Best Known (84, s)-Sequences in Base 8
(84, 97)-Sequence over F8 — Constructive and digital
Digital (84, 97)-sequence over F8, using
- t-expansion [i] based on digital (37, 97)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 37 and N(F) ≥ 98, using
(84, 103)-Sequence in Base 8 — Constructive
(84, 103)-sequence in base 8, using
- t-expansion [i] based on (83, 103)-sequence in base 8, using
- base expansion [i] based on digital (249, 103)-sequence over F2, using
- base reduction for sequences [i] based on digital (73, 103)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 73 and N(F) ≥ 104, using
- F6 from the tower of function fields by GarcÃa and Stichtenoth over F4 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 73 and N(F) ≥ 104, using
- base reduction for sequences [i] based on digital (73, 103)-sequence over F4, using
- base expansion [i] based on digital (249, 103)-sequence over F2, using
(84, 194)-Sequence over F8 — Digital
Digital (84, 194)-sequence over F8, using
- t-expansion [i] based on digital (77, 194)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 77 and N(F) ≥ 195, using
(84, 612)-Sequence in Base 8 — Upper bound on s
There is no (84, 613)-sequence in base 8, because
- net from sequence [i] would yield (84, m, 614)-net in base 8 for arbitrarily large m, but
- m-reduction [i] would yield (84, 1838, 614)-net in base 8, but
- extracting embedded OOA [i] would yield OOA(81838, 614, S8, 3, 1754), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 16 847321 905458 598011 723614 000648 108719 233555 999646 016398 826766 365670 252723 866439 314912 705584 376948 307536 871656 416863 987689 116870 131316 034607 263186 058340 077693 477354 655751 062084 831703 086524 609566 259380 938859 599081 514308 384496 302642 286163 762146 775329 027331 905039 439310 195610 406468 185182 809839 885489 275216 506779 930375 600957 320416 602827 205750 987370 692257 273977 276123 647061 762359 283007 135413 827546 561410 799258 580402 532880 335436 352667 876136 031431 821676 253940 978305 975325 914500 097231 320426 226985 429706 338001 849483 023694 960625 400816 042305 707561 981231 332658 305148 286883 005451 593621 798556 977840 644601 954569 215355 853495 341639 187433 383663 966168 315038 275198 687901 576901 671571 952192 108146 694888 976902 704505 047115 232578 393907 720487 015215 293845 745727 595935 485580 164608 384793 071918 378058 148548 271128 959705 857436 933410 020216 689708 794224 265365 598345 587929 983122 914403 833893 158199 702051 049486 636754 891863 165950 215065 224024 939015 694010 494428 483046 806570 354845 929618 719213 075481 738796 836756 417375 886999 094474 398931 500262 320217 306618 147101 496321 175060 876363 322793 862914 864825 971253 339881 621914 381560 523184 142818 384981 072367 542605 096784 804497 685289 820086 896458 144893 550893 363375 958082 499246 221622 499096 159376 330304 219003 647216 626557 225155 226046 512918 610293 710093 118455 734826 472772 507373 763810 972686 182006 302858 057000 329853 929740 752392 030996 067821 233116 469064 492216 143462 505979 409978 701788 827820 607772 540669 390114 321592 652227 855183 239189 832914 958327 255348 812138 991120 399639 516550 262193 082297 497627 478715 675960 062951 779554 787112 924480 957393 905044 634088 474742 658494 201148 543372 067794 912306 532606 920707 529431 864668 035343 226036 053222 866324 769623 088067 539732 063218 088716 681953 946527 891000 918016 / 1755 > 81838 [i]
- extracting embedded OOA [i] would yield OOA(81838, 614, S8, 3, 1754), but
- m-reduction [i] would yield (84, 1838, 614)-net in base 8, but