Best Known (129, 129+14, s)-Nets in Base 9
(129, 129+14, 2573890)-Net over F9 — Constructive and digital
Digital (129, 143, 2573890)-net over F9, using
- (u, u+v)-construction [i] based on
- digital (30, 37, 177148)-net over F9, using
- net defined by OOA [i] based on linear OOA(937, 177148, F9, 7, 7) (dual of [(177148, 7), 1239999, 8]-NRT-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OA(937, 531445, F9, 7) (dual of [531445, 531408, 8]-code), using
- discarding factors / shortening the dual code based on linear OA(937, 531447, F9, 7) (dual of [531447, 531410, 8]-code), using
- construction X applied to Ce(6) ⊂ Ce(5) [i] based on
- linear OA(937, 531441, F9, 7) (dual of [531441, 531404, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 531440 = 96−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(931, 531441, F9, 6) (dual of [531441, 531410, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 531440 = 96−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(90, 6, F9, 0) (dual of [6, 6, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(90, s, F9, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(6) ⊂ Ce(5) [i] based on
- discarding factors / shortening the dual code based on linear OA(937, 531447, F9, 7) (dual of [531447, 531410, 8]-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OA(937, 531445, F9, 7) (dual of [531445, 531408, 8]-code), using
- net defined by OOA [i] based on linear OOA(937, 177148, F9, 7, 7) (dual of [(177148, 7), 1239999, 8]-NRT-code), using
- digital (92, 106, 2396742)-net over F9, using
- trace code for nets [i] based on digital (39, 53, 1198371)-net over F81, using
- net defined by OOA [i] based on linear OOA(8153, 1198371, F81, 14, 14) (dual of [(1198371, 14), 16777141, 15]-NRT-code), using
- OA 7-folding and stacking [i] based on linear OA(8153, 8388597, F81, 14) (dual of [8388597, 8388544, 15]-code), using
- discarding factors / shortening the dual code based on linear OA(8153, large, F81, 14) (dual of [large, large−53, 15]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 21523360 | 814−1, defining interval I = [0,13], and designed minimum distance d ≥ |I|+1 = 15 [i]
- discarding factors / shortening the dual code based on linear OA(8153, large, F81, 14) (dual of [large, large−53, 15]-code), using
- OA 7-folding and stacking [i] based on linear OA(8153, 8388597, F81, 14) (dual of [8388597, 8388544, 15]-code), using
- net defined by OOA [i] based on linear OOA(8153, 1198371, F81, 14, 14) (dual of [(1198371, 14), 16777141, 15]-NRT-code), using
- trace code for nets [i] based on digital (39, 53, 1198371)-net over F81, using
- digital (30, 37, 177148)-net over F9, using
(129, 129+14, large)-Net over F9 — Digital
Digital (129, 143, large)-net over F9, using
- t-expansion [i] based on digital (124, 143, large)-net over F9, using
- 2 times m-reduction [i] based on digital (124, 145, large)-net over F9, using
(129, 129+14, large)-Net in Base 9 — Upper bound on s
There is no (129, 143, large)-net in base 9, because
- 12 times m-reduction [i] would yield (129, 131, large)-net in base 9, but