Best Known (29−22, 29, s)-Nets in Base 3
(29−22, 29, 16)-Net over F3 — Constructive and digital
Digital (7, 29, 16)-net over F3, using
- net from sequence [i] based on digital (7, 15)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 7 and N(F) ≥ 16, using
(29−22, 29, 24)-Net in Base 3 — Upper bound on s
There is no (7, 29, 25)-net in base 3, because
- 1 times m-reduction [i] would yield (7, 28, 25)-net in base 3, but
- extracting embedded OOA [i] would yield OOA(328, 25, S3, 2, 21), but
- the linear programming bound for OOAs shows that M ≥ 705 791411 666019 / 25 > 328 [i]
- extracting embedded OOA [i] would yield OOA(328, 25, S3, 2, 21), but