Information on Result #1767327
Digital (164, 193, 19687)-net over F3, using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(3193, 19687, F3, 3, 29) (dual of [(19687, 3), 58868, 30]-NRT-code), using
- OOA 3-folding [i] based on linear OA(3193, 59061, F3, 29) (dual of [59061, 58868, 30]-code), using
- 2 times code embedding in larger space [i] based on linear OA(3191, 59059, F3, 29) (dual of [59059, 58868, 30]-code), using
- construction X applied to Ce(28) ⊂ Ce(27) [i] based on
- linear OA(3191, 59049, F3, 29) (dual of [59049, 58858, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 59048 = 310−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(3181, 59049, F3, 28) (dual of [59049, 58868, 29]-code), using an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 59048 = 310−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [i]
- linear OA(30, 10, F3, 0) (dual of [10, 10, 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(28) ⊂ Ce(27) [i] based on
- 2 times code embedding in larger space [i] based on linear OA(3191, 59059, F3, 29) (dual of [59059, 58868, 30]-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 (165, 194, 19687)-net over F3 | [i] | Net Duplication | |