Details for entry \(A_4(19,4;3)\)

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Lower bounds

noted_linkage ( 7 ) : 18810411307369123749
generalized_linkage ( 16,0 ) : 18810411307339763733
noted_linkage ( 16 ) : 18810411307339763733
generalized_linkage ( 16,1 ) : 18810411307339763713
improved_linkage ( 16 ) : 18810411307339763713
linkage_GLT ( 16 ) : 18810411307339763713
linkage_ST ( 3 ) : 18810411307339763713
construction_D ( 3 ) : 18810411307339763712
noted_linkage ( 15 ) : 18810411307250286949
generalized_linkage ( 15,1 ) : 18810411307250286657
improved_linkage ( 15 ) : 18810411307250286657
generalized_linkage ( 15,0 ) : 18810411307250286613
linkage_GLT ( 15 ) : 18810411307250286593
linkage_ST ( 4 ) : 18810411307250286593
construction_D ( 4 ) : 18810411307250286592
noted_linkage ( 14 ) : 18810411306892400293
generalized_linkage ( 14,1 ) : 18810411306892398633
improved_linkage ( 14 ) : 18810411306892398633
generalized_linkage ( 14,0 ) : 18810411306892395861
linkage_GLT ( 14 ) : 18810411306892394561
linkage_ST ( 5 ) : 18810411306892394561
construction_D ( 5 ) : 18810411306892394496
noted_linkage ( 13 ) : 18810411305461181349
generalized_linkage ( 13,0 ) : 18810411305461175133
generalized_linkage ( 13,1 ) : 18810411305461155084
improved_linkage ( 13 ) : 18810411305461155084
linkage_GLT ( 13 ) : 18810411305461092393
linkage_ST ( 6 ) : 18810411305461092393
construction_D ( 6 ) : 18810411305461088256
noted_linkage ( 12 ) : 18810411299741548453
generalized_linkage ( 12,0 ) : 18810411299741460988
generalized_linkage ( 12,1 ) : 18810411299741111973
improved_linkage ( 12 ) : 18810411299741111973
linkage_GLT ( 12 ) : 18810411299740124428
linkage_ST ( 7 ) : 18810411299740124428
construction_D ( 7 ) : 18810411299740057600
noted_linkage ( 11 ) : 18810411276946902949
generalized_linkage ( 11,0 ) : 18810411276945185673
generalized_linkage ( 11,1 ) : 18810411276939991513
improved_linkage ( 11 ) : 18810411276939991513
linkage_GLT ( 11 ) : 18810411276924098213
linkage_ST ( 8 ) : 18810411276924098213
construction_D ( 8 ) : 18810411276923043840
generalized_linkage ( 7,0 ) : 18810411215178816393
noted_linkage ( 10 ) : 18810411187110498213
generalized_linkage ( 10,0 ) : 18810411187084631757
generalized_linkage ( 10,1 ) : 18810411187002458133
improved_linkage ( 10 ) : 18810411187002458133
linkage_GLT ( 10 ) : 18810411186745678297
linkage_ST ( 9 ) : 18810411186745678297
construction_D ( 9 ) : 18810411186728730624
generalized_linkage ( 7,1 ) : 18810410864807603109
improved_linkage ( 7 ) : 18810410864807603109
linkage_GLT ( 7 ) : 18810409813693961893
linkage_ST ( 12 ) : 18810409813693961893
