Information on Result #1764870
Digital (139, 158, 398584)-net over F3, using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(3158, 398584, F3, 4, 19) (dual of [(398584, 4), 1594178, 20]-NRT-code), using
- OOA 4-folding [i] based on linear OA(3158, 1594336, F3, 19) (dual of [1594336, 1594178, 20]-code), using
- discarding factors / shortening the dual code based on linear OA(3158, 1594337, F3, 19) (dual of [1594337, 1594179, 20]-code), using
- construction X applied to Ce(18) ⊂ Ce(16) [i] based on
- linear OA(3157, 1594323, F3, 19) (dual of [1594323, 1594166, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 1594322 = 313−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(3144, 1594323, F3, 17) (dual of [1594323, 1594179, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 1594322 = 313−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(31, 14, F3, 1) (dual of [14, 13, 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 X applied to Ce(18) ⊂ Ce(16) [i] based on
- discarding factors / shortening the dual code based on linear OA(3158, 1594337, F3, 19) (dual of [1594337, 1594179, 20]-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 (140, 159, 398584)-net over F3 | [i] | Net Duplication | |
| 2 | Digital (141, 160, 398584)-net over F3 | [i] | ||