Best Known (12−11, 12, s)-Nets in Base 8
(12−11, 12, 14)-Net over F8 — Constructive and digital
Digital (1, 12, 14)-net over F8, using
- net from sequence [i] based on digital (1, 13)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 1 and N(F) ≥ 14, using
(12−11, 12, 14)-Net over F8 — Upper bound on s (digital)
There is no digital (1, 12, 15)-net over F8, because
- 3 times m-reduction [i] would yield digital (1, 9, 15)-net over F8, but
- extracting embedded orthogonal array [i] would yield linear OA(89, 15, F8, 8) (dual of [15, 6, 9]-code), but
- “MPa†bound on codes from Brouwer’s database [i]
- extracting embedded orthogonal array [i] would yield linear OA(89, 15, F8, 8) (dual of [15, 6, 9]-code), but
(12−11, 12, 28)-Net in Base 8 — Upper bound on s
There is no (1, 12, 29)-net in base 8, because
- extracting embedded OOA [i] would yield OOA(812, 29, S8, 2, 11), but
- the linear programming bound for OOAs shows that M ≥ 859 306511 978861 690880 / 12060 994207 > 812 [i]