Information on Result #1191092
Digital (21, 28, 2734)-net over F8, using net defined by OOA based on linear OOA(828, 2734, F8, 7, 7) (dual of [(2734, 7), 19110, 8]-NRT-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OA(828, 8203, F8, 7) (dual of [8203, 8175, 8]-code), using
- discarding factors / shortening the dual code based on linear OA(828, 8204, F8, 7) (dual of [8204, 8176, 8]-code), using
- trace code [i] based on linear OA(6414, 4102, F64, 7) (dual of [4102, 4088, 8]-code), using
- construction X applied to C([0,3]) ⊂ C([0,2]) [i] based on
- linear OA(6413, 4097, F64, 7) (dual of [4097, 4084, 8]-code), using the expurgated narrow-sense BCH-code C(I) with length 4097 | 644−1, defining interval I = [0,3], and minimum distance d ≥ |{−3,−2,…,3}|+1 = 8 (BCH-bound) [i]
- linear OA(649, 4097, F64, 5) (dual of [4097, 4088, 6]-code), using the expurgated narrow-sense BCH-code C(I) with length 4097 | 644−1, defining interval I = [0,2], and minimum distance d ≥ |{−2,−1,0,1,2}|+1 = 6 (BCH-bound) [i]
- linear OA(641, 5, F64, 1) (dual of [5, 4, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(641, s, F64, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- construction X applied to C([0,3]) ⊂ C([0,2]) [i] based on
- trace code [i] based on linear OA(6414, 4102, F64, 7) (dual of [4102, 4088, 8]-code), using
- discarding factors / shortening the dual code based on linear OA(828, 8204, F8, 7) (dual of [8204, 8176, 8]-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 (120, 134, 2399476)-net over F8 | [i] | (u, u+v)-Construction for Nets | |
| 2 | Digital (127, 142, 2399476)-net over F8 | [i] | ||