Information on Result #1184828
Digital (158, 178, 159437)-net over F3, using net defined by OOA based on linear OOA(3178, 159437, F3, 20, 20) (dual of [(159437, 20), 3188562, 21]-NRT-code), using
- OA 10-folding and stacking [i] based on linear OA(3178, 1594370, F3, 20) (dual of [1594370, 1594192, 21]-code), using
- 2 times code embedding in larger space [i] based on linear OA(3176, 1594368, F3, 20) (dual of [1594368, 1594192, 21]-code), using
- construction X applied to Ce(19) ⊂ Ce(15) [i] based on
- linear OA(3170, 1594323, F3, 20) (dual of [1594323, 1594153, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 1594322 = 313−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(3131, 1594323, F3, 16) (dual of [1594323, 1594192, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 1594322 = 313−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(36, 45, F3, 3) (dual of [45, 39, 4]-code or 45-cap in PG(5,3)), using
- discarding factors / shortening the dual code based on linear OA(36, 48, F3, 3) (dual of [48, 42, 4]-code or 48-cap in PG(5,3)), using
- construction X applied to Ce(19) ⊂ Ce(15) [i] based on
- 2 times code embedding in larger space [i] based on linear OA(3176, 1594368, F3, 20) (dual of [1594368, 1594192, 21]-code), 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 | Digital (159, 179, 159437)-net over F3 | [i] | Net Duplication | |
| 2 | Digital (160, 180, 159437)-net over F3 | [i] | ||