Information on Result #1207919
Digital (171, 181, 7424651)-net over F3, using (u, u+v)-construction based on
- digital (38, 43, 2391491)-net over F3, using
- net defined by OOA [i] based on linear OOA(343, 2391491, F3, 5, 5) (dual of [(2391491, 5), 11957412, 6]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OA(343, 4782983, F3, 5) (dual of [4782983, 4782940, 6]-code), using
- construction X applied to Ce(4) ⊂ Ce(3) [i] based on
- linear OA(343, 4782969, F3, 5) (dual of [4782969, 4782926, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 314−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(329, 4782969, F3, 4) (dual of [4782969, 4782940, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 314−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [i]
- linear OA(30, 14, F3, 0) (dual of [14, 14, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(30, s, F3, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- construction X applied to Ce(4) ⊂ Ce(3) [i] based on
- OOA 2-folding and stacking with additional row [i] based on linear OA(343, 4782983, F3, 5) (dual of [4782983, 4782940, 6]-code), using
- net defined by OOA [i] based on linear OOA(343, 2391491, F3, 5, 5) (dual of [(2391491, 5), 11957412, 6]-NRT-code), using
- digital (128, 138, 5033160)-net over F3, using
- trace code for nets [i] based on digital (36, 46, 1677720)-net over F27, using
- net defined by OOA [i] based on linear OOA(2746, 1677720, F27, 10, 10) (dual of [(1677720, 10), 16777154, 11]-NRT-code), using
- OA 5-folding and stacking [i] based on linear OA(2746, 8388600, F27, 10) (dual of [8388600, 8388554, 11]-code), using
- discarding factors / shortening the dual code based on linear OA(2746, large, F27, 10) (dual of [large, large−46, 11]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 14348906 = 275−1, defining interval I = [0,9], and designed minimum distance d ≥ |I|+1 = 11 [i]
- discarding factors / shortening the dual code based on linear OA(2746, large, F27, 10) (dual of [large, large−46, 11]-code), using
- OA 5-folding and stacking [i] based on linear OA(2746, 8388600, F27, 10) (dual of [8388600, 8388554, 11]-code), using
- net defined by OOA [i] based on linear OOA(2746, 1677720, F27, 10, 10) (dual of [(1677720, 10), 16777154, 11]-NRT-code), using
- trace code for nets [i] based on digital (36, 46, 1677720)-net over F27, 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 | Linear OOA(3181, 7424651, F3, 5, 10) (dual of [(7424651, 5), 37123074, 11]-NRT-code) | [i] | Extracting Embedded OOA | |