Details for entry \(A_9(10,6;4)\)

Lower bounds

• construction_1 ( ) : 282430068103
• ef_computation ( show
  [(0, 1, 2, 3), (0, 4, 5, 6), (1, 4, 7, 8), (2, 5, 7, 9), (3, 6, 8, 9)]
  ) : 282430068013
• echelon_ferrers ( show
  optimal [(0, 1, 2, 3), (0, 5, 8, 9), (1, 6, 7, 8), (2, 4, 5, 6), (3, 4, 7, 9)] (if conjecture about Ferrers Diagram Rank-Metric Codes is true: 282430068013 with optimal [(0, 1, 2, 3), (0, 5, 7, 9), (1, 4, 5, 6), (2, 6, 8, 9), (3, 4, 7, 8)])
  ) : 282429595541
• pending_dots ( show
  optimal [(0, 1, 2, 3), (0, 6, 7, 8), (1, 5, 8, 9), (2, 4, 5, 6), (3, 4, 7, 9)] (if conjecture about Ferrers Diagram Rank-Metric Codes is true: 282430068013 with optimal [(0, 1, 2, 3), (0, 4, 7, 8), (1, 4, 5, 6), (2, 5, 7, 9), (3, 6, 8, 9)])
  ) : 282429595541
• generalized_linkage ( 4,1 ) : 282429543043
• generalized_linkage_multipleblocks ( show
  [4, 6],[0, 1]
  ) : 282429543043
• improved_linkage ( 4 ) : 282429543043
• multicomponent ( ) : 282429543043
• CKMP2019_Cor_42 ( (4, 6) ) : 282429536482
• CKMP2019_Lem_41 ( (4, 6) ) : 282429536482
• linkage_GLT ( 4 ) : 282429536482
• LMRD ( ) : 282429536481
• LiuChangFeng2019_Theo_2_6 ( ) : 282429536481
• JohnsonLB ( ) : 282424754332
• HKK_lemma_2_4_lower_bound ( ) : 43105779
• sphere_covering ( ) : 37907505
• graham_sloane ( ) : 59879
• trivial_1 ( ) : 0

Upper bounds

• improved_johnson ( ) : 282860600743
• Ahlswede_Aydinian ( 2, 2 ) : 282860600751
• anticode ( ) : 282860600751
• ilp_1 ( 1 ) : 282860600751
• ilp_2 ( 2 ) : 282860600751
• johnson_1 ( ) : 282860600751
• linear_programming_bound ( ) : 282860600751
• singleton ( ) : 321704819164
• ilp_4 ( 9 ) : 22896209364209
• johnson_2 ( ) : 22896209364209
• HKK_lemma_2_4_upper_bound ( ) : 22896554036105
• sphere_packing ( ) : 185613436292117
• ilp_3 ( 6 ) : 1855882892060622
• all_subs ( ) : 90997618413507253345810

Bound for codes containing the lifted MRD code

Do you have better bounds?