Best Known (9−4, 9, s)-Nets in Base 9
(9−4, 9, 164)-Net over F9 — Constructive and digital
Digital (5, 9, 164)-net over F9, using
- 1 times m-reduction [i] based on digital (5, 10, 164)-net over F9, using
- trace code for nets [i] based on digital (0, 5, 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]
- net from sequence [i] based on digital (0, 81)-sequence over F81, using
- trace code for nets [i] based on digital (0, 5, 82)-net over F81, using
(9−4, 9, 204)-Net over F9 — Digital
Digital (5, 9, 204)-net over F9, using
- net defined by OOA [i] based on linear OOA(99, 204, F9, 4, 4) (dual of [(204, 4), 807, 5]-NRT-code), using
- appending kth column [i] based on linear OOA(99, 204, F9, 3, 4) (dual of [(204, 3), 603, 5]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(99, 204, F9, 4) (dual of [204, 195, 5]-code), using
- 39 step Varšamov–Edel lengthening with (ri) = (1, 38 times 0) [i] based on linear OA(98, 164, F9, 4) (dual of [164, 156, 5]-code), using
- trace code [i] based on linear OA(814, 82, F81, 4) (dual of [82, 78, 5]-code or 82-arc in PG(3,81)), using
- extended Reed–Solomon code RSe(78,81) [i]
- trace code [i] based on linear OA(814, 82, F81, 4) (dual of [82, 78, 5]-code or 82-arc in PG(3,81)), using
- 39 step Varšamov–Edel lengthening with (ri) = (1, 38 times 0) [i] based on linear OA(98, 164, F9, 4) (dual of [164, 156, 5]-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(99, 204, F9, 4) (dual of [204, 195, 5]-code), using
- appending kth column [i] based on linear OOA(99, 204, F9, 3, 4) (dual of [(204, 3), 603, 5]-NRT-code), using
(9−4, 9, 351)-Net in Base 9 — Constructive
(5, 9, 351)-net in base 9, using
- base change [i] based on digital (2, 6, 351)-net over F27, using
- net defined by OOA [i] based on linear OOA(276, 351, F27, 4, 4) (dual of [(351, 4), 1398, 5]-NRT-code), using
- OA 2-folding and stacking [i] based on linear OA(276, 702, F27, 4) (dual of [702, 696, 5]-code), using
- 1 times truncation [i] based on linear OA(277, 703, F27, 5) (dual of [703, 696, 6]-code), using
- OA 2-folding and stacking [i] based on linear OA(276, 702, F27, 4) (dual of [702, 696, 5]-code), using
- net defined by OOA [i] based on linear OOA(276, 351, F27, 4, 4) (dual of [(351, 4), 1398, 5]-NRT-code), using
(9−4, 9, 3478)-Net in Base 9 — Upper bound on s
There is no (5, 9, 3479)-net in base 9, because
- the generalized Rao bound for nets shows that 9m ≥ 387 477105 > 99 [i]