Best Known (102−93, 102, s)-Nets in Base 3
(102−93, 102, 19)-Net over F3 — Constructive and digital
Digital (9, 102, 19)-net over F3, using
- net from sequence [i] based on digital (9, 18)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 9 and N(F) ≥ 19, using
(102−93, 102, 26)-Net in Base 3 — Upper bound on s
There is no (9, 102, 27)-net in base 3, because
- 25 times m-reduction [i] would yield (9, 77, 27)-net in base 3, but
- extracting embedded OOA [i] would yield OOA(377, 27, S3, 3, 68), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 147 808829 414345 923316 083210 206383 297601 / 23 > 377 [i]
- extracting embedded OOA [i] would yield OOA(377, 27, S3, 3, 68), but