Best Known (9−9, 9, s)-Nets in Base 81
(9−9, 9, 82)-Net over F81 — Constructive and digital
Digital (0, 9, 82)-net over F81, using
- net from sequence [i] based on digital (0, 81)-sequence over F81, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 0 and N(F) ≥ 82, using
- the rational function field F81(x) [i]
- Niederreiter sequence [i]
(9−9, 9, 82)-Net in Base 81 — Upper bound on s
There is no (0, 9, 83)-net in base 81, because
- 6 times m-reduction [i] would yield (0, 3, 83)-net in base 81, but
- extracting embedded orthogonal array [i] would yield OA(813, 83, S81, 3), but