Best Known (2, s)-Sequences in Base 49
(2, 51)-Sequence over F49 — Constructive and digital
Digital (2, 51)-sequence over F49, using
(2, 77)-Sequence over F49 — Digital
Digital (2, 77)-sequence over F49, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F49 with g(F) = 2 and N(F) ≥ 78, using
(2, 149)-Sequence in Base 49 — Upper bound on s
There is no (2, 150)-sequence in base 49, because
- net from sequence [i] would yield (2, m, 151)-net in base 49 for arbitrarily large m, but
- m-reduction [i] would yield (2, 149, 151)-net in base 49, but
- extracting embedded OOA [i] would yield OA(49149, 151, S49, 147), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 33 838570 200749 104093 688312 191360 663049 723538 032163 586311 882583 029937 928817 155484 694868 047033 872426 464394 494995 988271 332913 954603 498574 472214 519578 172866 008667 274238 025742 281231 442261 927858 597726 462360 331182 430633 401319 955052 400299 452568 317841 001584 180001 / 37 > 49149 [i]
- extracting embedded OOA [i] would yield OA(49149, 151, S49, 147), but
- m-reduction [i] would yield (2, 149, 151)-net in base 49, but