Best Known (12−12, 12, s)-Nets in Base 5
(12−12, 12, 6)-Net over F5 — Constructive and digital
Digital (0, 12, 6)-net over F5, using
- net from sequence [i] based on digital (0, 5)-sequence over F5, using
- Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 0 and N(F) ≥ 6, using
- the rational function field F5(x) [i]
- Niederreiter sequence [i]
(12−12, 12, 6)-Net in Base 5 — Upper bound on s
There is no (0, 12, 7)-net in base 5, because
- 9 times m-reduction [i] would yield (0, 3, 7)-net in base 5, but
- extracting embedded orthogonal array [i] would yield OA(53, 7, S5, 3), but