Best Known (212, s)-Sequences in Base 3
(212, 111)-Sequence over F3 — Constructive and digital
Digital (212, 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]
(212, 162)-Sequence over F3 — Digital
Digital (212, 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
(212, 437)-Sequence in Base 3 — Upper bound on s
There is no (212, 438)-sequence in base 3, because
- net from sequence [i] would yield (212, m, 439)-net in base 3 for arbitrarily large m, but
- m-reduction [i] would yield (212, 2627, 439)-net in base 3, but
- extracting embedded OOA [i] would yield OOA(32627, 439, S3, 6, 2415), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 327 445359 637587 185591 034667 431559 932280 267029 022538 545221 110314 287269 582907 297220 039355 995817 162874 307048 357520 960873 309605 754054 933079 874491 593019 571479 617841 188269 495401 318210 114374 274277 713094 041711 228157 777698 035246 957935 710525 608960 430671 963188 639505 693841 508492 683163 651172 860925 025071 206964 383633 910669 521556 293567 523527 183079 727114 129935 469229 011842 005327 109236 102590 897364 032416 326965 882897 932239 082297 759463 367727 955494 273288 180098 979863 403719 767898 233136 259019 227872 926365 878661 644463 372843 339525 730386 745530 799136 060638 118296 444913 028084 182172 153515 139108 862974 817420 817948 812029 836555 457567 114839 214454 944669 830092 406654 142655 906653 259003 025029 493472 302788 617375 790324 150630 729663 538361 482598 073744 982069 624988 357557 073038 555532 860620 240177 927805 608989 185846 897928 727535 961249 883871 730987 527245 297958 385763 639196 337274 623654 363030 904353 395681 018060 265229 690309 196534 977447 863436 676818 990036 318854 125132 229835 012045 873021 138936 961823 172974 609770 447930 015745 304205 765654 094868 511476 155504 018889 481355 631294 400889 319686 628353 292242 810438 039736 144610 119366 155187 897789 796978 907423 866322 548388 433028 792013 794445 117783 359124 999508 427690 435501 316637 206112 745573 484008 854881 798757 512485 188960 998902 185955 835761 608958 572435 931928 921210 644300 460089 221957 / 1208 > 32627 [i]
- extracting embedded OOA [i] would yield OOA(32627, 439, S3, 6, 2415), but
- m-reduction [i] would yield (212, 2627, 439)-net in base 3, but