Best Known (3, s)-Sequences in Base 81
(3, 115)-Sequence over F81 — Constructive and digital
Digital (3, 115)-sequence over F81, using
- t-expansion [i] based on digital (2, 115)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 2 and N(F) ≥ 116, using
(3, 135)-Sequence over F81 — Digital
Digital (3, 135)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 3 and N(F) ≥ 136, using
(3, 327)-Sequence in Base 81 — Upper bound on s
There is no (3, 328)-sequence in base 81, because
- net from sequence [i] would yield (3, m, 329)-net in base 81 for arbitrarily large m, but
- m-reduction [i] would yield (3, 327, 329)-net in base 81, but
- extracting embedded OOA [i] would yield OA(81327, 329, S81, 324), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 96 180314 357715 990587 866695 005009 421519 807533 203582 321833 064220 796030 452230 769369 687945 701177 630710 765596 423271 495781 781717 479503 570156 640146 116564 963592 577763 598390 994488 511154 583453 688264 431310 117070 951380 778300 070209 105896 789486 961155 378494 643669 625582 224205 312532 798313 616981 715184 545373 640952 467370 824158 784739 766606 613349 350438 756213 201331 977361 021132 375413 779689 587402 879444 281581 643812 465040 049223 744294 579683 117660 474637 395447 845689 412743 613834 000031 044683 855681 340292 750648 431890 523982 017601 911237 296710 374145 867627 961051 811893 251986 726523 390532 686358 417547 675267 228516 355341 891706 221124 323071 266810 959904 055422 157441 / 65 > 81327 [i]
- extracting embedded OOA [i] would yield OA(81327, 329, S81, 324), but
- m-reduction [i] would yield (3, 327, 329)-net in base 81, but