Details for entry \(A_9(8,4;3)\)

Lower bounds

• construction_1 ( ) : 3487389643
• construction_ST_A_1 ( ) : 3487389643
• pending_dots ( show
  optimal [(0, 1, 2), (0, 3, 4), (0, 3, 5), (0, 3, 7), (0, 4, 5), (0, 4, 6), (0, 5, 6), (0, 5, 7), (0, 6, 7), (2, 3, 6), (2, 4, 7)] (if conjecture about Ferrers Diagram Rank-Metric Codes is true: 3487389643 with optimal [(0, 1, 2), (0, 3, 4), (0, 3, 5), (0, 3, 7), (0, 4, 5), (0, 4, 6), (0, 5, 6), (0, 5, 7), (0, 6, 7), (2, 3, 6), (2, 4, 7)])
  ) : 3487389643
• 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: 3487388823 with optimal [(0, 1, 2), (0, 3, 4), (0, 5, 6), (1, 3, 5), (1, 4, 6), (2, 3, 6), (2, 4, 5)])
  ) : 3487388823
• ef_computation ( show
  [(0, 1, 2), (2, 3, 4), (1, 3, 5), (0, 4, 5), (0, 3, 6), (1, 4, 6), (2, 5, 6)]
  ) : 3487388823
• construction_ST_B_recursive ( ) : 3487316653
• generalized_linkage ( 3,1 ) : 3487316023
• generalized_linkage_multipleblocks ( show
  [3, 5],[0, 1]
  ) : 3487316023
• improved_linkage ( 3 ) : 3487316023
• two_pivot_block_construction ( ) : 3487315923
• multicomponent ( ) : 3487315843
• construction_ST_B ( ) : 3487309442
• JohnsonLB ( ) : 3486798148
• CKMP2019_Cor_42 ( (3, 5) ) : 3486785131
• CKMP2019_Lem_41 ( (3, 5) ) : 3486785131
• linkage_GLT ( 3 ) : 3486785131
• LMRD ( ) : 3486784401
• LiuChangFeng2019_Theo_2_6 ( ) : 3486784401
• graham_sloane ( ) : 43644583
• sphere_covering ( ) : 38849126
• HKK_lemma_2_4_lower_bound ( ) : 4842756
• trivial_1 ( ) : 0

Upper bounds

• improved_johnson ( ) : 3534738832
• Ahlswede_Aydinian ( 0, 7, o ) : 3534738839
• ilp_1 ( 1 ) : 3534738839
• johnson_1 ( ) : 3534738839
• anticode ( ) : 3535217793
• ilp_2 ( 2 ) : 3535217793
• linear_programming_bound ( ) : 3535217793
• singleton ( ) : 3971657053
• ilp_4 ( 7 ) : 31817439099
• johnson_2 ( ) : 31817439099
• HKK_lemma_2_4_upper_bound ( ) : 31821750405
• ilp_3 ( 4 ) : 286395753646
• all_subs ( ) : 234844517989720
• sphere_packing ( ) : 234844517989720

Bound for codes containing the lifted MRD code

Do you have better bounds?