Best Known (163−147, 163, s)-Nets in Base 3
(163−147, 163, 28)-Net over F3 — Constructive and digital
Digital (16, 163, 28)-net over F3, using
- t-expansion [i] based on digital (15, 163, 28)-net over F3, using
- net from sequence [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
- net from sequence [i] based on digital (15, 27)-sequence over F3, using
(163−147, 163, 41)-Net in Base 3 — Upper bound on s
There is no (16, 163, 42)-net in base 3, because
- 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]