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

Known codes

• 5687 extension of (8,4801,4;4)_2 file

Lower bounds

• echelon_ferrers ( show
  optimal [(0, 1, 2, 3), (0, 1, 2, 4, 7), (0, 1, 3, 5, 7), (0, 1, 4, 5), (0, 1, 6), (0, 2, 3, 4, 5), (0, 2, 3, 6, 7), (0, 2, 4, 6), (0, 2, 5, 7), (0, 3, 4, 7), (0, 3, 5, 6), (1, 2, 3, 4, 5, 6), (1, 2, 5), (1, 2, 6, 7), (1, 3, 4), (3, 4, 5, 6, 7), (7,)] (if conjecture about Ferrers Diagram Rank-Metric Codes is true: 4907 with optimal [(0, 1, 2, 3), (0, 1, 2, 4, 7), (0, 1, 3, 5, 7), (0, 1, 4, 5), (0, 1, 6), (0, 2, 3, 4, 5), (0, 2, 3, 6, 7), (0, 2, 4, 6), (0, 2, 5, 7), (0, 3, 4, 7), (0, 3, 5, 6), (1, 2, 3, 4, 5, 6), (1, 2, 5), (1, 2, 6, 7), (1, 3, 4), (3, 4, 5, 6, 7), (7,)])
  ) : 4907
• ef_computation ( show
  [(0, 1, 2, 3), (0, 1, 4, 5), (0, 1, 2, 4, 7), (1, 2, 5), (0, 2, 3, 4, 5), (0, 1, 6), (0, 2, 4, 6), (1, 3, 4), (0, 1, 3, 5, 7), (0, 2, 3, 6, 7), (0, 3, 5, 6), (0, 3, 4, 7), (0, 2, 5, 7), (1, 2, 6, 7), (3, 4, 5, 6, 7), (), (1, 2, 3, 4, 5, 7)]
  ) : 4907
• improved_cdc_lower_bound ( ) : 4803
• layer_construction ( ) : 4803
• cdc_lower_bound ( ) : 4801
• cdc_average_argument ( ) : 3355
• gilbert_varshamov ( ) : 672
• trivial_4 ( ) : 2
• trivial_2 ( ) : 0

Upper bounds

• heinlein_ihringer_semidefinite_programming ( ) : 9191
• johnson_MDC_Proposition_5 ( ) : 9260
• semidefinite_programming ( ) : 9268
• Etzion_Vardy_ilp ( ) : 9365
• special_improved_cdc_upper_bound ( ) : 9633
• Ahlswede_Aydinian_ilp ( ) : 9635
• improved_cdc_upper_bound ( ) : 9635
• cdc_upper_bound ( ) : 9637
• relax_d ( ) : 222379
• trivial_3 ( ) : 417199

Do you have better bounds?