Details for entry \(A_9(10,4;5)\)

Lower bounds

• CKMP2019_Cor_45 ( show
  (5,),(3,),(2,)
  ) : 12159772591358508651
• CossidentePavese14_theorem311 ( ) : 12159772590972225574
• CKMP2019_Cor_42 ( (5, 5) ) : 12159772590971088162
• CKMP2019_Lem_41 ( (5, 5) ) : 12159772590971088162
• LiuChangFeng2019_Theo_2_6 ( ) : 12159772590971088162
• generalized_linkage ( 5,0 ) : 12159772590971088162
• generalized_linkage_multipleblocks ( show
  [5, 5],[0, 0]
  ) : 12159772590971088162
• ChenHeWengXu2019_T31 ( ) : 12159772590971088161
• ChenHeWengXu2019_T41 ( ) : 12159772590971088161
• XuChen2018 ( ) : 12159772590971088161
• pending_dots ( show
  optimal [(0, 1, 2, 3, 4), (0, 1, 2, 5, 6), (0, 1, 2, 7, 8), (0, 1, 3, 5, 7), (0, 1, 3, 6, 8), (0, 1, 4, 5, 8), (0, 1, 4, 6, 7), (0, 2, 3, 5, 8), (0, 2, 3, 6, 7), (0, 2, 4, 5, 7), (0, 2, 4, 6, 8), (0, 3, 4, 5, 6), (0, 3, 4, 7, 8), (0, 5, 6, 7, 8), (1, 2, 3, 5, 9), (1, 2, 4, 6, 9), (1, 3, 4, 7, 9), (1, 5, 6, 7, 9), (2, 3, 4, 8, 9), (2, 5, 6, 8, 9), (3, 5, 7, 8, 9), (4, 6, 7, 8, 9)] (if conjecture about Ferrers Diagram Rank-Metric Codes is true: 12159543650778161152 with optimal [(0, 1, 2, 3, 4), (0, 1, 2, 5, 6), (0, 1, 2, 7, 8), (0, 1, 3, 5, 7), (0, 1, 3, 6, 8), (0, 1, 4, 5, 8), (0, 1, 4, 6, 7), (0, 2, 3, 5, 8), (0, 2, 3, 6, 7), (0, 2, 4, 5, 7), (0, 2, 4, 6, 8), (0, 3, 4, 5, 6), (0, 3, 4, 7, 8), (0, 5, 6, 7, 8), (1, 2, 3, 5, 9), (1, 2, 4, 6, 9), (1, 3, 4, 7, 9), (1, 5, 6, 7, 9), (2, 3, 4, 8, 9), (2, 5, 6, 8, 9), (3, 5, 7, 8, 9), (4, 6, 7, 8, 9)])
  ) : 12159543650778161152
• echelon_ferrers ( show
  optimal [(0, 1, 2, 3, 4), (0, 1, 2, 5, 6), (0, 1, 2, 7, 8), (0, 1, 3, 5, 7), (0, 1, 3, 6, 8), (0, 1, 4, 5, 8), (0, 1, 4, 6, 7), (0, 2, 3, 5, 8), (0, 2, 3, 6, 7), (0, 2, 4, 5, 7), (0, 2, 4, 6, 8), (0, 3, 4, 5, 6), (0, 3, 4, 7, 8), (0, 5, 6, 7, 8), (1, 2, 3, 5, 9), (1, 2, 4, 6, 9), (1, 3, 4, 7, 9), (1, 5, 6, 7, 9), (2, 3, 4, 8, 9), (2, 5, 6, 8, 9), (3, 5, 7, 8, 9), (4, 6, 7, 8, 9)] (if conjecture about Ferrers Diagram Rank-Metric Codes is true: 12159543650778159104 with optimal [(0, 1, 2, 3, 4), (0, 1, 2, 5, 6), (0, 1, 2, 7, 8), (0, 1, 3, 5, 7), (0, 1, 3, 6, 8), (0, 1, 4, 5, 8), (0, 1, 4, 6, 7), (0, 2, 3, 5, 8), (0, 2, 3, 6, 7), (0, 2, 4, 5, 7), (0, 2, 4, 6, 8), (0, 3, 4, 5, 6), (0, 3, 4, 7, 8), (0, 5, 6, 7, 8), (1, 2, 3, 5, 9), (1, 2, 4, 6, 9), (1, 3, 4, 7, 9), (1, 5, 6, 7, 9), (2, 3, 4, 8, 9), (2, 5, 6, 8, 9), (3, 5, 7, 8, 9), (4, 6, 7, 8, 9)])
  ) : 12159543650778159104
• ef_computation ( show
  [(0, 1, 2, 3, 4), (0, 1, 2, 5, 6), (0, 1, 3, 5, 7), (0, 1, 3, 6, 8), (0, 3, 4, 5, 6), (0, 2, 4, 5, 7), (0, 1, 4, 6, 7), (0, 1, 4, 5, 8), (0, 1, 2, 7, 8), (0, 2, 3, 6, 7), (0, 2, 3, 5, 8), (1, 2, 3, 5, 9), (0, 2, 4, 6, 8), (1, 2, 4, 6, 9), (0, 3, 4, 7, 8), (2, 3, 4, 7, 9), (1, 3, 4, 8, 9), (1, 3, 6, 7, 9), (1, 4, 5, 7, 9), (2, 4, 5, 8, 9), (2, 3, 6, 8, 9), (0, 5, 6, 7, 8), (1, 5, 6, 8, 9), (2, 5, 6, 7, 9), (3, 5, 7, 8, 9), (4, 6, 7, 8, 9)]
  ) : 12159543650774039506
• two_pivot_block_construction ( ) : 12159518761675317248
• improved_linkage ( 5 ) : 12157665462544318444
• multicomponent ( ) : 12157665462543713203
• linkage_GLT ( 5 ) : 12157665459056928802
• LMRD ( ) : 12157665459056928801
• JohnsonLB ( ) : 1351080793742922656
• HKK_lemma_2_4_lower_bound ( ) : 1351063712808578880
• graham_sloane ( ) : 1879074357110506
• sphere_covering ( ) : 1670344887941592
• trivial_1 ( ) : 0

Upper bounds

• Ahlswede_Aydinian ( 0, 9 ) : 12326959735315999300
• ilp_1 ( 1 ) : 12326959735315999300
• ilp_4 ( 9 ) : 12326959735315999300
• improved_johnson ( ) : 12326959735315999300
• johnson_1 ( ) : 12326959735315999300
• johnson_2 ( ) : 12326959735315999300
• anticode ( ) : 12328630051958712010
• ilp_2 ( 4 ) : 12328630051958712010
• ilp_3 ( 6 ) : 12328630051958712010
• linear_programming_bound ( ) : 12328630051958712010
• singleton ( ) : 13869447829832637406
• all_subs ( ) : 818990894351617238824300
• sphere_packing ( ) : 818990894351617238824300

Bound for codes containing the lifted MRD code

Do you have better bounds?