Details for entry \(A_2(9,4;4)\)

Known codes

• 36945 EtzionSilberstein2009
• 34944 SilbersteinEtzion2011

Lower bounds

• pending_dots ( show
  optimal [(0, 1, 2, 3), (0, 1, 4, 5), (0, 1, 6, 7), (0, 2, 4, 6), (0, 2, 4, 8), (0, 2, 5, 6), (0, 2, 5, 7), (0, 3, 4, 6), (0, 3, 4, 7), (0, 3, 5, 7), (0, 3, 5, 8), (0, 3, 6, 8), (1, 2, 4, 7), (1, 2, 5, 8), (1, 3, 4, 8), (1, 3, 5, 6), (1, 3, 7, 8), (1, 4, 6, 8), (2, 3, 4, 5), (2, 3, 6, 7), (4, 5, 6, 7)] (if conjecture about Ferrers Diagram Rank-Metric Codes is true: 37265 with optimal [(0, 1, 2, 3), (0, 1, 4, 5), (0, 1, 6, 7), (0, 2, 4, 6), (0, 2, 4, 8), (0, 2, 5, 6), (0, 2, 5, 7), (0, 3, 4, 6), (0, 3, 4, 7), (0, 3, 5, 7), (0, 3, 5, 8), (0, 3, 6, 8), (1, 2, 4, 7), (1, 2, 5, 8), (1, 3, 4, 8), (1, 3, 5, 6), (1, 3, 7, 8), (1, 4, 6, 8), (2, 3, 4, 5), (2, 3, 6, 7), (4, 5, 6, 7)])
  ) : 37265
• echelon_ferrers ( show
  optimal [(0, 1, 2, 3), (0, 1, 4, 5), (0, 1, 6, 7), (0, 2, 4, 6), (0, 2, 5, 7), (0, 3, 4, 7), (0, 3, 5, 6), (1, 2, 4, 7), (1, 2, 5, 6), (1, 3, 4, 6), (1, 3, 5, 7), (2, 3, 4, 5), (2, 3, 6, 7), (4, 5, 6, 7)] (if conjecture about Ferrers Diagram Rank-Metric Codes is true: 36945 with optimal [(0, 1, 2, 3), (0, 1, 4, 5), (0, 1, 6, 7), (0, 2, 4, 6), (0, 2, 5, 7), (0, 3, 4, 7), (0, 3, 5, 6), (1, 2, 4, 7), (1, 2, 5, 6), (1, 3, 4, 6), (1, 3, 5, 7), (2, 3, 4, 5), (2, 3, 6, 7), (4, 5, 6, 7)])
  ) : 36945
• ef_computation ( show
  [(0, 1, 2, 3), (0, 1, 4, 5), (0, 2, 4, 6), (1, 3, 4, 6), (2, 3, 4, 5), (1, 2, 5, 6), (1, 2, 4, 7), (0, 2, 5, 7), (0, 1, 6, 7), (0, 3, 5, 6), (0, 3, 4, 7), (1, 3, 5, 7), (2, 3, 6, 8), (4, 5, 6, 7)]
  ) : 36945
• JohnsonLB ( ) : 35722
• JohnsonLB_special ( ) : 35722
• two_pivot_block_construction ( ) : 34944
• LiuChangFeng2019_Theo_2_6 ( ) : 33854
• CKMP2019_Cor_45 ( show
  (5,),(2,),(1,)
  ) : 33422
• CKMP2019_Cor_42 ( (4, 5) ) : 33294
• CKMP2019_Lem_41 ( (4, 5) ) : 33294
• generalized_linkage ( 4,0 ) : 33294
• generalized_linkage_multipleblocks ( show
  [4, 5],[0, 0]
  ) : 33294
• improved_linkage ( 4 ) : 33101
• multicomponent ( ) : 33025
• linkage_GLT ( 4 ) : 32769
• LMRD ( ) : 32768
• HKK_lemma_2_4_lower_bound ( ) : 11972
• graham_sloane ( ) : 6477
• ChenHeWengXu2019_T31 ( ) : 4621
• sphere_covering ( ) : 3556
• trivial_1 ( ) : 0

Upper bounds

• Ahlswede_Aydinian ( 0, 8, o ) : 50861
• ilp_1 ( 1 ) : 50861
• improved_johnson ( ) : 50861
• johnson_1 ( ) : 50861
• anticode ( ) : 52535
• ilp_2 ( 3 ) : 52535
• linear_programming_bound ( ) : 52535
• singleton ( ) : 97155
• ilp_3 ( 5 ) : 106766
• ilp_4 ( 6 ) : 106766
• johnson_2 ( ) : 106766
• all_subs ( ) : 3309747
• sphere_packing ( ) : 3309747

Bound for codes containing the lifted MRD code

Do you have better bounds?