Details for entry \(A_2(18,10;8)\)

Lower bounds

• ef_computation ( show
  [(0, 1, 2, 3, 4, 5, 6, 7), (0, 2, 4, 8, 9, 10, 11, 12), (1, 3, 5, 8, 9, 10, 13, 15), (1, 3, 6, 8, 11, 12, 14, 16), (2, 6, 7, 8, 9, 13, 14, 17), (4, 5, 6, 10, 11, 13, 16, 17), (0, 5, 7, 9, 11, 14, 15, 16), (3, 4, 7, 10, 12, 14, 15, 17), (0, 1, 2, 12, 13, 15, 16, 17)] (if conjecture about Ferrers Diagram Rank-Metric Codes is true: 1099512709961)
  ) : 1099511761137
• greedy_multicomponent ( show
  [(0, 1, 2, 3, 4, 5, 6, 7), (0, 1, 2, 8, 9, 10, 11, 12), (3, 4, 5, 8, 9, 10, 13, 14), (3, 6, 7, 8, 9, 11, 15, 16), (0, 4, 5, 8, 12, 15, 16, 17), (1, 6, 7, 8, 12, 13, 14, 17), (0, 2, 3, 11, 13, 14, 15, 17)]
  ) : 1099511759433
• generalized_linkage ( 8,3 ) : 1099511628033
• generalized_linkage_multipleblocks ( show
  [8, 10],[0, 3]
  ) : 1099511628033
• improved_linkage ( 8 ) : 1099511628033
• multicomponent ( ) : 1099511628033
• CKMP2019_Cor_42 ( (8, 10) ) : 1099511627777
• CKMP2019_Lem_41 ( (8, 10) ) : 1099511627777
• LiuChangFeng2019_Theo_2_6 ( ) : 1099511627777
• LMRD ( ) : 1099511627776
• JohnsonLB ( ) : 1097366269935
• HKK_lemma_2_4_lower_bound ( ) : 17180000466
• sphere_covering ( ) : 5887908
• graham_sloane ( ) : 883

Upper bounds

• improved_johnson ( ) : 1166561566097
• Ahlswede_Aydinian ( 0, 17, o ) : 1166561566100
• linear_programming_bound ( ) : 1166564398383
• HKK_lemma_2_4_upper_bound ( ) : 18435537426946

Bound for codes containing the lifted MRD code

Do you have better bounds?