Details for entry \(A_5(8,4;3)\)

Lower bounds

• construction_1 ( ) : 9785931
• construction_ST_A_1 ( ) : 9785931
• pending_dots ( show
  optimal [(0, 1, 2), (0, 3, 6), (0, 3, 7), (0, 4, 5), (0, 4, 6), (0, 4, 7), (0, 5, 6), (1, 3, 4), (1, 5, 7), (2, 3, 5), (2, 6, 7)] (if conjecture about Ferrers Diagram Rank-Metric Codes is true: 9785931 with optimal [(0, 1, 2), (0, 3, 6), (0, 3, 7), (0, 4, 5), (0, 4, 6), (0, 4, 7), (0, 5, 6), (1, 3, 4), (1, 5, 7), (2, 3, 5), (2, 6, 7)])
  ) : 9785931
• 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: 9785775 with optimal [(0, 1, 2), (0, 3, 4), (0, 5, 6), (1, 3, 5), (1, 4, 6), (2, 3, 6), (2, 4, 5)])
  ) : 9785775
• ef_computation ( show
  [(0, 1, 2), (2, 3, 4), (1, 3, 5), (0, 4, 5), (0, 3, 6), (1, 4, 6), (2, 5, 6)]
  ) : 9785775
• construction_ST_B_recursive ( ) : 9781401
• generalized_linkage ( 3,1 ) : 9781311
• generalized_linkage_multipleblocks ( show
  [3, 5],[0, 1]
  ) : 9781311
• improved_linkage ( 3 ) : 9781311
• two_pivot_block_construction ( ) : 9781275
• multicomponent ( ) : 9781251
• construction_ST_B ( ) : 9780674
• JohnsonLB ( ) : 9766959
• CKMP2019_Cor_42 ( (3, 5) ) : 9765751
• CKMP2019_Lem_41 ( (3, 5) ) : 9765751
• linkage_GLT ( 3 ) : 9765751
• LMRD ( ) : 9765625
• LiuChangFeng2019_Theo_2_6 ( ) : 9765625
• graham_sloane ( ) : 410151
• sphere_covering ( ) : 330870
• HKK_lemma_2_4_lower_bound ( ) : 81380
• trivial_1 ( ) : 0

Upper bounds

• improved_johnson ( ) : 10241276
• Ahlswede_Aydinian ( 0, 7, o ) : 10241279
• ilp_1 ( 1 ) : 10241279
• johnson_1 ( ) : 10241279
• anticode ( ) : 10254405
• ilp_2 ( 2 ) : 10254405
• linear_programming_bound ( ) : 10254405
• singleton ( ) : 12714681
• ilp_4 ( 7 ) : 51285155
• johnson_2 ( ) : 51285155
• HKK_lemma_2_4_upper_bound ( ) : 51350905
• ilp_3 ( 4 ) : 256754526
• all_subs ( ) : 40053706056
• sphere_packing ( ) : 40053706056

Bound for codes containing the lifted MRD code

Do you have better bounds?