Details for entry \(A_3(8,4)\)

Known codes

• 729 LMRD KoetterKschischang2008, Gabidulin1985 file

Lower bounds

• improved_cdc_lower_bound ( ) : 543144
• layer_construction ( ) : 543144
• cdc_lower_bound ( ) : 543142
• 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: 539580 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)])
  ) : 539580
• 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)]
  ) : 539580
• gilbert_varshamov ( ) : 992
• cdc_average_argument ( ) : 967
• trivial_4 ( ) : 2
• trivial_2 ( ) : 0

Upper bounds

• heinlein_ihringer_semidefinite_programming ( ) : 627384
• relax_d ( ) : 758228
• special_improved_cdc_upper_bound ( ) : 765770
• improved_cdc_upper_bound ( ) : 765772
• cdc_upper_bound ( ) : 765774
• trivial_3 ( ) : 127902864

Do you have better bounds?