Details for entry \(A_5(10,4)\)

Lower bounds

• improved_cdc_lower_bound ( ) : 95563831276377
• layer_construction ( ) : 95563831276377
• cdc_lower_bound ( ) : 95563831276375
• echelon_ferrers ( show
  optimal [(0, 1, 2, 3, 4), (0, 1, 2, 5, 6), (0, 1, 2, 7, 8), (0, 1, 3, 5, 7), (0, 1, 3, 6, 8), (0, 1, 4, 5, 8), (0, 1, 4, 6, 7), (0, 1, 9), (0, 2, 3, 4, 5, 6, 7, 8, 9), (0, 2, 3, 5, 8), (0, 2, 3, 6, 7), (0, 2, 4, 5, 7), (0, 2, 4, 6, 8), (0, 3, 4, 5, 6), (0, 3, 4, 7, 8), (0, 5, 6, 7, 8), (1, 2, 3, 4, 5, 6, 7), (1, 2, 3, 5, 9), (1, 2, 3, 6, 7, 8, 9), (1, 2, 4, 5, 7, 8, 9), (1, 2, 4, 6, 9), (1, 3, 4, 5, 6, 8, 9), (1, 3, 4, 7, 9), (1, 5, 6, 7, 9), (2, 3, 4, 8, 9), (2, 5, 6, 8, 9), (2, 7, 9), (3, 5, 7, 8, 9), (3, 6, 9), (4, 5, 9), (4, 6, 7, 8, 9), (8,)] (if conjecture about Ferrers Diagram Rank-Metric Codes is true: 95528137360468 with optimal [(0, 1, 2, 3, 4), (0, 1, 2, 5, 6), (0, 1, 2, 7, 8), (0, 1, 3, 5, 7), (0, 1, 3, 6, 8), (0, 1, 4, 5, 8), (0, 1, 4, 6, 7), (0, 1, 9), (0, 2, 3, 4, 5, 6, 7, 8, 9), (0, 2, 3, 5, 8), (0, 2, 3, 6, 7), (0, 2, 4, 5, 7), (0, 2, 4, 6, 8), (0, 3, 4, 5, 6), (0, 3, 4, 7, 8), (0, 5, 6, 7, 8), (1, 2, 3, 4, 5, 6, 7), (1, 2, 3, 5, 9), (1, 2, 3, 6, 7, 8, 9), (1, 2, 4, 5, 7, 8, 9), (1, 2, 4, 6, 9), (1, 3, 4, 5, 6, 8, 9), (1, 3, 4, 7, 9), (1, 5, 6, 7, 9), (2, 3, 4, 8, 9), (2, 5, 6, 8, 9), (2, 7, 9), (3, 5, 7, 8, 9), (3, 6, 9), (4, 5, 9), (4, 6, 7, 8, 9), (8,)])
  ) : 95528137360468
• ef_computation ( show
  [(0, 1, 2, 3, 4), (0, 1, 2, 5, 6), (0, 1, 3, 5, 7), (0, 1, 3, 6, 8), (0, 2, 3, 6, 7), (0, 2, 3, 5, 8), (0, 3, 4, 5, 6), (0, 1, 2, 7, 8), (0, 1, 4, 6, 7), (0, 1, 4, 5, 8), (0, 2, 4, 5, 7), (1, 2, 3, 5, 9), (0, 2, 4, 6, 8), (1, 2, 4, 6, 9), (0, 3, 4, 7, 8), (1, 2, 3, 4, 5, 6, 7), (0, 1, 9), (1, 3, 4, 7, 9), (2, 3, 4, 8, 9), (0, 5, 6, 7, 8), (1, 5, 6, 7, 9), (1, 2, 3, 6, 7, 8, 9), (4, 5, 9), (2, 5, 6, 8, 9), (3, 6, 9), (1, 2, 4, 5, 7, 8, 9), (2, 7, 9), (1, 3, 4, 5, 6, 8, 9), (3, 5, 7, 8, 9), (0, 2, 3, 4, 5, 6, 7, 8, 9), 8, (4, 6, 7, 8, 9)]
  ) : 95528137360468
• cdc_average_argument ( ) : 1464688432
• gilbert_varshamov ( ) : 465998264
• trivial_4 ( ) : 2
• trivial_2 ( ) : 0

Upper bounds

• heinlein_ihringer_semidefinite_programming ( ) : 100215014898311
• relax_d ( ) : 108238287449582
• special_improved_cdc_upper_bound ( ) : 108241749890132
• improved_cdc_upper_bound ( ) : 108241749890134
• cdc_upper_bound ( ) : 108241749890136
• trivial_3 ( ) : 549874114073747456

Do you have better bounds?