Details for entry \(A_4(7,3)\)

Lower bounds

• cdc_average_argument ( ) : 131318
• echelon_ferrers ( show
  optimal [(), (0, 1, 2), (0, 1, 2, 3, 4, 5, 6), (0, 1, 3, 4), (0, 1, 5, 6), (0, 2, 3, 5), (0, 2, 4, 6), (0, 3, 6), (0, 4, 5), (1, 2, 3, 6), (1, 2, 4, 5), (1, 3, 5), (1, 4, 6), (2, 3, 4), (2, 5, 6), (3, 4, 5, 6)] (if conjecture about Ferrers Diagram Rank-Metric Codes is true: 70264 with optimal [(), (0, 1, 2), (0, 1, 2, 3, 4, 5, 6), (0, 1, 3, 4), (0, 1, 5, 6), (0, 2, 3, 5), (0, 2, 4, 6), (0, 3, 6), (0, 4, 5), (1, 2, 3, 6), (1, 2, 4, 5), (1, 3, 5), (1, 4, 6), (2, 3, 4), (2, 5, 6), (3, 4, 5, 6)])
  ) : 70264
• ef_computation ( show
  [(0, 1, 2), (0, 1, 3, 4), (0, 2, 3, 6), (0, 2, 4, 5), (1, 2, 3, 5), (2, 3, 4), (0, 3, 5), (0, 1, 5, 6), (1, 2, 4, 6), (1, 3, 6), (1, 4, 5), (0, 4, 6), (), (3, 4, 5, 6), (2, 5, 6), (0, 1, 2, 3, 4, 5, 6)]
  ) : 70264
• improved_cdc_lower_bound ( ) : 66830
• layer_construction ( ) : 66830
• cdc_lower_bound ( ) : 66828
• gilbert_varshamov ( ) : 6464
• trivial_4 ( ) : 2
• trivial_2 ( ) : 0

Upper bounds

• heinlein_ihringer_semidefinite_programming ( ) : 142313
• johnson_MDC_Lemma_5 ( ) : 143644
• Etzion_Vardy_ilp ( ) : 144060
• johnson_MDC_Lemma_4 ( ) : 144164
• Ahlswede_Aydinian_ilp ( ) : 144166
• improved_cdc_upper_bound ( ) : 144166
• cdc_upper_bound ( ) : 144168
• relax_d ( ) : 25704928
• trivial_3 ( ) : 51409856

Do you have better bounds?