Details for entry \(A_4(8,4;3)\)

Lower bounds

• construction_1 ( ) : 1054373
• construction_ST_A_1 ( ) : 1054373
• pending_dots ( show
  optimal [(0, 1, 2), (0, 3, 5), (0, 3, 6), (0, 3, 7), (0, 4, 5), (0, 4, 6), (0, 4, 7), (0, 6, 7), (1, 5, 6), (1, 5, 7), (2, 3, 4)] (if conjecture about Ferrers Diagram Rank-Metric Codes is true: 1054373 with optimal [(0, 1, 2), (0, 3, 5), (0, 3, 6), (0, 3, 7), (0, 4, 5), (0, 4, 6), (0, 4, 7), (0, 6, 7), (1, 5, 6), (1, 5, 7), (2, 3, 4)])
  ) : 1054373
• echelon_ferrers ( show
  optimal [(0, 1, 2), (0, 3, 4), (0, 5, 6), (1, 3, 5), (1, 4, 6), (2, 3, 6), (2, 4, 5)] (if conjecture about Ferrers Diagram Rank-Metric Codes is true: 1054288 with optimal [(0, 1, 2), (0, 3, 4), (0, 5, 6), (1, 3, 5), (1, 4, 6), (2, 3, 6), (2, 4, 5)])
  ) : 1054288
• ef_computation ( show
  [(0, 1, 2), (2, 3, 4), (1, 3, 5), (0, 4, 5), (0, 3, 6), (1, 4, 6), (2, 5, 6)]
  ) : 1054288
• construction_ST_B_recursive ( ) : 1052753
• generalized_linkage ( 3,1 ) : 1052713
• generalized_linkage_multipleblocks ( show
  [3, 5],[0, 1]
  ) : 1052713
• improved_linkage ( 3 ) : 1052713
• two_pivot_block_construction ( ) : 1052688
• multicomponent ( ) : 1052673
• construction_ST_B ( ) : 1052447
• generalized_linkage ( 3,0 ) : 1049941
• generalized_linkage_multipleblocks ( show
  [3, 5],[0, 0]
  ) : 1049941
• JohnsonLB ( ) : 1049169
• CKMP2019_Cor_42 ( (3, 5) ) : 1048641
• CKMP2019_Lem_41 ( (3, 5) ) : 1048641
• linkage_GLT ( 3 ) : 1048641
• LMRD ( ) : 1048576
• LiuChangFeng2019_Theo_2_6 ( ) : 1048576
• generalized_linkage_multipleblocks ( show
  [3, 2, 3],[0, 1, 0]
  ) : 266345
• generalized_linkage ( 5,0 ) : 266261
• generalized_linkage_multipleblocks ( show
  [5, 3],[0, 0]
  ) : 266261
• generalized_linkage_multipleblocks ( show
  [3, 2, 3],[0, 1, 1]
  ) : 266261
• CKMP2019_Cor_42 ( (5, 3) ) : 266241
• CKMP2019_Lem_41 ( (5, 3) ) : 266241
• generalized_linkage ( 5,1 ) : 266241
• generalized_linkage_multipleblocks ( show
  [5, 3],[0, 1]
  ) : 266241
• improved_linkage ( 5 ) : 266241
• linkage_GLT ( 5 ) : 266241
• generalized_linkage ( 6,1 ) : 264769
• generalized_linkage_multipleblocks ( show
  [6, 2],[0, 1]
  ) : 264769
• improved_linkage ( 6 ) : 264769
• generalized_linkage_multipleblocks ( show
  [3, 3, 2],[0, 0, 1]
  ) : 263509
• generalized_linkage_multipleblocks ( show
  [3, 3, 2],[0, 1, 1]
  ) : 262229
• graham_sloane ( ) : 70993
• generalized_linkage ( 4,1 ) : 65601
• generalized_linkage_multipleblocks ( show
  [4, 4],[0, 1]
  ) : 65601
• improved_linkage ( 4 ) : 65601
• generalized_linkage ( 4,0 ) : 65557
• generalized_linkage_multipleblocks ( show
  [4, 4],[0, 0]
  ) : 65557
• CKMP2019_Cor_42 ( (4, 4) ) : 65537
• CKMP2019_Lem_41 ( (4, 4) ) : 65537
• linkage_GLT ( 4 ) : 65537
• sphere_covering ( ) : 54141
• HKK_lemma_2_4_lower_bound ( ) : 17476
• generalized_linkage_multipleblocks ( show
  [4, 2, 2],[0, 1, 1]
  ) : 4181
• trivial_1 ( ) : 0

Upper bounds

• improved_johnson ( ) : 1132817
• Ahlswede_Aydinian ( 0, 7, o ) : 1132819
• ilp_1 ( 1 ) : 1132819
• johnson_1 ( ) : 1132819
• Ahlswede_Aydinian ( 1, 2 ) : 1136148
• Ahlswede_Aydinian ( 0, 6, o ) : 1136148
• anticode ( ) : 1136148
• ilp_2 ( 2 ) : 1136148
• linear_programming_bound ( ) : 1136148
• Ahlswede_Aydinian ( 1, 3 ) : 1136941
• Ahlswede_Aydinian ( 1, 4 ) : 1140125
• Ahlswede_Aydinian ( 1, 5 ) : 1153042
• Ahlswede_Aydinian ( 1, 6 ) : 1207776
• Ahlswede_Aydinian ( 1, 7 ) : 1490853
• singleton ( ) : 1490853
• Ahlswede_Aydinian ( 0, 7 ) : 4547924
• ilp_4 ( 7 ) : 4547924
• johnson_2 ( ) : 4547924
• HKK_lemma_2_4_upper_bound ( ) : 4561300
• Ahlswede_Aydinian ( 0, 5 ) : 17389121
• Ahlswede_Aydinian ( 0, 6 ) : 17389121
• ilp_4 ( 5 ) : 17389121
• ilp_4 ( 6 ) : 17389121
• Ahlswede_Aydinian ( 0, 4 ) : 18245201
• Ahlswede_Aydinian ( 1, 4, o ) : 18245201
• ilp_3 ( 4 ) : 18245201
• Ahlswede_Aydinian ( 1, 5, o ) : 18461761
• Ahlswede_Aydinian ( 1, 6, o ) : 19381973
• Ahlswede_Aydinian ( 1, 7, o ) : 24208613
• Ahlswede_Aydinian ( 0, 3 ) : 1550842085
• Ahlswede_Aydinian ( 0, 5, o ) : 1550842085
• all_subs ( ) : 1550842085
• sphere_packing ( ) : 1550842085

Bound for codes containing the lifted MRD code

Do you have better bounds?