Best Known (7, 12, s)-Nets in Base 9
(7, 12, 200)-Net over F9 — Constructive and digital
Digital (7, 12, 200)-net over F9, using
- trace code for nets [i] based on digital (1, 6, 100)-net over F81, using
- net from sequence [i] based on digital (1, 99)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 1 and N(F) ≥ 100, using
- net from sequence [i] based on digital (1, 99)-sequence over F81, using
(7, 12, 351)-Net in Base 9 — Constructive
(7, 12, 351)-net in base 9, using
- base change [i] based on digital (3, 8, 351)-net over F27, using
- 271 times duplication [i] based on digital (2, 7, 351)-net over F27, using
- net defined by OOA [i] based on linear OOA(277, 351, F27, 5, 5) (dual of [(351, 5), 1748, 6]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OA(277, 703, F27, 5) (dual of [703, 696, 6]-code), using
- net defined by OOA [i] based on linear OOA(277, 351, F27, 5, 5) (dual of [(351, 5), 1748, 6]-NRT-code), using
- 271 times duplication [i] based on digital (2, 7, 351)-net over F27, using
(7, 12, 364)-Net over F9 — Digital
Digital (7, 12, 364)-net over F9, using
(7, 12, 31314)-Net in Base 9 — Upper bound on s
There is no (7, 12, 31315)-net in base 9, because
- 1 times m-reduction [i] would yield (7, 11, 31315)-net in base 9, but
- the generalized Rao bound for nets shows that 9m ≥ 31381 638321 > 911 [i]