Best Known (52, s)-Sequences in Base 3
(52, 47)-Sequence over F3 — Constructive and digital
Digital (52, 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
(52, 63)-Sequence over F3 — Digital
Digital (52, 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
(52, 114)-Sequence in Base 3 — Upper bound on s
There is no (52, 115)-sequence in base 3, because
- net from sequence [i] would yield (52, m, 116)-net in base 3 for arbitrarily large m, but
- m-reduction [i] would yield (52, 574, 116)-net in base 3, but
- extracting embedded OOA [i] would yield OOA(3574, 116, S3, 5, 522), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 4 091600 209833 919750 115591 647196 387286 482529 830425 117722 012891 118712 647254 053292 184668 947662 871774 656252 028033 643900 510075 050301 142405 351332 494131 418115 957784 817623 188288 818826 148740 572583 161489 619110 247168 439753 193368 296065 191962 134004 236515 988234 796426 500480 497291 014699 291795 / 523 > 3574 [i]
- extracting embedded OOA [i] would yield OOA(3574, 116, S3, 5, 522), but
- m-reduction [i] would yield (52, 574, 116)-net in base 3, but