Information on Result #1221863
Digital (23, 30, 178856)-net over F27, using (u, u+v)-construction based on
- digital (2, 5, 1708)-net over F27, using
- net defined by OOA [i] based on linear OOA(275, 1708, F27, 3, 3) (dual of [(1708, 3), 5119, 4]-NRT-code), using
- appending kth column [i] based on linear OOA(275, 1708, F27, 2, 3) (dual of [(1708, 2), 3411, 4]-NRT-code), using
- net defined by OOA [i] based on linear OOA(275, 1708, F27, 3, 3) (dual of [(1708, 3), 5119, 4]-NRT-code), using
- digital (18, 25, 177148)-net over F27, using
- net defined by OOA [i] based on linear OOA(2725, 177148, F27, 7, 7) (dual of [(177148, 7), 1240011, 8]-NRT-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OA(2725, 531445, F27, 7) (dual of [531445, 531420, 8]-code), using
- construction X applied to Ce(6) ⊂ Ce(5) [i] based on
- linear OA(2725, 531441, F27, 7) (dual of [531441, 531416, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 531440 = 274−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(2721, 531441, F27, 6) (dual of [531441, 531420, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 531440 = 274−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(270, 4, F27, 0) (dual of [4, 4, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(270, s, F27, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- construction X applied to Ce(6) ⊂ Ce(5) [i] based on
- OOA 3-folding and stacking with additional row [i] based on linear OA(2725, 531445, F27, 7) (dual of [531445, 531420, 8]-code), using
- net defined by OOA [i] based on linear OOA(2725, 177148, F27, 7, 7) (dual of [(177148, 7), 1240011, 8]-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 (82, 96, 1377227)-net over F27 | [i] | (u, u+v)-Construction for Nets | |
| 2 | Digital (86, 101, 1377227)-net over F27 | [i] | ||