 16781313
• generalized_linkage_multipleblocks ( show
  [11, 5],[0, 2]
  ) : 16781313
• improved_linkage ( 11 ) : 16781313
• generalized_linkage_multipleblocks ( show
  [6, 6, 4],[0, 0, 2]
  ) : 16778581
• generalized_linkage ( 12,2 ) : 16778561
• generalized_linkage_multipleblocks ( show
  [12, 4],[0, 2]
  ) : 16778561
• improved_linkage ( 12 ) : 16778561
• generalized_linkage_multipleblocks ( show
  [6, 6, 4],[0, 1, 2]
  ) : 16777301
• generalized_linkage_multipleblocks ( show
  [6, 6, 4],[0, 2, 2]
  ) : 16777301
• generalized_linkage ( 8,2 ) : 16777281
• generalized_linkage_multipleblocks ( show
  [8, 8],[0, 2]
  ) : 16777281
• improved_linkage ( 8 ) : 16777281
• generalized_linkage ( 8,0 ) : 16777237
• generalized_linkage_multipleblocks ( show
  [8, 8],[0, 0]
  ) : 16777237
• CKMP2019_Cor_42 ( (8, 8) ) : 16777217
• CKMP2019_Lem_41 ( (8, 8) ) : 16777217
• generalized_linkage ( 8,1 ) : 16777217
• generalized_linkage_multipleblocks ( show
  [8, 8],[0, 1]
  ) : 16777217
• linkage_GLT ( 8 ) : 16777217
• HKK_lemma_2_4_lower_bound ( ) : 8421944
• generalized_linkage ( 9,0 ) : 2097173
• generalized_linkage_multipleblocks ( show
  [9, 7],[0, 0]
  ) : 2097173
• CKMP2019_Cor_42 ( (9, 7) ) : 2097153
• CKMP2019_Lem_41 ( (9, 7) ) : 2097153
• generalized_linkage ( 9,1 ) : 2097153
• generalized_linkage ( 9,2 ) : 2097153
• generalized_linkage_multipleblocks ( show
  [9, 7],[0, 1]
  ) : 2097153
• generalized_linkage_multipleblocks ( show
  [9, 7],[0, 2]
  ) : 2097153
• improved_linkage ( 9 ) : 2097153
• linkage_GLT ( 9 ) : 2097153
• sphere_covering ( ) : 865693
• generalized_linkage_multipleblocks ( show
  [7, 4, 5],[0, 2, 1]
  ) : 266261
• generalized_linkage_multipleblocks ( show
  [7, 4, 5],[0, 2, 2]
  ) : 266261
• generalized_linkage_multipleblocks ( show
  [7, 5, 4],[0, 1, 2]
  ) : 262229
• generalized_linkage_multipleblocks ( show
  [7, 5, 4],[0, 2, 2]
  ) : 262229
• graham_sloane ( ) : 13950
• generalized_linkage_multipleblocks ( show
  [8, 4, 4],[0, 2, 2]
  ) : 4181
• trivial_1 ( ) : 0

