Best Known (21, 21+112, s)-Nets in Base 3
(21, 21+112, 32)-Net over F3 — Constructive and digital
Digital (21, 133, 32)-net over F3, using
- net from sequence [i] based on digital (21, 31)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 21 and N(F) ≥ 32, using
(21, 21+112, 56)-Net in Base 3 — Upper bound on s
There is no (21, 133, 57)-net in base 3, because
- 23 times m-reduction [i] would yield (21, 110, 57)-net in base 3, but
- extracting embedded OOA [i] would yield OOA(3110, 57, S3, 2, 89), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 182595 163330 227222 518231 959509 181023 190720 482399 822294 / 5 > 3110 [i]
- extracting embedded OOA [i] would yield OOA(3110, 57, S3, 2, 89), but