Details for entry \(A_5(10,6;4)\)

Lower bounds

• construction_1 ( ) : 244156311
• ef_computation ( show
  [(0, 1, 2, 3), (0, 4, 5, 6), (1, 4, 7, 8), (2, 5, 7, 9), (3, 6, 8, 9)]
  ) : 244156281
• 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: 244156281 with optimal [(0, 1, 2, 3), (0, 4, 7, 8), (1, 4, 5, 6), (2, 5, 7, 9), (3, 6, 8, 9)])
  ) : 244143757
• 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: 244156281 with optimal [(0, 1, 2, 3), (0, 4, 5, 6), (1, 6, 8, 9), (2, 4, 7, 8), (3, 5, 7, 9)])
  ) : 244143757
• generalized_linkage ( 4,1 ) : 244141251
• generalized_linkage_multipleblocks ( show
  [4, 6],[0, 1]
  ) : 244141251
• improved_linkage ( 4 ) : 244141251
• multicomponent ( ) : 244141251
• CKMP2019_Cor_42 ( (4, 6) ) : 244140626
• CKMP2019_Lem_41 ( (4, 6) ) : 244140626
• linkage_GLT ( 4 ) : 244140626
• LMRD ( ) : 244140625
• LiuChangFeng2019_Theo_2_6 ( ) : 244140625
• JohnsonLB ( ) : 244062656
• HKK_lemma_2_4_lower_bound ( ) : 393755
• sphere_covering ( ) : 305946
• graham_sloane ( ) : 3287
• trivial_1 ( ) : 0

Upper bounds

• improved_johnson ( ) : 246503751
• Ahlswede_Aydinian ( 2, 2 ) : 246503755
• anticode ( ) : 246503755
• ilp_1 ( 1 ) : 246503755
• ilp_2 ( 2 ) : 246503755
• johnson_1 ( ) : 246503755
• linear_programming_bound ( ) : 246503755
• singleton ( ) : 317886556
• ilp_4 ( 9 ) : 6139112899
• johnson_2 ( ) : 6139112899
• HKK_lemma_2_4_upper_bound ( ) : 6140685015
• sphere_packing ( ) : 25719866955
• ilp_3 ( 6 ) : 154121660510
• all_subs ( ) : 78360229974772306

Bound for codes containing the lifted MRD code

Do you have better bounds?