Upper bounds

• Ahlswede_Aydinian ( 0, 14, o ) : 1197389985
• Ahlswede_Aydinian ( 0, 15, o ) : 1197389985
• ilp_1 ( 1 ) : 1197389985
• ilp_1 ( 2 ) : 1197389985
• improved_johnson ( ) : 1197389985
• johnson_1 ( ) : 1197389985
• Ahlswede_Aydinian ( 3, 3 ) : 1200908486
• Ahlswede_Aydinian ( 0, 13, o ) : 1200908486
• anticode ( ) : 1200908486
• ilp_2 ( 3 ) : 1200908486
• linear_programming_bound ( ) : 1200908486
• Ahlswede_Aydinian ( 3, 4 ) : 1201867123
• Ahlswede_Aydinian ( 3, 5 ) : 1203787632
• Ahlswede_Aydinian ( 3, 6 ) : 1207641630
• Ahlswede_Aydinian ( 3, 7 ) : 1215401910
• Ahlswede_Aydinian ( 3, 8 ) : 1231134514
• Ahlswede_Aydinian ( 3, 9 ) : 1263471874
• Ahlswede_Aydinian ( 3, 10 ) : 1331838223
• Ahlswede_Aydinian ( 1, 15 ) : 1349557517
• Ahlswede_Aydinian ( 3, 11 ) : 1485163326
• Ahlswede_Aydinian ( 2, 14 ) : 1744510989
• Ahlswede_Aydinian ( 3, 12 ) : 1876933882
• Ahlswede_Aydinian ( 2, 13 ) : 2054401322
• Ahlswede_Aydinian ( 3, 13 ) : 3269560515
• singleton ( ) : 3269560515
• Ahlswede_Aydinian ( 2, 12 ) : 3326919265
• Ahlswede_Aydinian ( 1, 14 ) : 3642910622
• Ahlswede_Aydinian ( 2, 11 ) : 5996331892
• Ahlswede_Aydinian ( 0, 15 ) : 9596612215
• ilp_4 ( 15 ) : 9596612215
• johnson_2 ( ) : 9596612215
• Ahlswede_Aydinian ( 2, 10 ) : 11576777824
• Ahlswede_Aydinian ( 1, 13 ) : 12441831018
• Ahlswede_Aydinian ( 2, 9 ) : 22077168156
• HKK_lemma_2_4_upper_bound ( ) : 38650922427
• Ahlswede_Aydinian ( 2, 5 ) : 45362305196
• Ahlswede_Aydinian ( 1, 11, o ) : 45362305196
• Ahlswede_Aydinian ( 2, 6 ) : 45426732146
• Ahlswede_Aydinian ( 2, 7 ) : 45556011792
• Ahlswede_Aydinian ( 2, 8 ) : 45816286128
• Ahlswede_Aydinian ( 1, 12 ) : 46658857087
• Ahlswede_Aydinian ( 1, 12, o ) : 46872817823
• Ahlswede_Aydinian ( 1, 13, o ) : 50217165621
• Ahlswede_Aydinian ( 1, 14, o ) : 58575872313
• Ahlswede_Aydinian ( 0, 14 ) : 77052759682
• ilp_4 ( 14 ) : 77052759682
• Ahlswede_Aydinian ( 1, 15, o ) : 87807051499
• Ahlswede_Aydinian ( 1, 11 ) : 183178498916
• Ahlswede_Aydinian ( 0, 13 ) : 598287311964
• ilp_4 ( 13 ) : 598287311964
• Ahlswede_Aydinian ( 1, 8 ) : 673533549850
• Ahlswede_Aydinian ( 1, 9 ) : 674819684561
• Ahlswede_Aydinian ( 1, 10 ) : 680089098891
• Ahlswede_Aydinian ( 1, 7 ) : 720253320256
• Ahlswede_Aydinian ( 2, 9, o ) : 720253320256
• Ahlswede_Aydinian ( 2, 10, o ) : 737643602946
• Ahlswede_Aydinian ( 2, 11, o ) : 774439299003
• Ahlswede_Aydinian ( 2, 12, o ) : 857224733555
• Ahlswede_Aydinian ( 2, 13, o ) : 1070936928838
• Ahlswede_Aydinian ( 2, 4 ) : 1405234487365
• Ahlswede_Aydinian ( 0, 12, o ) : 1405234487365
• ilp_2 ( 4 ) : 1405234487365
• Ahlswede_Aydinian ( 2, 14, o ) : 1870509701637
• Ahlswede_Aydinian ( 0, 11 ) : 4745361579903
• Ahlswede_Aydinian ( 0, 12 ) : 4745361579903
• ilp_4 ( 11 ) : 4745361579903
• ilp_4 ( 12 ) : 4745361579903
• Ahlswede_Aydinian ( 0, 10 ) : 4748787859520
• ilp_4 ( 10 ) : 4748787859520
• Ahlswede_Aydinian ( 0, 9 ) : 4982574338758
• Ahlswede_Aydinian ( 3, 7, o ) : 4982574338758
• ilp_3 ( 9 ) : 4982574338758
• Ahlswede_Aydinian ( 3, 8, o ) : 5051501623876
• Ahlswede_Aydinian ( 3, 9, o ) : 5193504913906
• Ahlswede_Aydinian ( 3, 10, o ) : 5495171967642
• Ahlswede_Aydinian ( 3, 11, o ) : 6178863412154
• Ahlswede_Aydinian ( 3, 12, o ) : 7970697904102
• Ahlswede_Aydinian ( 3, 13, o ) : 14877590196755
• Ahlswede_Aydinian ( 1, 6 ) : 30461392012691
• Ahlswede_Aydinian ( 1, 10, o ) : 30461392012691
• sphere_packing ( ) : 30461392012691
• Ahlswede_Aydinian ( 0, 8 ) : 363727926729401
• Ahlswede_Aydinian ( 2, 8, o ) : 363727926729401
• ilp_3 ( 8 ) : 363727926729401
• Ahlswede_Aydinian ( 1, 5 ) : 1918145075253485
• Ahlswede_Aydinian ( 0, 11, o ) : 1918145075253485
• ilp_2 ( 5 ) : 1918145075253485
• Ahlswede_Aydinian ( 0, 7 ) : 30916873771999085
• Ahlswede_Aydinian ( 1, 9, o ) : 30916873771999085
• ilp_3 ( 7 ) : 30916873771999085
• Ahlswede_Aydinian ( 0, 6 ) : 3926442969043883795
• Ahlswede_Aydinian ( 0, 10, o ) : 3926442969043883795
• all_subs ( ) : 3926442969043883795

Bound for codes containing the lifted MRD code

Do you have better bounds?