Information on Result #1192546
Digital (114, 137, 47664)-net over F8, using net defined by OOA based on linear OOA(8137, 47664, F8, 23, 23) (dual of [(47664, 23), 1096135, 24]-NRT-code), using
- OOA 11-folding and stacking with additional row [i] based on linear OA(8137, 524305, F8, 23) (dual of [524305, 524168, 24]-code), using
- 1 times code embedding in larger space [i] based on linear OA(8136, 524304, F8, 23) (dual of [524304, 524168, 24]-code), using
- trace code [i] based on linear OA(6468, 262152, F64, 23) (dual of [262152, 262084, 24]-code), using
- construction X applied to C([0,11]) ⊂ C([0,10]) [i] based on
- linear OA(6467, 262145, F64, 23) (dual of [262145, 262078, 24]-code), using the expurgated narrow-sense BCH-code C(I) with length 262145 | 646−1, defining interval I = [0,11], and minimum distance d ≥ |{−11,−10,…,11}|+1 = 24 (BCH-bound) [i]
- linear OA(6461, 262145, F64, 21) (dual of [262145, 262084, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 262145 | 646−1, defining interval I = [0,10], and minimum distance d ≥ |{−10,−9,…,10}|+1 = 22 (BCH-bound) [i]
- linear OA(641, 7, F64, 1) (dual of [7, 6, 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([0,11]) ⊂ C([0,10]) [i] based on
- trace code [i] based on linear OA(6468, 262152, F64, 23) (dual of [262152, 262084, 24]-code), using
- 1 times code embedding in larger space [i] based on linear OA(8136, 524304, F8, 23) (dual of [524304, 524168, 24]-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 (115, 138, 47664)-net over F8 | [i] | Net Duplication | |
| 2 | Digital (116, 139, 47664)-net over F8 | [i] | ||