Best Known (18−18, 18, s)-Nets in Base 49
(18−18, 18, 50)-Net over F49 — Constructive and digital
Digital (0, 18, 50)-net over F49, using
- net from sequence [i] based on digital (0, 49)-sequence over F49, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F49 with g(F) = 0 and N(F) ≥ 50, using
- the rational function field F49(x) [i]
- Niederreiter sequence [i]
(18−18, 18, 50)-Net in Base 49 — Upper bound on s
There is no (0, 18, 51)-net in base 49, because
- 15 times m-reduction [i] would yield (0, 3, 51)-net in base 49, but
- extracting embedded orthogonal array [i] would yield OA(493, 51, S49, 3), but