Best Known (130−24, 130, s)-Nets in Base 9
(130−24, 130, 44288)-Net over F9 — Constructive and digital
Digital (106, 130, 44288)-net over F9, using
- 91 times duplication [i] based on digital (105, 129, 44288)-net over F9, using
- net defined by OOA [i] based on linear OOA(9129, 44288, F9, 24, 24) (dual of [(44288, 24), 1062783, 25]-NRT-code), using
- OA 12-folding and stacking [i] based on linear OA(9129, 531456, F9, 24) (dual of [531456, 531327, 25]-code), using
- construction XX applied to Ce(23) ⊂ Ce(21) ⊂ Ce(20) [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(9109, 531441, F9, 21) (dual of [531441, 531332, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 531440 = 96−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(91, 14, F9, 1) (dual of [14, 13, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(91, 728, F9, 1) (dual of [728, 727, 2]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 93−1, defining interval I = [0,0], and designed minimum distance d ≥ |I|+1 = 2 [i]
- discarding factors / shortening the dual code based on linear OA(91, 728, F9, 1) (dual of [728, 727, 2]-code), using
- linear OA(90, 1, F9, 0) (dual of [1, 1, 1]-code), using
- dual of repetition code with length 1 [i]
- construction XX applied to Ce(23) ⊂ Ce(21) ⊂ Ce(20) [i] based on
- OA 12-folding and stacking [i] based on linear OA(9129, 531456, F9, 24) (dual of [531456, 531327, 25]-code), using
- net defined by OOA [i] based on linear OOA(9129, 44288, F9, 24, 24) (dual of [(44288, 24), 1062783, 25]-NRT-code), using
(130−24, 130, 445740)-Net over F9 — Digital
Digital (106, 130, 445740)-net over F9, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(9130, 445740, F9, 24) (dual of [445740, 445610, 25]-code), using
- discarding factors / shortening the dual code based on linear OA(9130, 531462, F9, 24) (dual of [531462, 531332, 25]-code), using
- construction X applied to Ce(23) ⊂ Ce(20) [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(9109, 531441, F9, 21) (dual of [531441, 531332, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 531440 = 96−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(93, 21, F9, 2) (dual of [21, 18, 3]-code), using
- discarding factors / shortening the dual code based on linear OA(93, 80, F9, 2) (dual of [80, 77, 3]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 80 = 92−1, defining interval I = [0,1], and designed minimum distance d ≥ |I|+1 = 3 [i]
- discarding factors / shortening the dual code based on linear OA(93, 80, F9, 2) (dual of [80, 77, 3]-code), using
- construction X applied to Ce(23) ⊂ Ce(20) [i] based on
- discarding factors / shortening the dual code based on linear OA(9130, 531462, F9, 24) (dual of [531462, 531332, 25]-code), using
(130−24, 130, large)-Net in Base 9 — Upper bound on s
There is no (106, 130, large)-net in base 9, because
- 22 times m-reduction [i] would yield (106, 108, large)-net in base 9, but