Information on Result #3248576
Digital (44, 76, 1026)-net over F128, using t-expansion based on digital (43, 76, 1026)-net over F128, using
- net defined by OOA [i] based on linear OOA(12876, 1026, F128, 33, 33) (dual of [(1026, 33), 33782, 34]-NRT-code), using
- OOA 16-folding and stacking with additional row [i] based on linear OA(12876, 16417, F128, 33) (dual of [16417, 16341, 34]-code), using
- discarding factors / shortening the dual code based on linear OA(12876, 16420, F128, 33) (dual of [16420, 16344, 34]-code), using
- construction X applied to C([0,16]) ⊂ C([0,10]) [i] based on
- linear OA(12865, 16385, F128, 33) (dual of [16385, 16320, 34]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385 | 1284−1, defining interval I = [0,16], and minimum distance d ≥ |{−16,−15,…,16}|+1 = 34 (BCH-bound) [i]
- linear OA(12841, 16385, F128, 21) (dual of [16385, 16344, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385 | 1284−1, defining interval I = [0,10], and minimum distance d ≥ |{−10,−9,…,10}|+1 = 22 (BCH-bound) [i]
- linear OA(12811, 35, F128, 11) (dual of [35, 24, 12]-code or 35-arc in PG(10,128)), using
- discarding factors / shortening the dual code based on linear OA(12811, 128, F128, 11) (dual of [128, 117, 12]-code or 128-arc in PG(10,128)), using
- Reed–Solomon code RS(117,128) [i]
- discarding factors / shortening the dual code based on linear OA(12811, 128, F128, 11) (dual of [128, 117, 12]-code or 128-arc in PG(10,128)), using
- construction X applied to C([0,16]) ⊂ C([0,10]) [i] based on
- discarding factors / shortening the dual code based on linear OA(12876, 16420, F128, 33) (dual of [16420, 16344, 34]-code), using
- OOA 16-folding and stacking with additional row [i] based on linear OA(12876, 16417, F128, 33) (dual of [16417, 16341, 34]-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 (45, 77, 1026)-net over F128 | [i] | Net Duplication | |
| 2 | Digital (46, 78, 1026)-net over F128 | [i] | ||