Best Known (36, s)-Sequences in Base 8
(36, 64)-Sequence over F8 — Constructive and digital
Digital (36, 64)-sequence over F8, using
- t-expansion [i] based on digital (14, 64)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 14 and N(F) ≥ 65, using
- the Suzuki function field over F8 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 14 and N(F) ≥ 65, using
(36, 111)-Sequence over F8 — Digital
Digital (36, 111)-sequence over F8, using
- t-expansion [i] based on digital (35, 111)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 35 and N(F) ≥ 112, using
(36, 273)-Sequence in Base 8 — Upper bound on s
There is no (36, 274)-sequence in base 8, because
- net from sequence [i] would yield (36, m, 275)-net in base 8 for arbitrarily large m, but
- m-reduction [i] would yield (36, 821, 275)-net in base 8, but
- extracting embedded OOA [i] would yield OOA(8821, 275, S8, 3, 785), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 1 170369 753080 412302 926409 140637 998819 026624 872297 999636 649854 098699 835301 386254 572231 654358 781364 756394 939118 158051 516521 753725 373844 589948 559706 165503 579113 333319 041262 069721 406427 926942 975350 716370 420265 614202 924680 930093 955078 833293 495730 037594 176119 468520 505668 691129 943766 894196 004281 217357 180934 930442 910018 157913 010635 504463 201291 070758 281926 097061 494937 734839 918905 747136 919942 299453 467253 231365 284880 392096 895559 431856 039375 901806 415943 439648 875564 850513 319740 585961 831509 902926 977846 717336 188426 615693 661021 467729 419310 753509 605406 267806 483317 173691 988538 629899 187567 296476 193400 883490 987144 340173 199733 078512 337984 556850 807890 482814 087290 201366 382733 529398 409901 735256 042324 401598 233908 179226 619572 324149 515194 730284 209446 637822 541824 / 393 > 8821 [i]
- extracting embedded OOA [i] would yield OOA(8821, 275, S8, 3, 785), but
- m-reduction [i] would yield (36, 821, 275)-net in base 8, but