Details for entry \(A_8(10,4;4)\)

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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, 8), (0, 2, 4, 9), (0, 2, 5, 6), (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, 2, 7, 9), (0, 3, 4, 6), (0, 3, 4, 7), (0, 3, 4, 8), (0, 3, 4, 9), (0, 3, 5, 6), (0, 3, 5, 7), (0, 3, 5, 8), (0, 3, 5, 9), (0, 3, 6, 8), (0, 3, 6, 9), (0, 3, 7, 8), (0, 3, 7, 9), (0, 4, 6, 8), (0, 4, 6, 9), (0, 4, 7, 8), (0, 4, 7, 9), (0, 5, 6, 8), (0, 5, 6, 9), (0, 5, 7, 8), (0, 5, 7, 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: 18018965764067904 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, 8), (0, 2, 4, 9), (0, 2, 5, 6), (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, 2, 7, 9), (0, 3, 4, 6), (0, 3, 4, 7), (0, 3, 4, 8), (0, 3, 4, 9), (0, 3, 5, 6), (0, 3, 5, 7), (0, 3, 5, 8), (0, 3, 5, 9), (0, 3, 6, 8), (0, 3, 6, 9), (0, 3, 7, 8), (0, 3, 7, 9), (0, 4, 6, 8), (0, 4, 6, 9), (0, 4, 7, 8), (0, 4, 7, 9), (0, 5, 6, 8), (0, 5, 6, 9), (0, 5, 7, 8), (0, 5, 7, 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)])

) : 18018965764067904
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)]

) : 18018964210982977
echelon_ferrers (

optimal [(0, 1, 2, 3), (0, 1, 4, 5), (0, 1, 6, 7), (0, 1, 8, 9), (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), (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: 18018964210982976 with optimal [(0, 1, 2, 3), (0, 1, 4, 5), (0, 1, 6, 7), (0, 1, 8, 9), (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), (2, 3, 8, 9), (4, 5, 6, 7), (4, 5, 8, 9), (6, 7, 8, 9)])

) : 18018964210982976
JohnsonLB ( ) : 18018874574903812
LiuChangFeng2019_Theo_3_12 ( ) : 18018866519338360
construction_ST_B_recursive ( ) : 18018866366259265
two_pivot_block_construction ( ) : 18018797629997056
construction_ST_B ( ) : 18018797629993024
LiuChangFeng2019_Theo_3_14 ( ) : 18018797629734912
CKMP2019_Cor_45 (

(6,),(2,),(1,)

) : 18014479377718136
CKMP2019_Cor_42 ( (4, 6) ) : 18014479360940920
CKMP2019_Lem_41 ( (4, 6) ) : 18014479360940920
generalized_linkage ( 4,0 ) : 18014479360940920
generalized_linkage_multipleblocks (

[4, 6],[0, 0]

) : 18014479360940920
improved_linkage ( 4 ) : 18014467248697921
multicomponent ( ) : 18014467228962817
LiuChangFeng2019_Theo_2_6 ( ) : 18014399753350520
linkage_GLT ( 4 ) : 18014398509486145
LMRD ( ) : 18014398509481984
ChenHeWengXu2019_T31 ( ) : 281555828165431
graham_sloane ( ) : 35821527074256
HKK_lemma_2_4_lower_bound ( ) : 35261798941256
sphere_covering ( ) : 31351609751243
coset_construction_parallelism_part (

[(266305, '(2,2), 8: 266305'), (69810257920, '(2,2), 2: 69810257920')]

) : 69810257920
trivial_1 ( ) : 0

Upper bounds

Ahlswede_Aydinian ( 1, 3 ) : 18340630590431809
anticode ( ) : 18340630590431809
ilp_1 ( 1 ) : 18340630590431809
ilp_2 ( 3 ) : 18340630590431809
improved_johnson ( ) : 18340630590431809
johnson_1 ( ) : 18340630590431809
linear_programming_bound ( ) : 18340630590431809
singleton ( ) : 20955593338439305
ilp_4 ( 9 ) : 146694189678400071
johnson_2 ( ) : 146694189678400071
HKK_lemma_2_4_upper_bound ( ) : 146698106955415624
ilp_3 ( 5 ) : 1173835620696269377
all_subs ( ) : 5494724540479236953737
sphere_packing ( ) : 5494724540479236953737

Bound for codes containing the lifted MRD code

(see EtzionSilberstein2012, Heinlein2018, and Kurz2019 for details)
18019584236625985

Do you have better bounds?

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