Best Known (1, 1+24, s)-Nets in Base 27
(1, 1+24, 38)-Net over F27 — Constructive and digital
Digital (1, 25, 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+24, 135)-Net in Base 27 — Upper bound on s
There is no (1, 25, 136)-net in base 27, because
- 16 times m-reduction [i] would yield (1, 9, 136)-net in base 27, but
- extracting embedded orthogonal array [i] would yield OA(279, 136, S27, 8), but
- the linear programming bound shows that M ≥ 35766 310676 101581 380904 / 4611 122641 > 279 [i]
- extracting embedded orthogonal array [i] would yield OA(279, 136, S27, 8), but