Best Known (89, s)-Sequences in Base 3
(89, 63)-Sequence over F3 — Constructive and digital
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
(89, 95)-Sequence over F3 — Digital
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
(89, 190)-Sequence in Base 3 — Upper bound on s
There is no (89, 191)-sequence in base 3, because
- net from sequence [i] would yield (89, m, 192)-net in base 3 for arbitrarily large m, but
- m-reduction [i] would yield (89, 953, 192)-net in base 3, but
- extracting embedded OOA [i] would yield OOA(3953, 192, S3, 5, 864), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 65 783290 317488 456994 913830 448995 737261 545705 681248 187858 942193 102479 717129 103663 175790 382905 241002 946873 436314 874351 099986 583326 615732 254366 151948 895493 538348 750800 349637 597224 202181 848517 911673 255955 181364 461881 398796 286857 356636 646208 047118 285428 893615 985304 705770 057272 875000 407495 118688 609960 934330 669288 391970 337258 197750 432358 387154 620531 981725 035481 569619 868169 499349 649267 492075 727260 643115 181324 252481 828983 448098 158979 178135 122983 038719 467342 306529 / 865 > 3953 [i]
- extracting embedded OOA [i] would yield OOA(3953, 192, S3, 5, 864), but
- m-reduction [i] would yield (89, 953, 192)-net in base 3, but