Details for entry \(A_7(9,3)\)

Lower bounds

• cdc_average_argument ( ) : 9499249784669
• ef_computation ( show
  [(0, 1, 2, 3), (0, 1, 2, 4, 5), (0, 1, 3, 4, 6), (1, 3, 4, 5), (0, 2, 3, 5, 6), (0, 1, 3, 5, 7), (0, 2, 3, 4, 8), (0, 1, 5, 6), (0, 2, 4, 6), (0, 1, 4, 7), (0, 1, 2, 6, 8), (1, 2, 3, 4, 7), (1, 2, 5, 7), (1, 2, 4, 8), (1, 2, 3, 5, 8), (0, 2, 3, 4, 5, 7), (0, 2, 7), (0, 2, 5, 8), (0, 3, 6, 7), (2, 3, 6, 8), (4, 5, 6), (1, 3, 7, 8), (0, 1, 4, 5, 6, 7, 8), (0, 3, 4, 5, 6, 8), (1, 6, 7), (2, 4, 5, 7, 8), (3, 4, 6, 7, 8), (1, 2, 3, 4, 5, 6, 7, 8), 3, (5, 6, 7, 8)]
  ) : 4846759284378
• echelon_ferrers ( show
  optimal [(), (0, 1, 2, 3, 4), (0, 1, 2, 3, 4, 5, 6, 7, 8), (0, 1, 2, 5), (0, 1, 2, 6, 8), (0, 1, 3, 5, 7), (0, 1, 3, 6), (0, 1, 4, 5, 6), (0, 1, 4, 7), (0, 2, 3, 4, 5, 7), (0, 2, 3, 5, 6), (0, 2, 3, 8), (0, 2, 4, 5, 8), (0, 2, 4, 6), (0, 2, 7), (0, 3, 4, 5, 6, 8), (0, 4, 6, 7, 8), (0, 5, 6, 7), (1, 2, 3, 5, 8), (1, 2, 3, 7), (1, 2, 4, 5, 7), (1, 2, 4, 8), (1, 3, 4, 5), (1, 3, 4, 7, 8), (1, 4, 5, 6, 7, 8), (1, 6, 7), (2, 3, 6, 7, 8), (2, 5, 6, 8), (3, 4, 6), (3, 5, 7, 8)] (if conjecture about Ferrers Diagram Rank-Metric Codes is true: 4846759284090 with optimal [(), (0, 1, 2, 3, 4), (0, 1, 2, 3, 4, 5, 6, 7, 8), (0, 1, 2, 5), (0, 1, 2, 6, 8), (0, 1, 3, 5, 7), (0, 1, 3, 6), (0, 1, 4, 5, 6), (0, 1, 4, 7), (0, 2, 3, 4, 5, 7), (0, 2, 3, 5, 6), (0, 2, 3, 8), (0, 2, 4, 5, 8), (0, 2, 4, 6), (0, 2, 7), (0, 3, 4, 5, 6, 8), (0, 4, 6, 7, 8), (0, 5, 6, 7), (1, 2, 3, 5, 8), (1, 2, 3, 7), (1, 2, 4, 5, 7), (1, 2, 4, 8), (1, 3, 4, 5), (1, 3, 4, 7, 8), (1, 4, 5, 6, 7, 8), (1, 6, 7), (2, 3, 6, 7, 8), (2, 5, 6, 8), (3, 4, 6), (3, 5, 7, 8)])
  ) : 4846759284090
• improved_cdc_lower_bound ( ) : 4749625733030
• layer_construction ( ) : 4749625733030
• cdc_lower_bound ( ) : 4749624892335
• gilbert_varshamov ( ) : 23945970858
• trivial_4 ( ) : 2
• trivial_2 ( ) : 0

Upper bounds

• heinlein_ihringer_semidefinite_programming ( ) : 9728400942608
• improved_cdc_upper_bound ( ) : 9750188344702
• cdc_upper_bound ( ) : 9750188344704
• relax_d ( ) : 97292877050623504
• trivial_3 ( ) : 194585754101247008

Do you have better bounds?