Best Known (45−45, 45, s)-Nets in Base 3
(45−45, 45, 4)-Net over F3 — Constructive and digital
Digital (0, 45, 4)-net over F3, using
- net from sequence [i] based on digital (0, 3)-sequence over F3, using
- Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 0 and N(F) ≥ 4, using
- the rational function field F3(x) [i]
- Niederreiter sequence [i]
(45−45, 45, 4)-Net in Base 3 — Upper bound on s
There is no (0, 45, 5)-net in base 3, because
- 42 times m-reduction [i] would yield (0, 3, 5)-net in base 3, but
- extracting embedded orthogonal array [i] would yield OA(33, 5, S3, 3), but
- the (dual) Plotkin bound shows that M ≥ 81 / 2 > 33 [i]
- extracting embedded orthogonal array [i] would yield OA(33, 5, S3, 3), but