Best Known (148, s)-Sequences in Base 3
(148, 80)-Sequence over F3 — Constructive and digital
Digital (148, 80)-sequence over F3, using
- t-expansion [i] based on digital (144, 80)-sequence over F3, using
- base reduction for sequences [i] based on digital (32, 80)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 32 and N(F) ≥ 81, using
- F4 from the tower of function fields by Bezerra and GarcÃa over F9 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 32 and N(F) ≥ 81, using
- base reduction for sequences [i] based on digital (32, 80)-sequence over F9, using
(148, 119)-Sequence over F3 — Digital
Digital (148, 119)-sequence over F3, using
- t-expansion [i] based on digital (113, 119)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 113 and N(F) ≥ 120, using
(148, 308)-Sequence in Base 3 — Upper bound on s
There is no (148, 309)-sequence in base 3, because
- net from sequence [i] would yield (148, m, 310)-net in base 3 for arbitrarily large m, but
- m-reduction [i] would yield (148, 1853, 310)-net in base 3, but
- extracting embedded OOA [i] would yield OOA(31853, 310, S3, 6, 1705), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 109821 696166 946325 970021 447229 962538 625657 206160 451144 134062 983394 634256 045501 873080 969460 347259 684077 176415 275356 776444 931826 843248 108513 338376 136341 548978 321792 704438 329852 140839 494643 689861 696863 860799 764426 018542 226453 958193 136414 386788 404308 284842 881418 543587 020746 540038 099260 507808 333975 401582 835386 362069 240325 078689 949930 170351 852359 206074 166072 239496 529185 567441 985047 285593 304813 998074 799012 216237 045851 097447 262226 999230 977646 157022 454415 782022 982082 228986 770810 771368 658569 646990 240028 916945 063633 567153 218882 874902 550023 622637 194339 414211 497031 340533 368640 315403 120317 432601 529083 282437 368509 928315 155394 775524 729895 798003 296629 718270 776645 032978 608988 835389 328537 495448 834949 488760 229804 654634 799089 025104 669229 932705 863300 990727 259370 153057 385018 006273 554101 195059 693577 667486 271989 016906 040385 975934 361062 159525 477724 963504 000099 261790 822904 257929 368112 545327 894090 166503 / 853 > 31853 [i]
- extracting embedded OOA [i] would yield OOA(31853, 310, S3, 6, 1705), but
- m-reduction [i] would yield (148, 1853, 310)-net in base 3, but