Information on Result #1768898
Digital (189, 212, 1195746)-net over F3, using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(3212, 1195746, F3, 4, 23) (dual of [(1195746, 4), 4782772, 24]-NRT-code), using
- OOA 4-folding [i] based on linear OA(3212, 4782984, F3, 23) (dual of [4782984, 4782772, 24]-code), using
- 1 times code embedding in larger space [i] based on linear OA(3211, 4782983, F3, 23) (dual of [4782983, 4782772, 24]-code), using
- construction X applied to Ce(22) ⊂ Ce(21) [i] based on
- linear OA(3211, 4782969, F3, 23) (dual of [4782969, 4782758, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 314−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(3197, 4782969, F3, 22) (dual of [4782969, 4782772, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 314−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [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(22) ⊂ Ce(21) [i] based on
- 1 times code embedding in larger space [i] based on linear OA(3211, 4782983, F3, 23) (dual of [4782983, 4782772, 24]-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 (190, 213, 1195746)-net over F3 | [i] | Net Duplication | |
| 2 | Digital (191, 214, 1195746)-net over F3 | [i] | ||