Best Known (201, s)-Sequences in Base 3
(201, 111)-Sequence over F3 — Constructive and digital
Digital (201, 111)-sequence over F3, using
- t-expansion [i] based on digital (189, 111)-sequence over F3, using
- Niederreiter–Xing sequence construction III based on function field F4/F3 with g(F4) = 79, N(F4) ≥ 2, and N(F4) + N2(F4) ≥ 112 from GarcÃa–Stichtenoth tower as constant field extension [i]
(201, 162)-Sequence over F3 — Digital
Digital (201, 162)-sequence over F3, using
- t-expansion [i] based on digital (151, 162)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 151 and N(F) ≥ 163, using
(201, 415)-Sequence in Base 3 — Upper bound on s
There is no (201, 416)-sequence in base 3, because
- net from sequence [i] would yield (201, m, 417)-net in base 3 for arbitrarily large m, but
- m-reduction [i] would yield (201, 2495, 417)-net in base 3, but
- extracting embedded OOA [i] would yield OOA(32495, 417, S3, 6, 2294), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 5143 530062 168223 245024 663427 425189 658153 848572 780211 837040 253671 195746 441928 070655 974909 737067 699257 936925 580784 600821 660510 866183 958008 145549 453970 579554 781867 404293 963871 412177 961380 616854 404108 870969 860776 657889 764491 829854 198804 265800 874010 699013 059120 196486 042439 874236 911810 575561 965348 506896 306409 340482 923806 655089 324252 104330 726793 857130 725170 785130 854585 041662 632802 392206 003791 253333 030114 369783 228603 263479 315604 829321 224815 843722 551394 185214 038165 835459 802961 345675 987526 685679 753469 758290 879531 166367 803206 061506 105846 399079 748409 124068 193085 561715 582330 614320 422559 117185 562755 507567 250310 280670 745020 106733 831350 003641 791711 634076 481269 084541 007947 232240 324503 354719 974962 709669 250763 075163 258614 812669 603100 475555 792185 220640 928150 029069 414010 639003 315695 686617 354699 365204 349757 421432 841058 242839 670630 968211 725410 014645 377537 942115 007908 917689 905305 104127 722002 253403 577812 166589 856905 882022 004354 159150 292173 533416 518217 333344 823250 241843 350496 005478 948087 938241 164496 767566 897986 924832 606748 891461 671296 599112 133113 365789 390554 493163 664559 865148 089830 733735 627728 598406 593105 276264 976829 589987 528165 293505 501265 812505 190420 114748 620137 177909 423809 395110 314317 865261 172771 / 17 > 32495 [i]
- extracting embedded OOA [i] would yield OOA(32495, 417, S3, 6, 2294), but
- m-reduction [i] would yield (201, 2495, 417)-net in base 3, but