Best Known (56−10, 56, s)-Nets in Base 9
(56−10, 56, 212577)-Net over F9 — Constructive and digital
Digital (46, 56, 212577)-net over F9, using
- net defined by OOA [i] based on linear OOA(956, 212577, F9, 10, 10) (dual of [(212577, 10), 2125714, 11]-NRT-code), using
- OA 5-folding and stacking [i] based on linear OA(956, 1062885, F9, 10) (dual of [1062885, 1062829, 11]-code), using
- discarding factors / shortening the dual code based on linear OA(956, 1062888, F9, 10) (dual of [1062888, 1062832, 11]-code), using
- trace code [i] based on linear OA(8128, 531444, F81, 10) (dual of [531444, 531416, 11]-code), using
- construction X applied to Ce(9) ⊂ Ce(8) [i] based on
- linear OA(8128, 531441, F81, 10) (dual of [531441, 531413, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 531440 = 813−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(8125, 531441, F81, 9) (dual of [531441, 531416, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 531440 = 813−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [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(9) ⊂ Ce(8) [i] based on
- trace code [i] based on linear OA(8128, 531444, F81, 10) (dual of [531444, 531416, 11]-code), using
- discarding factors / shortening the dual code based on linear OA(956, 1062888, F9, 10) (dual of [1062888, 1062832, 11]-code), using
- OA 5-folding and stacking [i] based on linear OA(956, 1062885, F9, 10) (dual of [1062885, 1062829, 11]-code), using
(56−10, 56, 1062888)-Net over F9 — Digital
Digital (46, 56, 1062888)-net over F9, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(956, 1062888, F9, 10) (dual of [1062888, 1062832, 11]-code), using
- trace code [i] based on linear OA(8128, 531444, F81, 10) (dual of [531444, 531416, 11]-code), using
- construction X applied to Ce(9) ⊂ Ce(8) [i] based on
- linear OA(8128, 531441, F81, 10) (dual of [531441, 531413, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 531440 = 813−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(8125, 531441, F81, 9) (dual of [531441, 531416, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 531440 = 813−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [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(9) ⊂ Ce(8) [i] based on
- trace code [i] based on linear OA(8128, 531444, F81, 10) (dual of [531444, 531416, 11]-code), using
(56−10, 56, large)-Net in Base 9 — Upper bound on s
There is no (46, 56, large)-net in base 9, because
- 8 times m-reduction [i] would yield (46, 48, large)-net in base 9, but