Details for entry \(A_2(9,4;3)\)

Known codes

• 5986 Östergård, ALCOMA15 BraunOstergardWassermann2016 file
• 5694 EtzionVardy2011 (Example 3)
• 5621 GutierrezMolina2020
• 4096 LMRD KoetterKschischang2008, Gabidulin1985 file

Lower bounds

• CossidenteMarinoPavese2019_T313 ( ) : 4977
• generalized_linkage ( 6,0 ) : 4935
• generalized_linkage_multipleblocks ( show
  [6, 3],[0, 0]
  ) : 4935
• CKMP2019_Cor_42 ( (6, 3) ) : 4929
• CKMP2019_Lem_41 ( (6, 3) ) : 4929
• improved_linkage ( 6 ) : 4929
• linkage_GLT ( 6 ) : 4929
• linkage_ST ( 3 ) : 4929
• construction_D ( 3 ) : 4928
• expurgation_augmentation_special_cases ( ) : 4852
• construction_1 ( ) : 4747
• construction_ST_A_1 ( ) : 4747
• pending_dots ( show
  optimal [(0, 1, 2), (0, 3, 4), (0, 3, 5), (0, 3, 6), (0, 3, 7), (0, 4, 5), (0, 4, 7), (0, 4, 8), (0, 5, 6), (0, 5, 8), (0, 6, 7), (0, 6, 8), (0, 7, 8), (2, 3, 8), (2, 4, 6), (2, 5, 7)] (if conjecture about Ferrers Diagram Rank-Metric Codes is true: 4747 with optimal [(0, 1, 2), (0, 3, 4), (0, 3, 5), (0, 3, 6), (0, 3, 7), (0, 4, 5), (0, 4, 7), (0, 4, 8), (0, 5, 6), (0, 5, 8), (0, 6, 7), (0, 6, 8), (0, 7, 8), (2, 3, 8), (2, 4, 6), (2, 5, 7)])
  ) : 4747
• 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: 4657 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)])
  ) : 4657
• 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)]
  ) : 4657
• Bardestani_Iranmanesh ( ) : 4599
• construction_ST_B_recursive ( ) : 4446
• JohnsonLB ( ) : 4417
• two_pivot_block_construction ( ) : 4369
• multicomponent ( ) : 4361
• construction_ST_B ( ) : 4315
• LMRD ( ) : 4096
• LiuChangFeng2019_Theo_2_6 ( ) : 4096
• graham_sloane ( ) : 1543
• sphere_covering ( ) : 893
• HKK_lemma_2_4_lower_bound ( ) : 338
• trivial_1 ( ) : 0

Upper bounds

• Ahlswede_Aydinian ( 1, 2 ) : 6205
• anticode ( ) : 6205
• ilp_1 ( 1 ) : 6205
• ilp_2 ( 2 ) : 6205
• improved_johnson ( ) : 6205
• johnson_1 ( ) : 6205
• linear_programming_bound ( ) : 6205
• singleton ( ) : 10795
• ilp_4 ( 8 ) : 12109
• johnson_2 ( ) : 12109
• HKK_lemma_2_4_upper_bound ( ) : 25430
• ilp_3 ( 4 ) : 52535
• all_subs ( ) : 788035
• sphere_packing ( ) : 788035

Bound for codes containing the lifted MRD code

Do you have better bounds?