Best Known (84−69, 84, s)-Nets in Base 3
(84−69, 84, 28)-Net over F3 — Constructive and digital
Digital (15, 84, 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
(84−69, 84, 42)-Net in Base 3 — Upper bound on s
There is no (15, 84, 43)-net in base 3, because
- 2 times m-reduction [i] would yield (15, 82, 43)-net in base 3, but
- extracting embedded OOA [i] would yield OOA(382, 43, S3, 2, 67), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 59862 575912 810098 943013 700133 585235 528405 / 34 > 382 [i]
- extracting embedded OOA [i] would yield OOA(382, 43, S3, 2, 67), but