Details for entry \(A_3(16,4;3)\)

Go to API

Lower bounds

improved_linkage ( 7 ) : 2703425259205
improved_linkage ( 13 ) : 2703425259205
linkage_GLT ( 13 ) : 2703425259205
linkage_ST ( 3 ) : 2703425259205
construction_D ( 3 ) : 2703425259204
improved_linkage ( 12 ) : 2703425119264
linkage_GLT ( 12 ) : 2703425119237
linkage_ST ( 4 ) : 2703425119237
construction_D ( 4 ) : 2703425119236
improved_linkage ( 11 ) : 2703421826368
linkage_GLT ( 11 ) : 2703421825642
linkage_ST ( 5 ) : 2703421825642
construction_D ( 5 ) : 2703421825614
linkage_GLT ( 7 ) : 2703420721909
linkage_ST ( 9 ) : 2703420721909
improved_linkage ( 10 ) : 2703420710661
linkage_GLT ( 10 ) : 2703420704437
linkage_ST ( 6 ) : 2703420704437
construction_D ( 6 ) : 2703420703683
construction_D ( 9 ) : 2703420172242
improved_linkage ( 6 ) : 2629081221040
linkage_GLT ( 6 ) : 2629040525317
linkage_ST ( 10 ) : 2629040525317
improved_linkage ( 9 ) : 2629040281582
linkage_GLT ( 9 ) : 2629040228301
linkage_ST ( 7 ) : 2629040228301
construction_D ( 7 ) : 2629040221323
construction_D ( 10 ) : 2629035438354
construction_1 ( ) : 2594821233559
construction_ST_A_1 ( ) : 2594821233559
improved_linkage ( 8 ) : 2593952910406
linkage_GLT ( 8 ) : 2593952420998
linkage_ST ( 8 ) : 2593952420998
construction_D ( 8 ) : 2593952360739
improved_linkage ( 3 ) : 2575241446270
construction_ST_B ( ) : 2573987829525
two_pivot_block_construction ( ) : 2573639151183
multicomponent ( ) : 2573639151175
linkage_GLT ( 3 ) : 2545574230605
linkage_ST ( 13 ) : 2545574230605
LMRD ( ) : 2541865828329
construction_D ( 13 ) : 2541865828329
improved_linkage ( 14 ) : 901141684408
improved_linkage ( 5 ) : 879081713728
linkage_GLT ( 5 ) : 878715451738
linkage_ST ( 11 ) : 878715451738
construction_D ( 11 ) : 878669669052
graham_sloane ( ) : 329953645351
linkage_ST ( 15 ) : 300380568805
improved_linkage ( 4 ) : 286137938757
linkage_GLT ( 4 ) : 282841581157
linkage_ST ( 12 ) : 282841581157
construction_D ( 12 ) : 282429536481
sphere_covering ( ) : 228429577405
linkage_ST ( 14 ) : 33375617941
HKK_lemma_2_4_lower_bound ( ) : 16142520
construction_D ( 14 ) : 0
construction_D ( 15 ) : 0
trivial_1 ( ) : 0

Upper bounds

improved_johnson ( ) : 2969579634841
Ahlswede_Aydinian ( 0, 15, o ) : 2969579634843
ilp_1 ( 1 ) : 2969579634843
johnson_1 ( ) : 2969579634843
Ahlswede_Aydinian ( 1, 2 ) : 2969583360040
Ahlswede_Aydinian ( 0, 14, o ) : 2969583360040
anticode ( ) : 2969583360040
ilp_2 ( 2 ) : 2969583360040
linear_programming_bound ( ) : 2969583360040
Ahlswede_Aydinian ( 1, 3 ) : 2969584506255
Ahlswede_Aydinian ( 1, 4 ) : 2969587944905
Ahlswede_Aydinian ( 1, 5 ) : 2969598260904
Ahlswede_Aydinian ( 1, 6 ) : 2969629209331
Ahlswede_Aydinian ( 1, 7 ) : 2969722058484
Ahlswede_Aydinian ( 1, 8 ) : 2970000640780
Ahlswede_Aydinian ( 1, 9 ) : 2970836701356
Ahlswede_Aydinian ( 1, 10 ) : 2973347709702
Ahlswede_Aydinian ( 1, 11 ) : 2980906267714
Ahlswede_Aydinian ( 1, 12 ) : 3003814289356
Ahlswede_Aydinian ( 1, 13 ) : 3074700763441
Ahlswede_Aydinian ( 1, 14 ) : 3308963682949
Ahlswede_Aydinian ( 1, 15 ) : 4289397389563
singleton ( ) : 4289397389563
Ahlswede_Aydinian ( 0, 15 ) : 8908753805319
ilp_4 ( 15 ) : 8908753805319
johnson_2 ( ) : 8908753805319
Ahlswede_Aydinian ( 0, 14 ) : 26726294942748
ilp_4 ( 14 ) : 26726294942748
Ahlswede_Aydinian ( 0, 13 ) : 80179186571550
ilp_4 ( 13 ) : 80179186571550
Ahlswede_Aydinian ( 0, 12 ) : 240540275443771
ilp_4 ( 12 ) : 240540275443771
Ahlswede_Aydinian ( 0, 11 ) : 721645267893403
ilp_4 ( 11 ) : 721645267893403
Ahlswede_Aydinian ( 0, 10 ) : 2165155820793262
ilp_4 ( 10 ) : 2165155820793262
Ahlswede_Aydinian ( 0, 9 ) : 6497448391767520
ilp_4 ( 9 ) : 6497448391767520
Ahlswede_Aydinian ( 0, 8 ) : 19510173539792166
ilp_4 ( 8 ) : 19510173539792166
Ahlswede_Aydinian ( 0, 7 ) : 58691827208280160
ilp_4 ( 7 ) : 58691827208280160
HKK_lemma_2_4_upper_bound ( ) : 59180925768349161
Ahlswede_Aydinian ( 0, 5 ) : 164337116183184448
ilp_4 ( 5 ) : 164337116183184448
Ahlswede_Aydinian ( 0, 4 ) : 177542777305047484
Ahlswede_Aydinian ( 0, 6 ) : 177542777305047484
Ahlswede_Aydinian ( 1, 12, o ) : 177542777305047484
ilp_3 ( 4 ) : 177542777305047484
ilp_4 ( 6 ) : 177542777305047484
Ahlswede_Aydinian ( 1, 13, o ) : 182095150353136460
Ahlswede_Aydinian ( 1, 14, o ) : 197269725065013983
Ahlswede_Aydinian ( 1, 15, o ) : 263026177881648511
Ahlswede_Aydinian ( 0, 3 ) : 7101711092201899360
Ahlswede_Aydinian ( 0, 13, o ) : 7101711092201899360
all_subs ( ) : 7101711092201899360
sphere_packing ( ) : 7101711092201899360

Bound for codes containing the lifted MRD code

(see EtzionSilberstein2012 and Heinlein2018 for details)
2594821233559

Do you have better bounds?

You are welcome to contribute more information, clarifications, corrections and feature requests. If you want to contact us, press the “Contribute” button in the upper right corner or visit the About page. The preferred syntax for codes is GAP but feel free to submit any data in any format.