# Details for entry $$A_4(10,4;4)$$

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## Lower bounds

• pending_dots (
optimal [(0, 1, 2, 3), (0, 1, 4, 5), (0, 1, 6, 7), (0, 1, 8, 9), (0, 2, 4, 6), (0, 2, 4, 7), (0, 2, 4, 9), (0, 2, 5, 7), (0, 2, 5, 8), (0, 2, 5, 9), (0, 2, 6, 8), (0, 2, 6, 9), (0, 2, 7, 8), (0, 3, 4, 8), (0, 3, 4, 9), (0, 3, 5, 6), (0, 3, 5, 9), (0, 3, 6, 8), (0, 3, 7, 8), (0, 3, 7, 9), (0, 4, 6, 8), (0, 4, 7, 8), (0, 4, 7, 9), (0, 5, 6, 8), (0, 5, 6, 9), (0, 5, 7, 8), (0, 5, 7, 9), (1, 2, 4, 8), (1, 2, 5, 6), (1, 2, 7, 9), (1, 3, 4, 6), (1, 3, 4, 7), (1, 3, 5, 7), (1, 3, 5, 8), (1, 3, 6, 9), (1, 4, 6, 9), (2, 3, 4, 5), (2, 3, 6, 7), (2, 3, 8, 9), (4, 5, 6, 7), (4, 5, 8, 9), (6, 7, 8, 9)] (if conjecture about Ferrers Diagram Rank-Metric Codes is true: 69040760145 with optimal [(0, 1, 2, 3), (0, 1, 4, 5), (0, 1, 6, 7), (0, 1, 8, 9), (0, 2, 4, 6), (0, 2, 4, 7), (0, 2, 4, 9), (0, 2, 5, 7), (0, 2, 5, 8), (0, 2, 5, 9), (0, 2, 6, 8), (0, 2, 6, 9), (0, 2, 7, 8), (0, 3, 4, 8), (0, 3, 4, 9), (0, 3, 5, 6), (0, 3, 5, 9), (0, 3, 6, 8), (0, 3, 7, 8), (0, 3, 7, 9), (0, 4, 6, 8), (0, 4, 7, 8), (0, 4, 7, 9), (0, 5, 6, 8), (0, 5, 6, 9), (0, 5, 7, 8), (0, 5, 7, 9), (1, 2, 4, 8), (1, 2, 5, 6), (1, 2, 7, 9), (1, 3, 4, 6), (1, 3, 4, 7), (1, 3, 5, 7), (1, 3, 5, 8), (1, 3, 6, 9), (1, 4, 6, 9), (2, 3, 4, 5), (2, 3, 6, 7), (2, 3, 8, 9), (4, 5, 6, 7), (4, 5, 8, 9), (6, 7, 8, 9)])
) : 69040760145
• ef_computation (
[(0, 1, 2, 3), (0, 1, 4, 5), (1, 2, 4, 6), (2, 3, 4, 5), (0, 3, 4, 6), (0, 2, 5, 6), (0, 2, 4, 7), (1, 3, 4, 7), (0, 1, 6, 7), (1, 2, 5, 7), (1, 3, 5, 6), (0, 3, 5, 7), (2, 3, 6, 7), (0, 1, 8, 9), (2, 3, 8, 9), (4, 5, 6, 7), (4, 5, 8, 9), (6, 7, 8, 9)]
) : 69038576145
• JohnsonLB ( ) : 69008974824
• LiuChangFeng2019_Theo_3_12 ( ) : 69006151324
• construction_ST_B_recursive ( ) : 69005808145
• two_pivot_block_construction ( ) : 68988964864
• LiuChangFeng2019_Theo_3_14 ( ) : 68988960768
• CKMP2019_Cor_45 (
(6,),(2,),(1,)
) : 68744395100
• CKMP2019_Cor_42 ( (4, 6) ) : 68744329564
• CKMP2019_Lem_41 ( (4, 6) ) : 68744329564
• generalized_linkage ( 4,0 ) : 68744329564
• generalized_linkage_multipleblocks (
[4, 6],[0, 0]
) : 68744329564
• improved_linkage ( 4 ) : 68736351057
• multicomponent ( ) : 68736254209
• LiuChangFeng2019_Theo_2_6 ( ) : 68720938652
• ChenHeWengXu2019_T31 ( ) : 4319819851
• graham_sloane ( ) : 1167973560
• HKK_lemma_2_4_lower_bound ( ) : 1094910036
• sphere_covering ( ) : 879627406
• coset_construction_parallelism_part (
[(4369, '(2,2), 8: 4369'), (17895424, '(2,2), 2: 17895424')]
) : 17895424

## Bound for codes containing the lifted MRD code

(see EtzionSilberstein2012, Heinlein2018, and Kurz2019 for details)
69124617745

## Do you have better bounds?

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