Best Known (1, 1+7, s)-Nets in Base 27
(1, 1+7, 38)-Net over F27 — Constructive and digital
Digital (1, 8, 38)-net over F27, using
- net from sequence [i] based on digital (1, 37)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 1 and N(F) ≥ 38, using
(1, 1+7, 147)-Net in Base 27 — Upper bound on s
There is no (1, 8, 148)-net in base 27, because
- 1 times m-reduction [i] would yield (1, 7, 148)-net in base 27, but
- extracting embedded orthogonal array [i] would yield OA(277, 148, S27, 6), but
- the linear programming bound shows that M ≥ 2 874662 066082 631977 / 269 773513 > 277 [i]
- extracting embedded orthogonal array [i] would yield OA(277, 148, S27, 6), but