Details for entry \(A_4(10,6;5)\)

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)]
  ) : 1073745960
• Gorla_Ravagnani_2014 ( ) : 1073745957
• echelon_ferrers ( show
  optimal [(0, 1, 2, 3, 4), (0, 1, 5, 6, 7), (0, 3, 6, 8, 9), (1, 2, 5, 8, 9), (2, 4, 6, 7, 8), (3, 4, 5, 7, 9)] (if conjecture about Ferrers Diagram Rank-Metric Codes is true: 1073745960 with optimal [(0, 1, 2, 3, 4), (0, 1, 5, 6, 7), (0, 4, 6, 8, 9), (1, 3, 5, 8, 9), (2, 3, 6, 7, 9), (2, 4, 5, 7, 8)])
  ) : 1073745939
• pending_dots ( show
  optimal [(0, 1, 2, 3, 4), (0, 1, 5, 6, 7), (0, 3, 7, 8, 9), (1, 4, 6, 8, 9), (2, 3, 5, 6, 9), (2, 4, 5, 7, 8)] (if conjecture about Ferrers Diagram Rank-Metric Codes is true: 1073745960 with optimal [(0, 1, 2, 3, 4), (0, 1, 5, 6, 7), (0, 4, 6, 8, 9), (1, 3, 5, 8, 9), (2, 3, 6, 7, 8), (2, 4, 5, 7, 9)])
  ) : 1073745939
• two_pivot_block_construction ( ) : 1073745920
• generalized_linkage ( 5,0 ) : 1073741889
• generalized_linkage_multipleblocks ( show
  [5, 5],[0, 0]
  ) : 1073741889
• CKMP2019_Cor_42 ( (5, 5) ) : 1073741825
• CKMP2019_Lem_41 ( (5, 5) ) : 1073741825
• LiuChangFeng2019_Theo_2_6 ( ) : 1073741825
• improved_linkage ( 5 ) : 1073741825
• linkage_GLT ( 5 ) : 1073741825
• multicomponent ( ) : 1073741825
• LMRD ( ) : 1073741824
• HKK_lemma_2_4_lower_bound ( ) : 67125412
• JohnsonLB ( ) : 67092818
• sphere_covering ( ) : 189942
• graham_sloane ( ) : 4459
• trivial_1 ( ) : 0

Upper bounds

• Ahlswede_Aydinian ( 0, 9 ) : 1088477225
• ilp_1 ( 1 ) : 1088477225
• ilp_4 ( 9 ) : 1088477225
• improved_johnson ( ) : 1088477225
• johnson_1 ( ) : 1088477225
• johnson_2 ( ) : 1088477225
• anticode ( ) : 1096111425
• ilp_2 ( 3 ) : 1096111425
• ilp_3 ( 7 ) : 1096111425
• linear_programming_bound ( ) : 1096111425
• singleton ( ) : 1550842085
• sphere_packing ( ) : 3513337288
• all_subs ( ) : 1634141006295525

Bound for codes containing the lifted MRD code

Do you have better bounds?