Best Known (16, s)-Sequences in Base 3
(16, 27)-Sequence over F3 — Constructive and digital
Digital (16, 27)-sequence over F3, using
- t-expansion [i] based on digital (15, 27)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 15 and N(F) ≥ 28, using
(16, 40)-Sequence in Base 3 — Upper bound on s
There is no (16, 41)-sequence in base 3, because
- net from sequence [i] would yield (16, m, 42)-net in base 3 for arbitrarily large m, but
- m-reduction [i] would yield (16, 163, 42)-net in base 3, but
- extracting embedded OOA [i] would yield OOA(3163, 42, S3, 4, 147), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 26 544651 814199 643338 440247 651133 135698 218965 877468 993535 187581 097625 462811 569215 / 37 > 3163 [i]
- extracting embedded OOA [i] would yield OOA(3163, 42, S3, 4, 147), but
- m-reduction [i] would yield (16, 163, 42)-net in base 3, but