# Details for entry $$A_8(10,6;4)$$

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## lower bounds

• ef_computation (
[(0, 1, 2, 3), (0, 4, 5, 6), (1, 4, 7, 8), (2, 5, 7, 9), (3, 6, 8, 9)]
) : 68719738953
• echelon_ferrers (
optimal [(0, 1, 2, 3), (0, 5, 8, 9), (1, 6, 7, 8), (2, 4, 5, 6), (3, 4, 7, 9)] (if conjecture about Ferrers Diagram Rank-Metric Codes is true: 68719738953 with optimal [(0, 1, 2, 3), (0, 4, 5, 6), (1, 5, 7, 9), (2, 6, 8, 9), (3, 4, 7, 8)])
) : 68719509514
• pending_dots (
optimal [(0, 1, 2, 3), (0, 6, 7, 8), (1, 5, 8, 9), (2, 4, 5, 6), (3, 4, 7, 9)] (if conjecture about Ferrers Diagram Rank-Metric Codes is true: 68719738953 with optimal [(0, 1, 2, 3), (0, 4, 7, 8), (1, 4, 5, 6), (2, 5, 7, 9), (3, 6, 8, 9)])
) : 68719509514
• improved_linkage ( 4 ) : 68719480833
• multicomponent ( ) : 68719480833
• linkage_GLT ( 4 ) : 68719476737
• lin_poly ( ) : 68719476736
• sphere_covering ( ) : 14514872
• graham_sloane ( ) : 33362
• trivial_1 ( ) : 0

## bound for codes containing the lifted MRD code

(see EtzionSilberstein2012 and Heinlein2017 for details)
68719743553

## Do you have better bounds?

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