Best Known (12−12, 12, s)-Nets in Base 7
(12−12, 12, 8)-Net over F7 — Constructive and digital
Digital (0, 12, 8)-net over F7, using
- net from sequence [i] based on digital (0, 7)-sequence over F7, using
- Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F7 with g(F) = 0 and N(F) ≥ 8, using
- the rational function field F7(x) [i]
- Niederreiter sequence [i]
(12−12, 12, 8)-Net in Base 7 — Upper bound on s
There is no (0, 12, 9)-net in base 7, because
- 9 times m-reduction [i] would yield (0, 3, 9)-net in base 7, but
- extracting embedded orthogonal array [i] would yield OA(73, 9, S7, 3), but