Information on Result #1763196
Digital (114, 128, 1594328)-net over F3, using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(3128, 1594328, F3, 3, 14) (dual of [(1594328, 3), 4782856, 15]-NRT-code), using
- OOA 3-folding [i] based on linear OA(3128, 4782984, F3, 14) (dual of [4782984, 4782856, 15]-code), using
- discarding factors / shortening the dual code based on linear OA(3128, 4782985, F3, 14) (dual of [4782985, 4782857, 15]-code), using
- construction X4 applied to Ce(13) ⊂ Ce(12) [i] based on
- linear OA(3127, 4782969, F3, 14) (dual of [4782969, 4782842, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 314−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(3113, 4782969, F3, 13) (dual of [4782969, 4782856, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 314−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(315, 16, F3, 15) (dual of [16, 1, 16]-code or 16-arc in PG(14,3)), using
- dual of repetition code with length 16 [i]
- linear OA(31, 16, F3, 1) (dual of [16, 15, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(31, s, F3, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- construction X4 applied to Ce(13) ⊂ Ce(12) [i] based on
- discarding factors / shortening the dual code based on linear OA(3128, 4782985, F3, 14) (dual of [4782985, 4782857, 15]-code), using
Mode: 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 (115, 129, 1594328)-net over F3 | [i] | Net Duplication | |