Details for entry \(A_8(7,4;3)\)

Lower bounds

• construction_HK15 ( ) : 16814136
• construction_honold ( ) : 16814071
• construction_1 ( ) : 16781961
• pending_dots ( show
  optimal [(0, 1, 2), (0, 3, 4), (0, 3, 5), (0, 5, 6), (1, 3, 6), (1, 4, 5), (2, 4, 6)] (if conjecture about Ferrers Diagram Rank-Metric Codes is true: 16781961 with optimal [(0, 1, 2), (0, 3, 4), (0, 3, 5), (0, 5, 6), (1, 3, 6), (1, 4, 5), (2, 4, 6)])
  ) : 16781961
• 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: 16781905 with optimal [(0, 1, 2), (0, 3, 4), (0, 5, 6), (1, 3, 5), (1, 4, 6), (2, 3, 6), (2, 4, 5)])
  ) : 16781905
• ef_computation ( show
  [(0, 1, 2), (0, 3, 4), (1, 3, 5), (2, 3, 6), (2, 4, 5), (1, 4, 6), (0, 5, 6)]
  ) : 16781905
• two_pivot_block_construction ( ) : 16781313
• JohnsonLB ( ) : 16777939
• JohnsonLB_special ( ) : 16777939
• generalized_linkage ( 3,1 ) : 16777729
• generalized_linkage_multipleblocks ( show
  [3, 4],[0, 1]
  ) : 16777729
• improved_linkage ( 3 ) : 16777729
• multicomponent ( ) : 16777729
• CKMP2019_Cor_42 ( (3, 4) ) : 16777217
• CKMP2019_Lem_41 ( (3, 4) ) : 16777217
• linkage_GLT ( 3 ) : 16777217
• LMRD ( ) : 16777216
• LiuChangFeng2019_Theo_2_6 ( ) : 16777216
• graham_sloane ( ) : 266817
• HKK_lemma_2_4_lower_bound ( ) : 266248
• sphere_covering ( ) : 233979
• trivial_1 ( ) : 0

Upper bounds

• Ahlswede_Aydinian ( 1, 2 ) : 17076801
• anticode ( ) : 17076801
• ilp_1 ( 1 ) : 17076801
• ilp_2 ( 2 ) : 17076801
• improved_johnson ( ) : 17076801
• johnson_1 ( ) : 17076801
• linear_programming_bound ( ) : 17076801
• singleton ( ) : 19477641
• ilp_4 ( 5 ) : 134775367
• johnson_2 ( ) : 134775367
• ilp_3 ( 4 ) : 136643599
• all_subs ( ) : 79936505481
• sphere_packing ( ) : 79936505481

Bound for codes containing the lifted MRD code

Do you have better bounds?