# Details for entry $$A_3(8,4;4)$$

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## Lower bounds

• CossidentePavese14_theorem43 ( ) : 543142
• construction_3 ( ) : 543142
• coset_construction ( ) : 543142
• CossidentePavese14_theorem38 ( ) : 542422
• echelon_ferrers (
optimal [(0, 1, 2, 3), (0, 1, 4, 5), (0, 1, 6, 7), (0, 2, 4, 6), (0, 2, 5, 7), (0, 3, 4, 7), (0, 3, 5, 6), (1, 2, 4, 7), (1, 2, 5, 6), (1, 3, 4, 6), (1, 3, 5, 7), (2, 3, 4, 5), (2, 3, 6, 7), (4, 5, 6, 7)] (if conjecture about Ferrers Diagram Rank-Metric Codes is true: 539578 with optimal [(0, 1, 2, 3), (0, 1, 4, 5), (0, 1, 6, 7), (0, 2, 4, 6), (0, 2, 5, 7), (0, 3, 4, 7), (0, 3, 5, 6), (1, 2, 4, 7), (1, 2, 5, 6), (1, 3, 4, 6), (1, 3, 5, 7), (2, 3, 4, 5), (2, 3, 6, 7), (4, 5, 6, 7)])
) : 539578
• ef_computation (
[(0, 1, 2, 3), (0, 1, 4, 5), (0, 2, 4, 6), (1, 2, 4, 7), (2, 3, 4, 5), (0, 2, 5, 7), (0, 1, 6, 7), (1, 2, 5, 6), (1, 3, 4, 6), (0, 3, 5, 6), (0, 3, 4, 7), (1, 3, 5, 7), (2, 3, 6, 7), (4, 5, 6, 7)]
) : 539578
• pending_dots (
optimal [(0, 1, 2, 3), (0, 1, 4, 5), (0, 1, 6, 7), (0, 2, 4, 6), (0, 2, 5, 7), (0, 3, 4, 7), (0, 3, 5, 6), (1, 2, 4, 7), (1, 2, 5, 6), (1, 3, 4, 6), (1, 3, 5, 7), (2, 3, 4, 5), (2, 3, 6, 7), (4, 5, 6, 7)] (if conjecture about Ferrers Diagram Rank-Metric Codes is true: 539578 with optimal [(0, 1, 2, 3), (0, 1, 4, 5), (0, 1, 6, 7), (0, 2, 4, 6), (0, 2, 5, 7), (0, 3, 4, 7), (0, 3, 5, 6), (1, 2, 4, 7), (1, 2, 5, 6), (1, 3, 4, 6), (1, 3, 5, 7), (2, 3, 4, 5), (2, 3, 6, 7), (4, 5, 6, 7)])
) : 539578
• two_pivot_block_construction ( ) : 538083
• improved_linkage ( 4 ) : 531532
• multicomponent ( ) : 531523
• linkage_GLT ( 4 ) : 531442
• LMRD ( ) : 531441
• HKK_lemma_2_4_lower_bound ( ) : 180777
• graham_sloane ( ) : 23145
• sphere_covering ( ) : 15812
• coset_construction_parallelism_part (
[(11700, '(2,2), 4: 11700')]
) : 11700
• trivial_1 ( ) : 0

## Bound for codes containing the lifted MRD code

(see EtzionSilberstein2012 and Heinlein2018 for details)
543142

## Do you have better bounds?

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