Details for entry \(A_2(8,4)\)

Known codes

• 4096 LMRD KoetterKschischang2008, Gabidulin1985 file
• 1024 LMRD KoetterKschischang2008, Gabidulin1985 file
• 64 LMRD KoetterKschischang2008, Gabidulin1985 file

Lower bounds

• improved_cdc_lower_bound ( ) : 4803
• layer_construction ( ) : 4803
• cdc_lower_bound ( ) : 4801
• echelon_ferrers ( show
  optimal [(), (0, 1, 2, 3), (0, 1, 2, 3, 4, 5, 6, 7), (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: 4575 with optimal [(), (0, 1, 2, 3), (0, 1, 2, 3, 4, 5, 6, 7), (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)])
  ) : 4575
• ef_computation ( show
  [(0, 1, 2, 3), (0, 1, 4, 5), (0, 2, 4, 6), (1, 2, 4, 7), (0, 3, 5, 6), (1, 2, 5, 6), (0, 3, 4, 7), (0, 1, 6, 7), (1, 3, 4, 6), (0, 2, 5, 7), (2, 3, 4, 5), (1, 3, 5, 7), (2, 3, 6, 7), (), (4, 5, 6, 7), (0, 1, 2, 3, 4, 5, 6, 7)]
  ) : 4575
• cdc_average_argument ( ) : 93
• gilbert_varshamov ( ) : 74
• trivial_4 ( ) : 2
• trivial_2 ( ) : 0

Upper bounds

• heinlein_ihringer_semidefinite_programming ( ) : 6479
• special_cases_upper_notderived_2 ( ) : 6479
• johnson_MDC_Lemma_6 ( ) : 6596
• relax_d ( ) : 9191
• special_improved_cdc_upper_bound ( ) : 9633
• improved_cdc_upper_bound ( ) : 9635
• cdc_upper_bound ( ) : 9637
• trivial_3 ( ) : 417199

Do you have better bounds?