Information on Result #1221840
Digital (19, 25, 177878)-net over F27, using (u, u+v)-construction based on
- digital (1, 4, 730)-net over F27, using
- net defined by OOA [i] based on linear OOA(274, 730, F27, 3, 3) (dual of [(730, 3), 2186, 4]-NRT-code), using
- appending kth column [i] based on linear OOA(274, 730, F27, 2, 3) (dual of [(730, 2), 1456, 4]-NRT-code), using
- net defined by OOA [i] based on linear OOA(274, 730, F27, 3, 3) (dual of [(730, 3), 2186, 4]-NRT-code), using
- digital (15, 21, 177148)-net over F27, using
- net defined by OOA [i] based on linear OOA(2721, 177148, F27, 6, 6) (dual of [(177148, 6), 1062867, 7]-NRT-code), using
- OA 3-folding and stacking [i] based on linear OA(2721, 531444, F27, 6) (dual of [531444, 531423, 7]-code), using
- discarding factors / shortening the dual code based on linear OA(2721, 531445, F27, 6) (dual of [531445, 531424, 7]-code), using
- construction X applied to Ce(5) ⊂ Ce(4) [i] based on
- 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(2717, 531441, F27, 5) (dual of [531441, 531424, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 531440 = 274−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [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(5) ⊂ Ce(4) [i] based on
- discarding factors / shortening the dual code based on linear OA(2721, 531445, F27, 6) (dual of [531445, 531424, 7]-code), using
- OA 3-folding and stacking [i] based on linear OA(2721, 531444, F27, 6) (dual of [531444, 531423, 7]-code), using
- net defined by OOA [i] based on linear OOA(2721, 177148, F27, 6, 6) (dual of [(177148, 6), 1062867, 7]-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 (69, 81, 1575978)-net over F27 | [i] | (u, u+v)-Construction for Nets | |
| 2 | Digital (73, 86, 1575978)-net over F27 | [i] | ||