Details for entry \(A_5(9,4;3)\)

Lower bounds

• CossidenteMarinoPavese2019_T313 ( ) : 245097501
• generalized_linkage ( 6,0 ) : 245093781
• generalized_linkage_multipleblocks ( show
  [6, 3],[0, 0]
  ) : 245093781
• CKMP2019_Cor_42 ( (6, 3) ) : 245093751
• CKMP2019_Lem_41 ( (6, 3) ) : 245093751
• improved_linkage ( 6 ) : 245093751
• linkage_GLT ( 6 ) : 245093751
• linkage_ST ( 3 ) : 245093751
• construction_D ( 3 ) : 245093750
• construction_1 ( ) : 244649056
• construction_ST_A_1 ( ) : 244649056
• pending_dots ( show
  optimal [(0, 1, 2), (0, 3, 6), (0, 3, 8), (0, 4, 5), (0, 4, 6), (0, 4, 7), (0, 5, 6), (0, 5, 7), (0, 7, 8), (1, 3, 4), (1, 3, 7), (1, 5, 8), (1, 6, 8), (2, 3, 5), (2, 4, 8), (2, 6, 7)] (if conjecture about Ferrers Diagram Rank-Metric Codes is true: 244649056 with optimal [(0, 1, 2), (0, 3, 6), (0, 3, 8), (0, 4, 5), (0, 4, 6), (0, 4, 7), (0, 5, 6), (0, 5, 7), (0, 7, 8), (1, 3, 4), (1, 3, 7), (1, 5, 8), (1, 6, 8), (2, 3, 5), (2, 4, 8), (2, 6, 7)])
  ) : 244649056
• echelon_ferrers ( show
  optimal [(0, 1, 2), (0, 3, 4), (0, 5, 6), (0, 7, 8), (1, 3, 5), (1, 4, 6), (2, 3, 6), (2, 4, 5)] (if conjecture about Ferrers Diagram Rank-Metric Codes is true: 244644376 with optimal [(0, 1, 2), (0, 3, 4), (0, 5, 6), (0, 7, 8), (1, 3, 5), (1, 4, 6), (2, 3, 6), (2, 4, 5)])
  ) : 244644376
• ef_computation ( show
  [(0, 1, 2), (2, 3, 4), (1, 3, 5), (0, 4, 5), (0, 3, 6), (1, 4, 6), (2, 5, 6), (5, 7, 8)]
  ) : 244644376
• construction_ST_B_recursive ( ) : 244547562
• two_pivot_block_construction ( ) : 244531875
• multicomponent ( ) : 244531376
• construction_ST_B ( ) : 244516828
• JohnsonLB ( ) : 244184355
• LMRD ( ) : 244140625
• LiuChangFeng2019_Theo_2_6 ( ) : 244140625
• graham_sloane ( ) : 10254406
• sphere_covering ( ) : 8270193
• HKK_lemma_2_4_lower_bound ( ) : 406880
• trivial_1 ( ) : 0

Upper bounds

• Ahlswede_Aydinian ( 1, 2 ) : 256363276
• anticode ( ) : 256363276
• ilp_1 ( 1 ) : 256363276
• ilp_2 ( 2 ) : 256363276
• improved_johnson ( ) : 256363276
• johnson_1 ( ) : 256363276
• linear_programming_bound ( ) : 256363276
• singleton ( ) : 317886556
• ilp_4 ( 8 ) : 1280240779
• johnson_2 ( ) : 1280240779
• HKK_lemma_2_4_upper_bound ( ) : 6411051905
• ilp_3 ( 4 ) : 32096353484
• all_subs ( ) : 5007031143556
• sphere_packing ( ) : 5007031143556

Bound for codes containing the lifted MRD code

Do you have better bounds?