Details for entry \(A_2(8,6;3)\)

Known codes

• 34 optimal The file contains 1 maximum code with hole space dimension 7, 224 nonisomorphic maximum codes with hole space dimension 8, and 399 nonisomorphic maximum codes with hole space dimension 6. All of these codes have trivial automorphism group. ElZanatiJordonSeelingerSissokhoSpence2010, HonoldKiermaierKurz20162 file
• 32 LMRD KoetterKschischang2008, Gabidulin1985 file

Exact bounds

• partial_spread_1 ( ) : 34

Lower bounds

• CKMP2019_Cor_42 ( (3, 5) ) : 33
• CKMP2019_Lem_41 ( (3, 5) ) : 33
• ef_computation ( show
  [(0, 1, 2), (3, 4, 6)]
  ) : 33
• generalized_linkage ( 3,0 ) : 33
• generalized_linkage_multipleblocks ( show
  [3, 5],[0, 0]
  ) : 33
• improved_linkage ( 3 ) : 33
• multicomponent ( ) : 33
• partial_spread_3 ( ) : 33
• pending_dots ( show
  optimal [(0, 1, 2), (3, 4, 5)] (if conjecture about Ferrers Diagram Rank-Metric Codes is true: 33 with optimal [(0, 1, 2), (3, 4, 5)])
  ) : 33
• LiuChangFeng2019_Theo_2_6 ( ) : 32
• JohnsonLB ( ) : 31
• sphere_covering ( ) : 6
• HKK_lemma_2_4_lower_bound ( ) : 2
• graham_sloane ( ) : 2

Upper bounds

• DrakeFreeman ( ) : 34
• partial_spread_HKK16_T10 ( 2 ) : 34
• partial_spread_NS_2_Theorem6 ( ) : 34
• partial_spread_NS_2_Theorem7 ( ) : 34
• partial_spread_NS_upper_bound ( ) : 34
• partial_spread_kurz16_28 ( ) : 34
• improved_johnson ( ) : 35
• partial_spread_5 ( ) : 35
• Ahlswede_Aydinian ( 2, 1 ) : 36
• XiaFuJohnson1 ( ) : 36
• ilp_2 ( 1 ) : 36
• linear_programming_bound ( ) : 36
• spread_bound ( ) : 36
• HKK_lemma_2_4_upper_bound ( ) : 128

Bound for codes containing the lifted MRD code

(see EtzionSilberstein2012, Heinlein2018, and Kurz2019 for details)
33

Do you have better bounds?