Best Known (119−26, 119, s)-Nets in Base 9
(119−26, 119, 4543)-Net over F9 — Constructive and digital
Digital (93, 119, 4543)-net over F9, using
- 92 times duplication [i] based on digital (91, 117, 4543)-net over F9, using
- net defined by OOA [i] based on linear OOA(9117, 4543, F9, 26, 26) (dual of [(4543, 26), 118001, 27]-NRT-code), using
- OA 13-folding and stacking [i] based on linear OA(9117, 59059, F9, 26) (dual of [59059, 58942, 27]-code), using
- discarding factors / shortening the dual code based on linear OA(9117, 59060, F9, 26) (dual of [59060, 58943, 27]-code), using
- construction X applied to Ce(25) ⊂ Ce(23) [i] based on
- linear OA(9116, 59049, F9, 26) (dual of [59049, 58933, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 59048 = 95−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(9106, 59049, F9, 24) (dual of [59049, 58943, 25]-code), using an extension Ce(23) of the primitive narrow-sense BCH-code C(I) with length 59048 = 95−1, defining interval I = [1,23], and designed minimum distance d ≥ |I|+1 = 24 [i]
- linear OA(91, 11, F9, 1) (dual of [11, 10, 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(25) ⊂ Ce(23) [i] based on
- discarding factors / shortening the dual code based on linear OA(9117, 59060, F9, 26) (dual of [59060, 58943, 27]-code), using
- OA 13-folding and stacking [i] based on linear OA(9117, 59059, F9, 26) (dual of [59059, 58942, 27]-code), using
- net defined by OOA [i] based on linear OOA(9117, 4543, F9, 26, 26) (dual of [(4543, 26), 118001, 27]-NRT-code), using
(119−26, 119, 59067)-Net over F9 — Digital
Digital (93, 119, 59067)-net over F9, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(9119, 59067, F9, 26) (dual of [59067, 58948, 27]-code), using
- construction X applied to Ce(25) ⊂ Ce(22) [i] based on
- linear OA(9116, 59049, F9, 26) (dual of [59049, 58933, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 59048 = 95−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(9101, 59049, F9, 23) (dual of [59049, 58948, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 59048 = 95−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(93, 18, F9, 2) (dual of [18, 15, 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(25) ⊂ Ce(22) [i] based on
(119−26, 119, large)-Net in Base 9 — Upper bound on s
There is no (93, 119, large)-net in base 9, because
- 24 times m-reduction [i] would yield (93, 95, large)-net in base 9, but