Details for entry \(A_8(10,6;5)\)

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)]
  ) : 35184372351120
• Gorla_Ravagnani_2014 ( ) : 35184372351113
• 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: 35184372351057 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)])
  ) : 35184372350987
• 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: 35184372351057 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)])
  ) : 35184372350987
• two_pivot_block_construction ( ) : 35184372350976
• generalized_linkage ( 5,0 ) : 35184372089345
• generalized_linkage_multipleblocks ( show
  [5, 5],[0, 0]
  ) : 35184372089345
• CKMP2019_Cor_42 ( (5, 5) ) : 35184372088833
• CKMP2019_Lem_41 ( (5, 5) ) : 35184372088833
• LiuChangFeng2019_Theo_2_6 ( ) : 35184372088833
• improved_linkage ( 5 ) : 35184372088833
• linkage_GLT ( 5 ) : 35184372088833
• multicomponent ( ) : 35184372088833
• LMRD ( ) : 35184372088832
• HKK_lemma_2_4_lower_bound ( ) : 549757912200
• JohnsonLB ( ) : 549753721410
• sphere_covering ( ) : 115926672
• graham_sloane ( ) : 266899
• trivial_1 ( ) : 0

Upper bounds

• Ahlswede_Aydinian ( 0, 9 ) : 35229480583473
• ilp_1 ( 1 ) : 35229480583473
• ilp_4 ( 9 ) : 35229480583473
• improved_johnson ( ) : 35229480583473
• johnson_1 ( ) : 35229480583473
• johnson_2 ( ) : 35229480583473
• anticode ( ) : 35262908633601
• ilp_2 ( 3 ) : 35262908633601
• ilp_3 ( 7 ) : 35262908633601
• linear_programming_bound ( ) : 35262908633601
• singleton ( ) : 40928737412745
• sphere_packing ( ) : 250772689542626
• all_subs ( ) : 43958970159454591899273

Bound for codes containing the lifted MRD code

Do you have better bounds?