Best Known (34−8, 34, s)-Nets in Base 9
(34−8, 34, 3291)-Net over F9 — Constructive and digital
Digital (26, 34, 3291)-net over F9, using
- (u, u+v)-construction [i] based on
- digital (0, 4, 10)-net over F9, using
- net from sequence [i] based on digital (0, 9)-sequence over F9, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 0 and N(F) ≥ 10, using
- the rational function field F9(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 9)-sequence over F9, using
- digital (22, 30, 3281)-net over F9, using
- net defined by OOA [i] based on linear OOA(930, 3281, F9, 8, 8) (dual of [(3281, 8), 26218, 9]-NRT-code), using
- OA 4-folding and stacking [i] based on linear OA(930, 13124, F9, 8) (dual of [13124, 13094, 9]-code), using
- discarding factors / shortening the dual code based on linear OA(930, 13126, F9, 8) (dual of [13126, 13096, 9]-code), using
- trace code [i] based on linear OA(8115, 6563, F81, 8) (dual of [6563, 6548, 9]-code), using
- construction X applied to Ce(7) ⊂ Ce(6) [i] based on
- linear OA(8115, 6561, F81, 8) (dual of [6561, 6546, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(8113, 6561, F81, 7) (dual of [6561, 6548, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(810, 2, F81, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(810, s, F81, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(7) ⊂ Ce(6) [i] based on
- trace code [i] based on linear OA(8115, 6563, F81, 8) (dual of [6563, 6548, 9]-code), using
- discarding factors / shortening the dual code based on linear OA(930, 13126, F9, 8) (dual of [13126, 13096, 9]-code), using
- OA 4-folding and stacking [i] based on linear OA(930, 13124, F9, 8) (dual of [13124, 13094, 9]-code), using
- net defined by OOA [i] based on linear OOA(930, 3281, F9, 8, 8) (dual of [(3281, 8), 26218, 9]-NRT-code), using
- digital (0, 4, 10)-net over F9, using
(34−8, 34, 4921)-Net in Base 9 — Constructive
(26, 34, 4921)-net in base 9, using
- 91 times duplication [i] based on (25, 33, 4921)-net in base 9, using
- base change [i] based on digital (14, 22, 4921)-net over F27, using
- net defined by OOA [i] based on linear OOA(2722, 4921, F27, 8, 8) (dual of [(4921, 8), 39346, 9]-NRT-code), using
- OA 4-folding and stacking [i] based on linear OA(2722, 19684, F27, 8) (dual of [19684, 19662, 9]-code), using
- discarding factors / shortening the dual code based on linear OA(2722, 19686, F27, 8) (dual of [19686, 19664, 9]-code), using
- construction X applied to Ce(7) ⊂ Ce(6) [i] based on
- linear OA(2722, 19683, F27, 8) (dual of [19683, 19661, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 19682 = 273−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(2719, 19683, F27, 7) (dual of [19683, 19664, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 19682 = 273−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(270, 3, F27, 0) (dual of [3, 3, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(270, s, F27, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(7) ⊂ Ce(6) [i] based on
- discarding factors / shortening the dual code based on linear OA(2722, 19686, F27, 8) (dual of [19686, 19664, 9]-code), using
- OA 4-folding and stacking [i] based on linear OA(2722, 19684, F27, 8) (dual of [19684, 19662, 9]-code), using
- net defined by OOA [i] based on linear OOA(2722, 4921, F27, 8, 8) (dual of [(4921, 8), 39346, 9]-NRT-code), using
- base change [i] based on digital (14, 22, 4921)-net over F27, using
(34−8, 34, 18231)-Net over F9 — Digital
Digital (26, 34, 18231)-net over F9, using
(34−8, 34, large)-Net in Base 9 — Upper bound on s
There is no (26, 34, large)-net in base 9, because
- 6 times m-reduction [i] would yield (26, 28, large)-net in base 9, but