construction_D ( 12 ) : 18810409743619719168
noted_linkage ( 9 ) : 18634163533353734053
generalized_linkage ( 9,0 ) : 18634163532993642937
generalized_linkage ( 9,1 ) : 18634163531625005413
improved_linkage ( 9 ) : 18634163531625005413
linkage_GLT ( 9 ) : 18634163527519092757
linkage_ST ( 10 ) : 18634163527519092757
construction_D ( 10 ) : 18634163527245365248
noted_linkage ( 6 ) : 18631416678427807653
generalized_linkage ( 6,0 ) : 18631415203377304713
generalized_linkage ( 6,1 ) : 18631409597437886373
improved_linkage ( 6 ) : 18631409597437886373
linkage_GLT ( 6 ) : 18631392779619625893
linkage_ST ( 13 ) : 18631392779619625893
construction_D ( 13 ) : 18631391658431741952
construction_1 ( ) : 18549225985110855589
construction_ST_A_1 ( ) : 18549225985110855589
noted_linkage ( 3 ) : 18549225985110855589
noted_linkage ( 8 ) : 18548726073943281573
generalized_linkage ( 8,0 ) : 18548726068181474633
generalized_linkage ( 8,1 ) : 18548726046283273893
improved_linkage ( 8 ) : 18548726046283273893
linkage_GLT ( 8 ) : 18548725980588671333
linkage_ST ( 11 ) : 18548725980588671333
construction_D ( 11 ) : 18548725976209031168
generalized_linkage ( 3,0 ) : 18543184170744252553
construction_ST_B_recursive ( ) : 18523676632120709286
generalized_linkage ( 3,1 ) : 18520222242878934949
improved_linkage ( 3 ) : 18520222242878934949
construction_ST_B ( ) : 18519350268011996132
multicomponent ( ) : 18519084246547628097
two_pivot_block_construction ( ) : 18519084246547628032
linkage_GLT ( 3 ) : 18451336459282632613
linkage_ST ( 16 ) : 18451336459282632613
LMRD ( ) : 18446744073709551616
construction_D ( 16 ) : 18446744073709551616
generalized_linkage ( 17,1 ) : 4702602826840533313
improved_linkage ( 17 ) : 4702602826840533313
noted_linkage ( 5 ) : 4684143932424736677
generalized_linkage ( 5,0 ) : 4684120331594348681
generalized_linkage ( 5,1 ) : 4684030636563632037
improved_linkage ( 5 ) : 4684030636563632037
linkage_GLT ( 5 ) : 4683761551471460261
linkage_ST ( 14 ) : 4683761551471460261
construction_D ( 14 ) : 4683743612465315840
graham_sloane ( ) : 1249303302255568209
linkage_ST ( 18 ) : 1175650706710482853
noted_linkage ( 4 ) : 1159326624047058853
generalized_linkage ( 4,0 ) : 1158949010671487113
generalized_linkage ( 4,1 ) : 1157513890179927973
improved_linkage ( 4 ) : 1157513890179927973
linkage_GLT ( 4 ) : 1153208528705163173
linkage_ST ( 15 ) : 1153208528705163173
construction_D ( 15 ) : 1152921504606846976
sphere_covering ( ) : 951850135262103566
linkage_ST ( 17 ) : 73478169169383333
HKK_lemma_2_4_lower_bound ( ) : 73300775172
construction_D ( 17 ) : 0
construction_D ( 18 ) : 0
construction_D ( 19 ) : 0
trivial_1 ( ) : 0

