Best Known (60, s)-Sequences in Base 3
(60, 47)-Sequence over F3 — Constructive and digital
Digital (60, 47)-sequence over F3, using
- t-expansion [i] based on digital (45, 47)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 45 and N(F) ≥ 48, using
(60, 63)-Sequence over F3 — Digital
Digital (60, 63)-sequence over F3, using
- t-expansion [i] based on digital (49, 63)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 49 and N(F) ≥ 64, using
(60, 131)-Sequence in Base 3 — Upper bound on s
There is no (60, 132)-sequence in base 3, because
- net from sequence [i] would yield (60, m, 133)-net in base 3 for arbitrarily large m, but
- m-reduction [i] would yield (60, 526, 133)-net in base 3, but
- extracting embedded OOA [i] would yield OOA(3526, 133, S3, 4, 466), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 45 749376 695876 574596 544178 102538 190422 581384 179693 504822 412055 940395 131223 460005 421772 207849 589406 242393 199955 789579 652324 605064 265082 190889 099392 682399 599960 399439 496719 183057 488035 454230 521296 021782 069992 567481 246842 388517 406099 652987 529213 428861 572855 / 467 > 3526 [i]
- extracting embedded OOA [i] would yield OOA(3526, 133, S3, 4, 466), but
- m-reduction [i] would yield (60, 526, 133)-net in base 3, but