Details for entry \(A_8(10,4;3)\)

Lower bounds

• EF_Kurz2020_linkage_special ( ) : 4407724867657
• generalized_linkage ( 7,0 ) : 4407724867657
• generalized_linkage_multipleblocks ( show
  [7, 3],[0, 0]
  ) : 4407724867657
• CKMP2019_Cor_42 ( (7, 3) ) : 4407724867585
• CKMP2019_Lem_41 ( (7, 3) ) : 4407724867585
• improved_linkage ( 7 ) : 4407724867585
• linkage_GLT ( 7 ) : 4407724867585
• linkage_ST ( 3 ) : 4407724867585
• construction_D ( 3 ) : 4407724867584
• construction_1 ( ) : 4399293117577
• construction_ST_A_1 ( ) : 4399293117577
• pending_dots ( show
  optimal [(0, 1, 2), (0, 3, 6), (0, 3, 8), (0, 3, 9), (0, 4, 6), (0, 4, 7), (0, 5, 7), (0, 6, 9), (0, 7, 9), (1, 3, 4), (1, 3, 5), (1, 3, 7), (1, 4, 5), (1, 4, 8), (1, 4, 9), (1, 5, 6), (1, 5, 8), (1, 5, 9), (1, 6, 7), (1, 6, 8), (1, 7, 8), (1, 8, 9)] (if conjecture about Ferrers Diagram Rank-Metric Codes is true: 4399293117577 with optimal [(0, 1, 2), (0, 3, 6), (0, 3, 8), (0, 3, 9), (0, 4, 6), (0, 4, 7), (0, 5, 7), (0, 6, 9), (0, 7, 9), (1, 3, 4), (1, 3, 5), (1, 3, 7), (1, 4, 5), (1, 4, 8), (1, 4, 9), (1, 5, 6), (1, 5, 8), (1, 5, 9), (1, 6, 7), (1, 6, 8), (1, 7, 8), (1, 8, 9)])
  ) : 4399293117577
• echelon_ferrers ( show
  optimal [(0, 1, 2), (0, 3, 4), (0, 5, 6), (0, 7, 8), (1, 3, 5), (1, 4, 6), (1, 7, 9), (2, 3, 6), (2, 4, 5), (2, 8, 9)] (if conjecture about Ferrers Diagram Rank-Metric Codes is true: 4399290384457 with optimal [(0, 1, 2), (0, 3, 4), (0, 5, 6), (0, 7, 8), (1, 3, 5), (1, 4, 6), (1, 7, 9), (2, 3, 6), (2, 4, 5), (2, 8, 9)])
  ) : 4399290384457
• ef_computation ( show
  [(0, 1, 2), (2, 3, 4), (1, 3, 5), (0, 4, 5), (0, 3, 6), (1, 4, 6), (2, 5, 6), (0, 7, 8), (5, 7, 9), (4, 8, 9)]
  ) : 4399290384457
• construction_ST_B_recursive ( ) : 4399137329272
• two_pivot_block_construction ( ) : 4399120515136
• multicomponent ( ) : 4399120515073
• construction_ST_B ( ) : 4399103991998
• JohnsonLB ( ) : 4398087170882
• LMRD ( ) : 4398046511104
• LiuChangFeng2019_Theo_2_6 ( ) : 4398046511104
• graham_sloane ( ) : 69946872385
• sphere_covering ( ) : 61323314213
• HKK_lemma_2_4_lower_bound ( ) : 136348168
• trivial_1 ( ) : 0

Upper bounds

• improved_johnson ( ) : 4476585153025
• Ahlswede_Aydinian ( 0, 9, o ) : 4476585153032
• ilp_1 ( 1 ) : 4476585153032
• johnson_1 ( ) : 4476585153032
• anticode ( ) : 4476600095297
• ilp_2 ( 2 ) : 4476600095297
• linear_programming_bound ( ) : 4476600095297
• singleton ( ) : 5106121684105
• ilp_4 ( 9 ) : 35812815704648
• johnson_2 ( ) : 35812815704648
• HKK_lemma_2_4_upper_bound ( ) : 2292578823803976
• ilp_3 ( 4 ) : 18340630590431809
• all_subs ( ) : 10729268895402608265
• sphere_packing ( ) : 10729268895402608265

Bound for codes containing the lifted MRD code

Do you have better bounds?