Details for entry \(A_8(6,2)\)

Known codes

• 156162843 optimal classified, number of isomorphism types: 1 HonoldKiermaierKurz20163

Exact bounds

• d2 ( ) : 156162843

Lower bounds

• echelon_ferrers ( show
  optimal [(0,), (0, 1, 2), (0, 1, 2, 3, 4), (0, 1, 2, 3, 5), (0, 1, 2, 4, 5), (0, 1, 3), (0, 1, 3, 4, 5), (0, 1, 4), (0, 1, 5), (0, 2, 3), (0, 2, 3, 4, 5), (0, 2, 4), (0, 2, 5), (0, 3, 4), (0, 3, 5), (0, 4, 5), (1,), (1, 2, 3), (1, 2, 3, 4, 5), (1, 2, 4), (1, 2, 5), (1, 3, 4), (1, 3, 5), (1, 4, 5), (2,), (2, 3, 4), (2, 3, 5), (2, 4, 5), (3,), (3, 4, 5), (4,), (5,)] (if conjecture about Ferrers Diagram Rank-Metric Codes is true: 156162843 with optimal [(0,), (0, 1, 2), (0, 1, 2, 3, 4), (0, 1, 2, 3, 5), (0, 1, 2, 4, 5), (0, 1, 3), (0, 1, 3, 4, 5), (0, 1, 4), (0, 1, 5), (0, 2, 3), (0, 2, 3, 4, 5), (0, 2, 4), (0, 2, 5), (0, 3, 4), (0, 3, 5), (0, 4, 5), (1,), (1, 2, 3), (1, 2, 3, 4, 5), (1, 2, 4), (1, 2, 5), (1, 3, 4), (1, 3, 5), (1, 4, 5), (2,), (2, 3, 4), (2, 3, 5), (2, 4, 5), (3,), (3, 4, 5), (4,), (5,)])
  ) : 156162843
• improved_cdc_lower_bound ( ) : 156162843
• layer_construction ( ) : 156162843
• cdc_lower_bound ( ) : 156087945
• gilbert_varshamov ( ) : 819189
• cdc_average_argument ( ) : 36930
• trivial_4 ( ) : 2
• trivial_2 ( ) : 0

Upper bounds

• special_improved_cdc_upper_bound ( ) : 195118125
• cdc_upper_bound ( ) : 195118127
• improved_cdc_upper_bound ( ) : 195118127
• relax_d ( ) : 195118127
• trivial_3 ( ) : 195118127

Do you have better bounds?