Best Known (7, s)-Sequences in Base 81
(7, 171)-Sequence over F81 — Constructive and digital
Digital (7, 171)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 7 and N(F) ≥ 172, using
(7, 189)-Sequence over F81 — Digital
Digital (7, 189)-sequence over F81, using
- t-expansion [i] based on digital (6, 189)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 6 and N(F) ≥ 190, using
(7, 655)-Sequence in Base 81 — Upper bound on s
There is no (7, 656)-sequence in base 81, because
- net from sequence [i] would yield (7, m, 657)-net in base 81 for arbitrarily large m, but
- m-reduction [i] would yield (7, 655, 657)-net in base 81, but
- extracting embedded OOA [i] would yield OA(81655, 657, S81, 648), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 83255 875829 541618 507763 708983 361284 586897 286809 697062 095375 111692 669611 723187 698967 545384 138612 477576 162816 557579 677932 775426 914552 016240 653850 246522 115336 344060 073606 763620 190723 207290 688459 978144 345595 768567 937461 288318 824233 543251 706186 288320 159837 148663 575262 774646 113310 748248 391819 240072 963230 011164 675698 336204 822660 444236 735247 168606 645173 971271 762523 602112 696695 293897 117730 082971 514335 849970 058246 198260 733121 720812 482652 755703 050846 647191 385651 639520 248222 481369 914296 050312 398078 938055 642852 663547 009088 617035 122313 917650 215216 097896 792316 850280 578474 220407 570510 404479 519148 749004 972147 868577 380934 262635 308881 284619 032327 143632 507820 748290 116830 275185 046686 340145 009954 393778 200747 104368 827377 001012 476385 707693 251226 300166 675021 769702 562402 188052 120311 682404 761944 453587 909962 845596 488056 762089 488529 306798 676922 775139 500219 433232 736688 451822 542655 791937 530942 419267 085650 505130 134500 390622 642798 152105 221208 249649 890958 285522 965464 778695 593808 271043 922019 884506 904168 540175 813922 070688 759085 012873 453953 951009 327899 403328 818410 993653 632378 492275 455417 032264 884260 609943 408051 442295 547529 374216 123517 529905 360630 339435 420398 599144 546482 745285 052821 147593 188114 640681 097765 696717 254258 556365 612976 293315 270422 689024 136516 961770 734925 016329 / 649 > 81655 [i]
- extracting embedded OOA [i] would yield OA(81655, 657, S81, 648), but
- m-reduction [i] would yield (7, 655, 657)-net in base 81, but