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

Known codes

• 4096 LMRD KoetterKschischang2008, Gabidulin1985 file
• 128 LMRD KoetterKschischang2008, Gabidulin1985 file

Lower bounds

• improved_cdc_lower_bound ( ) : 37267
• layer_construction ( ) : 37267
• cdc_lower_bound ( ) : 37265
• 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: 36947 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)])
  ) : 36947
• ef_computation ( show
  [(0, 1, 2, 3), (0, 1, 4, 5), (0, 2, 4, 6), (1, 2, 5, 6), (2, 3, 4, 5), (1, 2, 4, 7), (1, 3, 4, 6), (0, 3, 5, 6), (0, 3, 4, 7), (0, 2, 5, 7), (0, 1, 6, 7), (1, 3, 5, 7), (2, 3, 6, 8), (5, 8), (2, 4, 5, 6, 7, 8), (0, 1, 3, 4, 5, 6, 7, 8)]
  ) : 36947
• cdc_average_argument ( ) : 1996
• gilbert_varshamov ( ) : 492
• trivial_4 ( ) : 2
• trivial_2 ( ) : 0

Upper bounds

• heinlein_ihringer_semidefinite_programming ( ) : 53710
• relax_d ( ) : 107419
• improved_cdc_upper_bound ( ) : 114472
• cdc_upper_bound ( ) : 114474
• trivial_3 ( ) : 8283458

Do you have better bounds?