Best Known (128−24, 128, s)-Nets in Base 9
(128−24, 128, 44287)-Net over F9 — Constructive and digital
Digital (104, 128, 44287)-net over F9, using
- 91 times duplication [i] based on digital (103, 127, 44287)-net over F9, using
- net defined by OOA [i] based on linear OOA(9127, 44287, F9, 24, 24) (dual of [(44287, 24), 1062761, 25]-NRT-code), using
- OA 12-folding and stacking [i] based on linear OA(9127, 531444, F9, 24) (dual of [531444, 531317, 25]-code), using
- discarding factors / shortening the dual code based on linear OA(9127, 531447, F9, 24) (dual of [531447, 531320, 25]-code), using
- construction X applied to Ce(23) ⊂ Ce(22) [i] based on
- linear OA(9127, 531441, F9, 24) (dual of [531441, 531314, 25]-code), using an extension Ce(23) of the primitive narrow-sense BCH-code C(I) with length 531440 = 96−1, defining interval I = [1,23], and designed minimum distance d ≥ |I|+1 = 24 [i]
- linear OA(9121, 531441, F9, 23) (dual of [531441, 531320, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 531440 = 96−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [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(23) ⊂ Ce(22) [i] based on
- discarding factors / shortening the dual code based on linear OA(9127, 531447, F9, 24) (dual of [531447, 531320, 25]-code), using
- OA 12-folding and stacking [i] based on linear OA(9127, 531444, F9, 24) (dual of [531444, 531317, 25]-code), using
- net defined by OOA [i] based on linear OOA(9127, 44287, F9, 24, 24) (dual of [(44287, 24), 1062761, 25]-NRT-code), using
(128−24, 128, 365031)-Net over F9 — Digital
Digital (104, 128, 365031)-net over F9, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(9128, 365031, F9, 24) (dual of [365031, 364903, 25]-code), using
- discarding factors / shortening the dual code based on linear OA(9128, 531454, F9, 24) (dual of [531454, 531326, 25]-code), using
- construction X applied to Ce(23) ⊂ Ce(21) [i] based on
- linear OA(9127, 531441, F9, 24) (dual of [531441, 531314, 25]-code), using an extension Ce(23) of the primitive narrow-sense BCH-code C(I) with length 531440 = 96−1, defining interval I = [1,23], and designed minimum distance d ≥ |I|+1 = 24 [i]
- linear OA(9115, 531441, F9, 22) (dual of [531441, 531326, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 531440 = 96−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(91, 13, F9, 1) (dual of [13, 12, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(91, s, F9, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to Ce(23) ⊂ Ce(21) [i] based on
- discarding factors / shortening the dual code based on linear OA(9128, 531454, F9, 24) (dual of [531454, 531326, 25]-code), using
(128−24, 128, large)-Net in Base 9 — Upper bound on s
There is no (104, 128, large)-net in base 9, because
- 22 times m-reduction [i] would yield (104, 106, large)-net in base 9, but