Information on Result #1179670
Digital (8, 12, 131138)-net over F64, using net defined by OOA based on linear OOA(6412, 131138, F64, 4, 4) (dual of [(131138, 4), 524540, 5]-NRT-code), using
- appending kth column [i] based on linear OOA(6412, 131138, F64, 3, 4) (dual of [(131138, 3), 393402, 5]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(642, 65, F64, 3, 2) (dual of [(65, 3), 193, 3]-NRT-code), using
- extended Reed–Solomon NRT-code RSe(3;193,64) [i]
- linear OOA(6410, 131073, F64, 3, 4) (dual of [(131073, 3), 393209, 5]-NRT-code), using
- OA 2-folding and stacking [i] based on linear OA(6410, 262146, F64, 4) (dual of [262146, 262136, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(6410, 262147, F64, 4) (dual of [262147, 262137, 5]-code), using
- construction X applied to Ce(3) ⊂ Ce(2) [i] based on
- linear OA(6410, 262144, F64, 4) (dual of [262144, 262134, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [i]
- linear OA(647, 262144, F64, 3) (dual of [262144, 262137, 4]-code or 262144-cap in PG(6,64)), using an extension Ce(2) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,2], and designed minimum distance d ≥ |I|+1 = 3 [i]
- linear OA(640, 3, F64, 0) (dual of [3, 3, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(640, s, F64, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- construction X applied to Ce(3) ⊂ Ce(2) [i] based on
- discarding factors / shortening the dual code based on linear OA(6410, 262147, F64, 4) (dual of [262147, 262137, 5]-code), using
- OA 2-folding and stacking [i] based on linear OA(6410, 262146, F64, 4) (dual of [262146, 262136, 5]-code), using
- linear OOA(642, 65, F64, 3, 2) (dual of [(65, 3), 193, 3]-NRT-code), using
- (u, u+v)-construction [i] based on
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 (33, 41, 2228288)-net over F64 | [i] | (u, u+v)-Construction for Nets | |
| 2 | Digital (36, 45, 2228288)-net over F64 | [i] | ||
| 3 | Digital (76, 90, 2527880)-net over F64 | [i] | Generalized (u, u+v)-Construction for Nets | |
| 4 | Digital (69, 82, 2927338)-net over F64 | [i] | ||
| 5 | Digital (66, 78, 2927338)-net over F64 | [i] | ||