Information on Result #1217260
Digital (77, 86, 4725744)-net over F9, using (u, u+v)-construction based on
- digital (16, 20, 531444)-net over F9, using
- net defined by OOA [i] based on linear OOA(920, 531444, F9, 4, 4) (dual of [(531444, 4), 2125756, 5]-NRT-code), using
- appending kth column [i] based on linear OOA(920, 531444, F9, 3, 4) (dual of [(531444, 3), 1594312, 5]-NRT-code), using
- OA 2-folding and stacking [i] based on linear OA(920, 1062888, F9, 4) (dual of [1062888, 1062868, 5]-code), using
- trace code [i] based on linear OA(8110, 531444, F81, 4) (dual of [531444, 531434, 5]-code), using
- construction X applied to Ce(3) ⊂ Ce(2) [i] based on
- linear OA(8110, 531441, F81, 4) (dual of [531441, 531431, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 531440 = 813−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [i]
- linear OA(817, 531441, F81, 3) (dual of [531441, 531434, 4]-code or 531441-cap in PG(6,81)), using an extension Ce(2) of the primitive narrow-sense BCH-code C(I) with length 531440 = 813−1, defining interval I = [1,2], and designed minimum distance d ≥ |I|+1 = 3 [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) for arbitrarily large s, using
- construction X applied to Ce(3) ⊂ Ce(2) [i] based on
- trace code [i] based on linear OA(8110, 531444, F81, 4) (dual of [531444, 531434, 5]-code), using
- OA 2-folding and stacking [i] based on linear OA(920, 1062888, F9, 4) (dual of [1062888, 1062868, 5]-code), using
- appending kth column [i] based on linear OOA(920, 531444, F9, 3, 4) (dual of [(531444, 3), 1594312, 5]-NRT-code), using
- net defined by OOA [i] based on linear OOA(920, 531444, F9, 4, 4) (dual of [(531444, 4), 2125756, 5]-NRT-code), using
- digital (57, 66, 4194300)-net over F9, using
- net defined by OOA [i] based on linear OOA(966, 4194300, F9, 10, 9) (dual of [(4194300, 10), 41942934, 10]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OOA(966, 8388601, F9, 2, 9) (dual of [(8388601, 2), 16777136, 10]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(966, 8388602, F9, 2, 9) (dual of [(8388602, 2), 16777138, 10]-NRT-code), using
- trace code [i] based on linear OOA(8133, 4194301, F81, 2, 9) (dual of [(4194301, 2), 8388569, 10]-NRT-code), using
- OOA 2-folding [i] based on linear OA(8133, 8388602, F81, 9) (dual of [8388602, 8388569, 10]-code), using
- discarding factors / shortening the dual code based on linear OA(8133, large, F81, 9) (dual of [large, large−33, 10]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 21523361 | 818−1, defining interval I = [0,4], and minimum distance d ≥ |{−4,−3,…,4}|+1 = 10 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(8133, large, F81, 9) (dual of [large, large−33, 10]-code), using
- OOA 2-folding [i] based on linear OA(8133, 8388602, F81, 9) (dual of [8388602, 8388569, 10]-code), using
- trace code [i] based on linear OOA(8133, 4194301, F81, 2, 9) (dual of [(4194301, 2), 8388569, 10]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(966, 8388602, F9, 2, 9) (dual of [(8388602, 2), 16777138, 10]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OOA(966, 8388601, F9, 2, 9) (dual of [(8388601, 2), 16777136, 10]-NRT-code), using
- net defined by OOA [i] based on linear OOA(966, 4194300, F9, 10, 9) (dual of [(4194300, 10), 41942934, 10]-NRT-code), using
Mode: Constructive and linear.
Optimality
Show details for fixed k and m, k and s, k and t, m and s, m and t, t and s.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Digital (78, 87, 4725744)-net over F9 | [i] | Net Duplication | |