Information on Result #1192810
Digital (138, 166, 37450)-net over F8, using net defined by OOA based on linear OOA(8166, 37450, F8, 28, 28) (dual of [(37450, 28), 1048434, 29]-NRT-code), using
- OA 14-folding and stacking [i] based on linear OA(8166, 524300, F8, 28) (dual of [524300, 524134, 29]-code), using
- discarding factors / shortening the dual code based on linear OA(8166, 524302, F8, 28) (dual of [524302, 524136, 29]-code), using
- trace code [i] based on linear OA(6483, 262151, F64, 28) (dual of [262151, 262068, 29]-code), using
- construction X applied to Ce(27) ⊂ Ce(25) [i] based on
- linear OA(6482, 262144, F64, 28) (dual of [262144, 262062, 29]-code), using an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [i]
- linear OA(6476, 262144, F64, 26) (dual of [262144, 262068, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [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 Ce(27) ⊂ Ce(25) [i] based on
- trace code [i] based on linear OA(6483, 262151, F64, 28) (dual of [262151, 262068, 29]-code), using
- discarding factors / shortening the dual code based on linear OA(8166, 524302, F8, 28) (dual of [524302, 524136, 29]-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 (139, 167, 37450)-net over F8 | [i] | Net Duplication | |
| 2 | Digital (140, 168, 37450)-net over F8 | [i] | ||