Details for entry \(A_8(9,4;3)\)

Lower bounds

• CossidenteMarinoPavese2019_T313 ( ) : 68757524481
• generalized_linkage ( 6,0 ) : 68757487689
• generalized_linkage_multipleblocks ( show
  [6, 3],[0, 0]
  ) : 68757487689
• CKMP2019_Cor_42 ( (6, 3) ) : 68757487617
• CKMP2019_Lem_41 ( (6, 3) ) : 68757487617
• improved_linkage ( 6 ) : 68757487617
• linkage_GLT ( 6 ) : 68757487617
• linkage_ST ( 3 ) : 68757487617
• construction_D ( 3 ) : 68757487616
• construction_1 ( ) : 68738954377
• construction_ST_A_1 ( ) : 68738954377
• pending_dots ( show
  optimal [(0, 1, 2), (0, 3, 5), (0, 3, 6), (0, 3, 7), (0, 3, 8), (0, 4, 5), (0, 4, 6), (0, 4, 7), (0, 4, 8), (0, 5, 6), (0, 5, 7), (0, 6, 7), (0, 7, 8), (2, 3, 4), (2, 5, 8), (2, 6, 8)] (if conjecture about Ferrers Diagram Rank-Metric Codes is true: 68738954377 with optimal [(0, 1, 2), (0, 3, 5), (0, 3, 6), (0, 3, 7), (0, 3, 8), (0, 4, 5), (0, 4, 6), (0, 4, 7), (0, 4, 8), (0, 5, 6), (0, 5, 7), (0, 6, 7), (0, 7, 8), (2, 3, 4), (2, 5, 8), (2, 6, 8)])
  ) : 68738954377
• 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: 68738912257 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)])
  ) : 68738912257
• 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)]
  ) : 68738912257
• construction_ST_B_recursive ( ) : 68736520338
• two_pivot_block_construction ( ) : 68736258049
• multicomponent ( ) : 68736254465
• construction_ST_B ( ) : 68735999875
• JohnsonLB ( ) : 68720118024
• LMRD ( ) : 68719476736
• LiuChangFeng2019_Theo_2_6 ( ) : 68719476736
• graham_sloane ( ) : 1092919369
• sphere_covering ( ) : 958179489
• HKK_lemma_2_4_lower_bound ( ) : 17043464
• trivial_1 ( ) : 0

Upper bounds

• Ahlswede_Aydinian ( 1, 2 ) : 69946872385
• anticode ( ) : 69946872385
• ilp_1 ( 1 ) : 69946872385
• ilp_2 ( 2 ) : 69946872385
• improved_johnson ( ) : 69946872385
• johnson_1 ( ) : 69946872385
• linear_programming_bound ( ) : 69946872385
• singleton ( ) : 79783113865
• ilp_4 ( 8 ) : 559457305159
• johnson_2 ( ) : 559457305159
• HKK_lemma_2_4_upper_bound ( ) : 4476734320712
• ilp_3 ( 4 ) : 35821527074255
• all_subs ( ) : 20955593338439305
• sphere_packing ( ) : 20955593338439305

Bound for codes containing the lifted MRD code

Do you have better bounds?