Information on Result #3248445
Digital (40, 70, 1094)-net over F128, using t-expansion based on digital (39, 70, 1094)-net over F128, using
- net defined by OOA [i] based on linear OOA(12870, 1094, F128, 31, 31) (dual of [(1094, 31), 33844, 32]-NRT-code), using
- OOA 15-folding and stacking with additional row [i] based on linear OA(12870, 16411, F128, 31) (dual of [16411, 16341, 32]-code), using
- discarding factors / shortening the dual code based on linear OA(12870, 16414, F128, 31) (dual of [16414, 16344, 32]-code), using
- construction X applied to C([0,15]) ⊂ C([0,10]) [i] based on
- linear OA(12861, 16385, F128, 31) (dual of [16385, 16324, 32]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385 | 1284−1, defining interval I = [0,15], and minimum distance d ≥ |{−15,−14,…,15}|+1 = 32 (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(1289, 29, F128, 9) (dual of [29, 20, 10]-code or 29-arc in PG(8,128)), using
- discarding factors / shortening the dual code based on linear OA(1289, 128, F128, 9) (dual of [128, 119, 10]-code or 128-arc in PG(8,128)), using
- Reed–Solomon code RS(119,128) [i]
- discarding factors / shortening the dual code based on linear OA(1289, 128, F128, 9) (dual of [128, 119, 10]-code or 128-arc in PG(8,128)), using
- construction X applied to C([0,15]) ⊂ C([0,10]) [i] based on
- discarding factors / shortening the dual code based on linear OA(12870, 16414, F128, 31) (dual of [16414, 16344, 32]-code), using
- OOA 15-folding and stacking with additional row [i] based on linear OA(12870, 16411, F128, 31) (dual of [16411, 16341, 32]-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 (41, 71, 1094)-net over F128 | [i] | Net Duplication | |