Upper bounds

Ahlswede_Aydinian ( 1, 2 ) : 19988852837179876689
Ahlswede_Aydinian ( 0, 17, o ) : 19988852837179876689
Ahlswede_Aydinian ( 0, 18, o ) : 19988852837179876689
anticode ( ) : 19988852837179876689
ilp_1 ( 1 ) : 19988852837179876689
ilp_2 ( 2 ) : 19988852837179876689
improved_johnson ( ) : 19988852837179876689
johnson_1 ( ) : 19988852837179876689
linear_programming_bound ( ) : 19988852837179876689
Ahlswede_Aydinian ( 1, 3 ) : 19988852840504174884
Ahlswede_Aydinian ( 1, 4 ) : 19988852853801367675
Ahlswede_Aydinian ( 1, 5 ) : 19988852906990139016
Ahlswede_Aydinian ( 1, 6 ) : 19988853119745227213
Ahlswede_Aydinian ( 1, 7 ) : 19988853970765625288
Ahlswede_Aydinian ( 1, 8 ) : 19988857374847942232
Ahlswede_Aydinian ( 1, 9 ) : 19988870991188804250
Ahlswede_Aydinian ( 1, 10 ) : 19988925456737760920
Ahlswede_Aydinian ( 1, 11 ) : 19989143321901767600
Ahlswede_Aydinian ( 1, 12 ) : 19990014830051391944
Ahlswede_Aydinian ( 1, 13 ) : 19993501622721418482
Ahlswede_Aydinian ( 1, 14 ) : 20007460965690216346
Ahlswede_Aydinian ( 1, 15 ) : 20063493810067772022
Ahlswede_Aydinian ( 1, 16 ) : 20290799253535946765
Ahlswede_Aydinian ( 1, 17 ) : 21253970104181314563
Ahlswede_Aydinian ( 1, 18 ) : 26235369347366932389
singleton ( ) : 26235369347366932389
Ahlswede_Aydinian ( 0, 18 ) : 79955411139288720467
ilp_4 ( 18 ) : 79955411139288720467
johnson_2 ( ) : 79955411139288720467
Ahlswede_Aydinian ( 0, 17 ) : 319821645674119063119
ilp_4 ( 17 ) : 319821645674119063119
Ahlswede_Aydinian ( 0, 16 ) : 1279286529082193979711
ilp_4 ( 16 ) : 1279286529082193979711
Ahlswede_Aydinian ( 0, 15 ) : 5117146402271614706944
ilp_4 ( 15 ) : 5117146402271614706944
Ahlswede_Aydinian ( 0, 14 ) : 20468571883826975773440
ilp_4 ( 14 ) : 20468571883826975773440
Ahlswede_Aydinian ( 0, 13 ) : 81874360736691812717653
ilp_4 ( 13 ) : 81874360736691812717653
Ahlswede_Aydinian ( 0, 12 ) : 327493929277041049948816
ilp_4 ( 12 ) : 327493929277041049948816
Ahlswede_Aydinian ( 0, 11 ) : 1309994455835608113435156
ilp_4 ( 11 ) : 1309994455835608113435156
Ahlswede_Aydinian ( 0, 10 ) : 5239078256337174454441046
ilp_4 ( 10 ) : 5239078256337174454441046
Ahlswede_Aydinian ( 0, 9 ) : 20961110716046431066171713
ilp_4 ( 9 ) : 20961110716046431066171713
Ahlswede_Aydinian ( 0, 8 ) : 83613932278182192373144502
ilp_4 ( 8 ) : 83613932278182192373144502
Ahlswede_Aydinian ( 0, 7 ) : 335685119121201055872034384
ilp_4 ( 7 ) : 335685119121201055872034384
HKK_lemma_2_4_upper_bound ( ) : 336672427354435043110252052
Ahlswede_Aydinian ( 0, 5 ) : 1283501926051651095981307939
Ahlswede_Aydinian ( 0, 6 ) : 1283501926051651095981307939
ilp_4 ( 5 ) : 1283501926051651095981307939
ilp_4 ( 6 ) : 1283501926051651095981307939
Ahlswede_Aydinian ( 0, 4 ) : 1346689713180347765321926176
Ahlswede_Aydinian ( 1, 15, o ) : 1346689713180347765321926176
ilp_3 ( 4 ) : 1346689713180347765321926176
Ahlswede_Aydinian ( 1, 16, o ) : 1362721733564020356155971684
Ahlswede_Aydinian ( 1, 17, o ) : 1430857820191654335530178558
Ahlswede_Aydinian ( 1, 18, o ) : 1788572274907721729765574885
Ahlswede_Aydinian ( 0, 3 ) : 114468625620329560052363725029
Ahlswede_Aydinian ( 0, 16, o ) : 114468625620329560052363725029
all_subs ( ) : 114468625620329560052363725029
sphere_packing ( ) : 114468625620329560052363725029

Bound for codes containing the lifted MRD code

(see EtzionSilberstein2012 and Heinlein2018 for details)
18549225985110855589

Do you have better bounds?

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