Information on Result #3248575
Digital (42, 76, 965)-net over F128, using t-expansion based on digital (41, 76, 965)-net over F128, using
- net defined by OOA [i] based on linear OOA(12876, 965, F128, 35, 35) (dual of [(965, 35), 33699, 36]-NRT-code), using
- OOA 17-folding and stacking with additional row [i] based on linear OA(12876, 16406, F128, 35) (dual of [16406, 16330, 36]-code), using
- discarding factors / shortening the dual code based on linear OA(12876, 16408, F128, 35) (dual of [16408, 16332, 36]-code), using
- construction X applied to C([0,17]) ⊂ C([0,13]) [i] based on
- linear OA(12869, 16385, F128, 35) (dual of [16385, 16316, 36]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385 | 1284−1, defining interval I = [0,17], and minimum distance d ≥ |{−17,−16,…,17}|+1 = 36 (BCH-bound) [i]
- linear OA(12853, 16385, F128, 27) (dual of [16385, 16332, 28]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385 | 1284−1, defining interval I = [0,13], and minimum distance d ≥ |{−13,−12,…,13}|+1 = 28 (BCH-bound) [i]
- linear OA(1287, 23, F128, 7) (dual of [23, 16, 8]-code or 23-arc in PG(6,128)), using
- discarding factors / shortening the dual code based on linear OA(1287, 128, F128, 7) (dual of [128, 121, 8]-code or 128-arc in PG(6,128)), using
- Reed–Solomon code RS(121,128) [i]
- discarding factors / shortening the dual code based on linear OA(1287, 128, F128, 7) (dual of [128, 121, 8]-code or 128-arc in PG(6,128)), using
- construction X applied to C([0,17]) ⊂ C([0,13]) [i] based on
- discarding factors / shortening the dual code based on linear OA(12876, 16408, F128, 35) (dual of [16408, 16332, 36]-code), using
- OOA 17-folding and stacking with additional row [i] based on linear OA(12876, 16406, F128, 35) (dual of [16406, 16330, 36]-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 (43, 77, 965)-net over F128 | [i] | Net Duplication | |
| 2 | Digital (44, 78, 965)-net over F128 | [i] | ||