Best Known (91, s)-Sequences in Base 3
(91, 63)-Sequence over F3 — Constructive and digital
Digital (91, 63)-sequence over F3, using
- t-expansion [i] based on digital (89, 63)-sequence over F3, using
- base reduction for sequences [i] based on digital (13, 63)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 13 and N(F) ≥ 64, using
- base reduction for sequences [i] based on digital (13, 63)-sequence over F9, using
(91, 95)-Sequence over F3 — Digital
Digital (91, 95)-sequence over F3, using
- t-expansion [i] based on digital (89, 95)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 89 and N(F) ≥ 96, using
(91, 194)-Sequence in Base 3 — Upper bound on s
There is no (91, 195)-sequence in base 3, because
- net from sequence [i] would yield (91, m, 196)-net in base 3 for arbitrarily large m, but
- m-reduction [i] would yield (91, 973, 196)-net in base 3, but
- extracting embedded OOA [i] would yield OOA(3973, 196, S3, 5, 882), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 226251 440994 514271 805283 045241 931895 277976 485980 254575 831504 747987 864833 028397 398650 537986 763079 262462 647841 988270 528538 179656 174264 703300 196510 883548 711748 728260 818583 879927 895564 726287 338448 379276 718666 509020 950026 959647 705361 243190 573879 601653 347776 319465 146126 054999 366196 510322 039322 329441 321653 478344 505748 023259 271809 447001 507097 591674 820872 714750 097311 079353 848963 126998 796280 984186 080649 162653 957245 313679 531553 025842 228471 964458 011455 913058 319092 402981 359515 / 883 > 3973 [i]
- extracting embedded OOA [i] would yield OOA(3973, 196, S3, 5, 882), but
- m-reduction [i] would yield (91, 973, 196)-net in base 3, but