Details for entry \(A_8(10,6;4)\)

Lower bounds

• construction_1 ( ) : 68719739025
• ef_computation ( show
  [(0, 1, 2, 3), (0, 4, 5, 6), (1, 4, 7, 8), (2, 5, 7, 9), (3, 6, 8, 9)]
  ) : 68719738953
• 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: 68719738953 with optimal [(0, 1, 2, 3), (0, 4, 5, 6), (1, 5, 7, 9), (2, 6, 8, 9), (3, 4, 7, 8)])
  ) : 68719509514
• 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: 68719738953 with optimal [(0, 1, 2, 3), (0, 4, 7, 8), (1, 4, 5, 6), (2, 5, 7, 9), (3, 6, 8, 9)])
  ) : 68719509514
• generalized_linkage ( 4,1 ) : 68719480833
• generalized_linkage_multipleblocks ( show
  [4, 6],[0, 1]
  ) : 68719480833
• improved_linkage ( 4 ) : 68719480833
• multicomponent ( ) : 68719480833
• CKMP2019_Cor_42 ( (4, 6) ) : 68719476737
• CKMP2019_Lem_41 ( (4, 6) ) : 68719476737
• linkage_GLT ( 4 ) : 68719476737
• LMRD ( ) : 68719476736
• LiuChangFeng2019_Theo_2_6 ( ) : 68719476736
• JohnsonLB ( ) : 68717380169
• HKK_lemma_2_4_lower_bound ( ) : 16809992
• sphere_covering ( ) : 14514872
• graham_sloane ( ) : 33362
• trivial_1 ( ) : 0

Upper bounds

• improved_johnson ( ) : 68870770689
• Ahlswede_Aydinian ( 2, 2 ) : 68870770696
• anticode ( ) : 68870770696
• ilp_1 ( 1 ) : 68870770696
• ilp_2 ( 2 ) : 68870770696
• johnson_1 ( ) : 68870770696
• linear_programming_bound ( ) : 68870770696
• singleton ( ) : 79783113865
• ilp_4 ( 9 ) : 4403567481407
• johnson_2 ( ) : 4403567481407
• HKK_lemma_2_4_upper_bound ( ) : 4403685072934
• sphere_packing ( ) : 31351609751242
• ilp_3 ( 6 ) : 282104210693648
• all_subs ( ) : 5494724540479236953737

Bound for codes containing the lifted MRD code

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