Best Known (41−7, 41, s)-Nets in Base 9
(41−7, 41, 354305)-Net over F9 — Constructive and digital
Digital (34, 41, 354305)-net over F9, using
- net defined by OOA [i] based on linear OOA(941, 354305, F9, 9, 7) (dual of [(354305, 9), 3188704, 8]-NRT-code), using
- OOA stacking with additional row [i] based on linear OOA(941, 354306, F9, 3, 7) (dual of [(354306, 3), 1062877, 8]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(93, 10, F9, 3, 3) (dual of [(10, 3), 27, 4]-NRT-code), using
- extended Reed–Solomon NRT-code RSe(3;27,9) [i]
- linear OOA(938, 354296, F9, 3, 7) (dual of [(354296, 3), 1062850, 8]-NRT-code), using
- OOA 3-folding [i] based on linear OA(938, 1062888, F9, 7) (dual of [1062888, 1062850, 8]-code), using
- trace code [i] based on linear OA(8119, 531444, F81, 7) (dual of [531444, 531425, 8]-code), using
- construction X applied to Ce(6) ⊂ Ce(5) [i] based on
- linear OA(8119, 531441, F81, 7) (dual of [531441, 531422, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 531440 = 813−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(8116, 531441, F81, 6) (dual of [531441, 531425, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 531440 = 813−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [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(6) ⊂ Ce(5) [i] based on
- trace code [i] based on linear OA(8119, 531444, F81, 7) (dual of [531444, 531425, 8]-code), using
- OOA 3-folding [i] based on linear OA(938, 1062888, F9, 7) (dual of [1062888, 1062850, 8]-code), using
- linear OOA(93, 10, F9, 3, 3) (dual of [(10, 3), 27, 4]-NRT-code), using
- (u, u+v)-construction [i] based on
- OOA stacking with additional row [i] based on linear OOA(941, 354306, F9, 3, 7) (dual of [(354306, 3), 1062877, 8]-NRT-code), using
(41−7, 41, 1241053)-Net over F9 — Digital
Digital (34, 41, 1241053)-net over F9, using
(41−7, 41, large)-Net in Base 9 — Upper bound on s
There is no (34, 41, large)-net in base 9, because
- 5 times m-reduction [i] would yield (34, 36, large)-net in base 9, but