Information on Result #1187908
Digital (222, 256, 61683)-net over F4, using net defined by OOA based on linear OOA(4256, 61683, F4, 34, 34) (dual of [(61683, 34), 2096966, 35]-NRT-code), using
- OA 17-folding and stacking [i] based on linear OA(4256, 1048611, F4, 34) (dual of [1048611, 1048355, 35]-code), using
- construction X applied to Ce(33) ⊂ Ce(29) [i] based on
- linear OA(4251, 1048576, F4, 34) (dual of [1048576, 1048325, 35]-code), using an extension Ce(33) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 410−1, defining interval I = [1,33], and designed minimum distance d ≥ |I|+1 = 34 [i]
- linear OA(4221, 1048576, F4, 30) (dual of [1048576, 1048355, 31]-code), using an extension Ce(29) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 410−1, defining interval I = [1,29], and designed minimum distance d ≥ |I|+1 = 30 [i]
- linear OA(45, 35, F4, 3) (dual of [35, 30, 4]-code or 35-cap in PG(4,4)), using
- discarding factors / shortening the dual code based on linear OA(45, 41, F4, 3) (dual of [41, 36, 4]-code or 41-cap in PG(4,4)), using
- construction X applied to Ce(33) ⊂ Ce(29) [i] based on
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 (223, 257, 61683)-net over F4 | [i] | Net Duplication | |
| 2 | Digital (224, 258, 61683)-net over F4 | [i] | ||
| 3 | Digital (225, 259, 61683)-net over F4 | [i] | ||
| 4 | Digital (226, 260, 61683)-net over F4 | [i] | ||