Best Known (71, 86, s)-Nets in Base 9
(71, 86, 151841)-Net over F9 — Constructive and digital
Digital (71, 86, 151841)-net over F9, using
- net defined by OOA [i] based on linear OOA(986, 151841, F9, 15, 15) (dual of [(151841, 15), 2277529, 16]-NRT-code), using
- OOA 7-folding and stacking with additional row [i] based on linear OA(986, 1062888, F9, 15) (dual of [1062888, 1062802, 16]-code), using
- trace code [i] based on linear OA(8143, 531444, F81, 15) (dual of [531444, 531401, 16]-code), using
- construction X applied to Ce(14) ⊂ Ce(13) [i] based on
- linear OA(8143, 531441, F81, 15) (dual of [531441, 531398, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 531440 = 813−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(8140, 531441, F81, 14) (dual of [531441, 531401, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 531440 = 813−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(810, 3, F81, 0) (dual of [3, 3, 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(14) ⊂ Ce(13) [i] based on
- trace code [i] based on linear OA(8143, 531444, F81, 15) (dual of [531444, 531401, 16]-code), using
- OOA 7-folding and stacking with additional row [i] based on linear OA(986, 1062888, F9, 15) (dual of [1062888, 1062802, 16]-code), using
(71, 86, 1062888)-Net over F9 — Digital
Digital (71, 86, 1062888)-net over F9, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(986, 1062888, F9, 15) (dual of [1062888, 1062802, 16]-code), using
- trace code [i] based on linear OA(8143, 531444, F81, 15) (dual of [531444, 531401, 16]-code), using
- construction X applied to Ce(14) ⊂ Ce(13) [i] based on
- linear OA(8143, 531441, F81, 15) (dual of [531441, 531398, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 531440 = 813−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(8140, 531441, F81, 14) (dual of [531441, 531401, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 531440 = 813−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(810, 3, F81, 0) (dual of [3, 3, 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(14) ⊂ Ce(13) [i] based on
- trace code [i] based on linear OA(8143, 531444, F81, 15) (dual of [531444, 531401, 16]-code), using
(71, 86, large)-Net in Base 9 — Upper bound on s
There is no (71, 86, large)-net in base 9, because
- 13 times m-reduction [i] would yield (71, 73, large)-net in base 9, but