Details for entry \(A_2(8,4;3)\)

Known codes

• 1326 Östergård, ALCOMA15 BraunOstergardWassermann2016 file
• 1312 BraunReichelt2014
• 1275 GutierrezMolina2020
• 1024 LMRD KoetterKschischang2008, Gabidulin1985 file

Lower bounds

• construction_1 ( ) : 1179
• construction_ST_A_1 ( ) : 1179
• pending_dots ( show
  optimal [(0, 1, 2), (0, 3, 5), (0, 3, 6), (0, 4, 5), (0, 4, 7), (1, 3, 4), (1, 4, 6), (1, 5, 7), (1, 6, 7), (2, 3, 7), (2, 5, 6)] (if conjecture about Ferrers Diagram Rank-Metric Codes is true: 1179 with optimal [(0, 1, 2), (0, 3, 5), (0, 3, 6), (0, 4, 5), (0, 4, 7), (1, 3, 4), (1, 4, 6), (1, 5, 7), (1, 6, 7), (2, 3, 7), (2, 5, 6)])
  ) : 1179
• echelon_ferrers ( show
  optimal [(0, 1, 2), (0, 3, 4), (0, 5, 6), (1, 3, 5), (1, 4, 6), (2, 3, 6), (2, 4, 5)] (if conjecture about Ferrers Diagram Rank-Metric Codes is true: 1164 with optimal [(0, 1, 2), (0, 3, 4), (0, 5, 6), (1, 3, 5), (1, 4, 6), (2, 3, 6), (2, 4, 5)])
  ) : 1164
• ef_computation ( show
  [(0, 1, 2), (2, 3, 4), (1, 3, 5), (0, 4, 5), (0, 3, 6), (1, 4, 6), (2, 5, 6)]
  ) : 1164
• expurgation_augmentation_special_cases ( ) : 1117
• construction_ST_B_recursive ( ) : 1101
• generalized_linkage ( 3,1 ) : 1101
• generalized_linkage_multipleblocks ( show
  [3, 5],[0, 1]
  ) : 1101
• improved_linkage ( 3 ) : 1101
• JohnsonLB ( ) : 1094
• two_pivot_block_construction ( ) : 1092
• multicomponent ( ) : 1089
• construction_ST_B ( ) : 1079
• CKMP2019_Cor_42 ( (3, 5) ) : 1033
• CKMP2019_Lem_41 ( (3, 5) ) : 1033
• linkage_GLT ( 3 ) : 1033
• LMRD ( ) : 1024
• LiuChangFeng2019_Theo_2_6 ( ) : 1024
• Bardestani_Iranmanesh ( ) : 510
• graham_sloane ( ) : 381
• sphere_covering ( ) : 224
• HKK_lemma_2_4_lower_bound ( ) : 170
• trivial_1 ( ) : 0

Upper bounds

• Ahlswede_Aydinian ( 0, 7, o ) : 1493
• ilp_1 ( 1 ) : 1493
• improved_johnson ( ) : 1493
• johnson_1 ( ) : 1493
• anticode ( ) : 1542
• ilp_2 ( 2 ) : 1542
• linear_programming_bound ( ) : 1542
• singleton ( ) : 2667
• ilp_4 ( 7 ) : 3134
• johnson_2 ( ) : 3134
• HKK_lemma_2_4_upper_bound ( ) : 3238
• ilp_3 ( 4 ) : 6477
• all_subs ( ) : 97155
• sphere_packing ( ) : 97155

Bound for codes containing the lifted MRD code

Do you have better bounds?