Details for entry \(A_5(10,3)\)

Lower bounds

• echelon_ferrers ( show
  optimal [(0, 1, 2, 3, 4), (0, 1, 2, 3, 4, 5, 6, 7, 8), (0, 1, 2, 3, 5, 7), (0, 1, 2, 4, 6, 7), (0, 1, 2, 5, 6), (0, 1, 2, 7, 9), (0, 1, 2, 8), (0, 1, 3, 4, 5, 7, 9), (0, 1, 3, 4, 8, 9), (0, 1, 3, 5, 8), (0, 1, 3, 6), (0, 1, 3, 6, 7, 8, 9), (0, 1, 4, 5), (0, 1, 4, 6, 8), (0, 1, 5, 6, 7, 8), (0, 2, 3, 4, 5, 6), (0, 2, 3, 4, 7, 9), (0, 2, 3, 5, 9), (0, 2, 3, 6, 7), (0, 2, 3, 6, 8, 9), (0, 2, 4, 5, 7), (0, 2, 4, 5, 8, 9), (0, 2, 4, 6, 9), (0, 2, 5, 6, 7, 8, 9), (0, 3, 4, 5, 6, 8, 9), (0, 3, 4, 7, 8), (0, 3, 5, 6, 7, 9), (0, 4, 6, 7, 8, 9), (0, 7), (1, 2, 3, 4, 5, 8), (1, 2, 3, 4, 6, 7, 9), (1, 2, 3, 5, 7, 8, 9), (1, 2, 3, 6, 8), (1, 2, 3, 9), (1, 2, 4, 5, 9), (1, 2, 4, 7, 8), (1, 2, 5, 6, 8, 9), (1, 3, 4, 5, 6), (1, 3, 4, 7), (1, 4, 5, 6, 7, 8, 9), (1, 4, 6, 9), (1, 5, 7), (2, 3, 4, 5, 6, 7, 8, 9), (2, 3, 4, 8, 9), (2, 3, 7, 8), (2, 4, 6, 8), (2, 5, 6, 7), (2, 5, 8), (3, 4, 5, 9), (3, 5, 6, 7, 8), (3, 6, 9), (4, 5, 7, 8), (4, 6, 7)] (if conjecture about Ferrers Diagram Rank-Metric Codes is true: 95568374169013 with optimal [(0, 1, 2, 3, 4), (0, 1, 2, 3, 4, 5, 6, 7, 8), (0, 1, 2, 3, 5, 7), (0, 1, 2, 4, 6, 7), (0, 1, 2, 5, 6), (0, 1, 2, 7, 9), (0, 1, 2, 8), (0, 1, 3, 4, 5, 7, 9), (0, 1, 3, 4, 8, 9), (0, 1, 3, 5, 8), (0, 1, 3, 6), (0, 1, 3, 6, 7, 8, 9), (0, 1, 4, 5), (0, 1, 4, 6, 8), (0, 1, 5, 6, 7, 8), (0, 2, 3, 4, 5, 6), (0, 2, 3, 4, 7, 9), (0, 2, 3, 5, 9), (0, 2, 3, 6, 7), (0, 2, 3, 6, 8, 9), (0, 2, 4, 5, 7), (0, 2, 4, 5, 8, 9), (0, 2, 4, 6, 9), (0, 2, 5, 6, 7, 8, 9), (0, 3, 4, 5, 6, 8, 9), (0, 3, 4, 7, 8), (0, 3, 5, 6, 7, 9), (0, 4, 6, 7, 8, 9), (0, 7), (1, 2, 3, 4, 5, 8), (1, 2, 3, 4, 6, 7, 9), (1, 2, 3, 5, 7, 8, 9), (1, 2, 3, 6, 8), (1, 2, 3, 9), (1, 2, 4, 5, 9), (1, 2, 4, 7, 8), (1, 2, 5, 6, 8, 9), (1, 3, 4, 5, 6), (1, 3, 4, 7), (1, 4, 5, 6, 7, 8, 9), (1, 4, 6, 9), (1, 5, 7), (2, 3, 4, 5, 6, 7, 8, 9), (2, 3, 4, 8, 9), (2, 3, 7, 8), (2, 4, 6, 8), (2, 5, 6, 7), (2, 5, 8), (3, 4, 5, 9), (3, 5, 6, 7, 8), (3, 6, 9), (4, 5, 7, 8), (4, 6, 7)])
  ) : 95568374169013
• ef_computation ( show
  [(0, 1, 2, 3, 4), (0, 1, 2, 5, 6), (0, 1, 3, 5), (0, 1, 2, 7), (0, 1, 2, 4, 5, 9), (0, 2, 3, 4, 5, 6), (0, 1, 4, 6), (0, 1, 4, 5, 7), (1, 2, 3, 6), (0, 2, 3, 5, 7), (0, 1, 3, 6, 7), (0, 1, 2, 3, 8, 9), (1, 2, 3, 5, 8), (0, 2, 4, 6, 7), (0, 2, 4, 5, 8), (1, 3, 4, 5, 6), (0, 2, 3, 6, 8), (1, 2, 3, 4, 5, 7), (1, 2, 4, 8), (0, 1, 3, 4, 7, 9), (0, 3, 4, 5, 9), (1, 2, 4, 6, 9), (1, 2, 3, 7, 9), (0, 3, 4, 8), (2, 3, 4, 9), (0, 1, 8), (0, 1, 2, 4, 7, 8, 9), (1, 3, 4, 7, 8), (0, 2, 3, 6, 7, 9), (0, 1, 5, 6, 7, 9), (1, 2, 6, 7, 8), (2, 3, 7, 8), (2, 5, 6, 7), (3, 4, 6, 7), (0, 2, 9), (2, 3, 5, 6, 9), (0, 1, 3, 4, 6, 8, 9), (0, 2, 4, 6, 8, 9), (0, 1, 3, 5, 7, 8, 9), (1, 3, 4, 5, 8, 9), (1, 5, 6, 8), (0, 1, 2, 3, 4, 6, 7, 8), (2, 4, 5, 7, 9), (1, 2, 5, 7, 8, 9), (0, 3, 5, 6, 8, 9), (4, 5), (0, 5, 7, 8), (4, 6, 8), (3, 5, 7, 9), (1, 5, 9), (0, 2, 5, 6, 7, 8, 9), (1, 3, 6, 7, 8, 9), (0, 3, 4, 5, 6, 7, 8), (0, 2, 3, 4, 5, 7, 8, 9), (1, 4, 5, 6, 7, 8, 9), (3, 8, 9), (4, 7, 8, 9), 7, (2, 3, 4, 6, 7, 8, 9), (6, 9), (0, 1, 2, 3, 4, 5, 6, 7, 9)]
  ) : 95565751172337
• improved_cdc_lower_bound ( ) : 95563832090177
• layer_construction ( ) : 95563832090177
• cdc_lower_bound ( ) : 95563831276375
• cdc_average_argument ( ) : 22931475630879
• gilbert_varshamov ( ) : 168961356489
• trivial_4 ( ) : 2
• trivial_2 ( ) : 0

Upper bounds

• heinlein_ihringer_semidefinite_programming ( ) : 108238287449582
• special_improved_cdc_upper_bound ( ) : 108241749890132
• improved_cdc_upper_bound ( ) : 108241749890134
• cdc_upper_bound ( ) : 108241749890136
• relax_d ( ) : 393153256760148480
• trivial_3 ( ) : 549874114073747456

Do you have better bounds?