Details for entry \(A_9(10,6;5)\)

Lower bounds

• ef_computation ( show
  [(0, 1, 2, 3, 4), (0, 1, 5, 6, 7), (0, 4, 5, 8, 9), (2, 3, 5, 7, 9), (2, 4, 6, 7, 8), (1, 3, 6, 8, 9)]
  ) : 205891132626270
• Gorla_Ravagnani_2014 ( ) : 205891132626262
• echelon_ferrers ( show
  optimal [(0, 1, 2, 3, 4), (0, 1, 5, 6, 7), (0, 2, 5, 8, 9), (1, 3, 6, 8, 9), (2, 4, 6, 7, 8), (3, 4, 5, 7, 9)] (if conjecture about Ferrers Diagram Rank-Metric Codes is true: 205891132626190 with optimal [(0, 1, 2, 3, 4), (0, 1, 5, 6, 7), (0, 2, 5, 8, 9), (1, 3, 6, 8, 9), (2, 4, 6, 7, 8), (3, 4, 5, 7, 9)])
  ) : 205891132626102
• pending_dots ( show
  optimal [(0, 1, 2, 3, 4), (0, 1, 5, 6, 7), (0, 2, 5, 8, 9), (1, 3, 6, 8, 9), (2, 4, 6, 7, 8), (3, 4, 5, 7, 9)] (if conjecture about Ferrers Diagram Rank-Metric Codes is true: 205891132626190 with optimal [(0, 1, 2, 3, 4), (0, 1, 5, 6, 7), (0, 2, 5, 8, 9), (1, 3, 6, 8, 9), (2, 4, 6, 7, 8), (3, 4, 5, 7, 9)])
  ) : 205891132626102
• two_pivot_block_construction ( ) : 205891132626090
• generalized_linkage ( 5,0 ) : 205891132095379
• generalized_linkage_multipleblocks ( show
  [5, 5],[0, 0]
  ) : 205891132095379
• CKMP2019_Cor_42 ( (5, 5) ) : 205891132094650
• CKMP2019_Lem_41 ( (5, 5) ) : 205891132094650
• LiuChangFeng2019_Theo_2_6 ( ) : 205891132094650
• improved_linkage ( 5 ) : 205891132094650
• linkage_GLT ( 5 ) : 205891132094650
• multicomponent ( ) : 205891132094650
• LMRD ( ) : 205891132094649
• HKK_lemma_2_4_lower_bound ( ) : 2541870612927
• JohnsonLB ( ) : 2541861052733
• sphere_covering ( ) : 340761744
• graham_sloane ( ) : 538914
• trivial_1 ( ) : 0

Upper bounds

• Ahlswede_Aydinian ( 0, 9 ) : 206068986324950
• ilp_1 ( 1 ) : 206068986324950
• ilp_4 ( 9 ) : 206068986324950
• improved_johnson ( ) : 206068986324950
• johnson_1 ( ) : 206068986324950
• johnson_2 ( ) : 206068986324950
• anticode ( ) : 206208865323100
• ilp_2 ( 3 ) : 206208865323100
• ilp_3 ( 7 ) : 206208865323100
• linear_programming_bound ( ) : 206208865323100
• singleton ( ) : 234844517989720
• sphere_packing ( ) : 1670344887941591
• all_subs ( ) : 818990894351617238824300

Bound for codes containing the lifted MRD code

Do you have better bounds?