Information on Result #1187360
Digital (111, 136, 1368)-net over F4, using net defined by OOA based on linear OOA(4136, 1368, F4, 25, 25) (dual of [(1368, 25), 34064, 26]-NRT-code), using
- OOA 12-folding and stacking with additional row [i] based on linear OA(4136, 16417, F4, 25) (dual of [16417, 16281, 26]-code), using
- construction XX applied to Ce(24) ⊂ Ce(20) ⊂ Ce(18) [i] based on
- linear OA(4127, 16384, F4, 25) (dual of [16384, 16257, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(4106, 16384, F4, 21) (dual of [16384, 16278, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(499, 16384, F4, 19) (dual of [16384, 16285, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(45, 29, F4, 3) (dual of [29, 24, 4]-code or 29-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
- linear OA(41, 4, F4, 1) (dual of [4, 3, 2]-code), using
- Reed–Solomon code RS(3,4) [i]
- construction XX applied to Ce(24) ⊂ Ce(20) ⊂ Ce(18) [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 (112, 136, 1368)-net over F4 | [i] | t-Expansion | |
| 2 | Digital (112, 137, 1368)-net over F4 | [i] | Net Duplication | |
| 3 | Digital (113, 138, 1368)-net over F4 | [i] | ||
| 4 | Digital (111, 135, 1368)-net over F4 | [i] | m-Reduction | |