Details for entry \(A_5(8,3)\)

Lower bounds

• echelon_ferrers ( show
  optimal [(), (0, 1, 2, 3), (0, 1, 2, 4, 7), (0, 1, 3, 5, 7), (0, 1, 4, 5), (0, 1, 6), (0, 2, 3, 4, 5), (0, 2, 4, 6), (0, 2, 5, 7), (0, 3, 4, 7), (0, 3, 5, 6), (1, 2, 5), (1, 2, 6, 7), (1, 3, 4), (1, 4, 5, 6, 7), (2, 3, 4, 5, 6, 7), (2, 3, 6)] (if conjecture about Ferrers Diagram Rank-Metric Codes is true: 244693253 with optimal [(), (0, 1, 2, 3), (0, 1, 2, 4, 7), (0, 1, 3, 5, 7), (0, 1, 4, 5), (0, 1, 6), (0, 2, 3, 4, 5), (0, 2, 4, 6), (0, 2, 5, 7), (0, 3, 4, 7), (0, 3, 5, 6), (1, 2, 5), (1, 2, 6, 7), (1, 3, 4), (1, 4, 5, 6, 7), (2, 3, 4, 5, 6, 7), (2, 3, 6)])
  ) : 244693253
• ef_computation ( show
  [(0, 1, 2, 3), (0, 1, 4, 5), (0, 1, 2, 4, 7), (1, 2, 5), (0, 2, 3, 4, 5), (0, 1, 6), (0, 2, 4, 6), (1, 3, 4), (0, 1, 3, 5, 7), (0, 2, 3, 6, 7), (0, 3, 5, 6), (0, 3, 4, 7), (0, 2, 5, 7), (1, 2, 6, 7), (3, 4, 5, 6, 7), (), (1, 2, 3, 4, 5, 7)]
  ) : 244693253
• improved_cdc_lower_bound ( ) : 244664528
• layer_construction ( ) : 244664528
• cdc_lower_bound ( ) : 244664526
• cdc_average_argument ( ) : 58664362
• gilbert_varshamov ( ) : 2162694
• trivial_4 ( ) : 2
• trivial_2 ( ) : 0

Upper bounds

• johnson_MDC_Proposition_5 ( ) : 276861484
• heinlein_ihringer_semidefinite_programming ( ) : 277100135
• special_improved_cdc_upper_bound ( ) : 277269630
• improved_cdc_upper_bound ( ) : 277269632
• cdc_upper_bound ( ) : 277269634
• relax_d ( ) : 201161057920
• trivial_3 ( ) : 281268665344

Do you have better bounds?