Details for entry \(A_5(7,4;3)\)

Lower bounds

• construction_HK15 ( ) : 394395
• construction_honold ( ) : 394369
• construction_1 ( ) : 391431
• pending_dots ( show
  optimal [(0, 1, 2), (0, 3, 4), (0, 3, 5), (0, 4, 6), (0, 5, 6), (1, 4, 5), (2, 3, 6)] (if conjecture about Ferrers Diagram Rank-Metric Codes is true: 391431 with optimal [(0, 1, 2), (0, 3, 4), (0, 3, 5), (0, 4, 6), (0, 5, 6), (1, 4, 5), (2, 3, 6)])
  ) : 391431
• 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: 391411 with optimal [(0, 1, 2), (0, 3, 4), (0, 5, 6), (1, 3, 5), (1, 4, 6), (2, 3, 6), (2, 4, 5)])
  ) : 391411
• ef_computation ( show
  [(0, 1, 2), (0, 3, 4), (1, 3, 5), (2, 3, 6), (2, 4, 5), (1, 4, 6), (0, 5, 6)]
  ) : 391411
• two_pivot_block_construction ( ) : 391251
• JohnsonLB ( ) : 390838
• JohnsonLB_special ( ) : 390838
• generalized_linkage ( 3,1 ) : 390751
• generalized_linkage_multipleblocks ( show
  [3, 4],[0, 1]
  ) : 390751
• improved_linkage ( 3 ) : 390751
• multicomponent ( ) : 390751
• CKMP2019_Cor_42 ( (3, 4) ) : 390626
• CKMP2019_Lem_41 ( (3, 4) ) : 390626
• linkage_GLT ( 3 ) : 390626
• LMRD ( ) : 390625
• LiuChangFeng2019_Theo_2_6 ( ) : 390625
• graham_sloane ( ) : 16401
• HKK_lemma_2_4_lower_bound ( ) : 16255
• sphere_covering ( ) : 13248
• trivial_1 ( ) : 0

Upper bounds

• Ahlswede_Aydinian ( 1, 2 ) : 410151
• anticode ( ) : 410151
• ilp_1 ( 1 ) : 410151
• ilp_2 ( 2 ) : 410151
• improved_johnson ( ) : 410151
• johnson_1 ( ) : 410151
• linear_programming_bound ( ) : 410151
• singleton ( ) : 508431
• ilp_4 ( 5 ) : 1987654
• johnson_2 ( ) : 1987654
• ilp_3 ( 4 ) : 2053384
• all_subs ( ) : 320327931
• sphere_packing ( ) : 320327931

Bound for codes containing the lifted MRD code

Do you have better bounds?