Information on Result #1753140
Digital (137, 168, 687)-net over F2, using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(2168, 687, F2, 3, 31) (dual of [(687, 3), 1893, 32]-NRT-code), using
- OOA 3-folding [i] based on linear OA(2168, 2061, F2, 31) (dual of [2061, 1893, 32]-code), using
- 1 times code embedding in larger space [i] based on linear OA(2167, 2060, F2, 31) (dual of [2060, 1893, 32]-code), using
- construction X applied to Ce(30) ⊂ Ce(28) [i] based on
- linear OA(2166, 2048, F2, 31) (dual of [2048, 1882, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 2047 = 211−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(2155, 2048, F2, 29) (dual of [2048, 1893, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 2047 = 211−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(21, 12, F2, 1) (dual of [12, 11, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(21, s, F2, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- construction X applied to Ce(30) ⊂ Ce(28) [i] based on
- 1 times code embedding in larger space [i] based on linear OA(2167, 2060, F2, 31) (dual of [2060, 1893, 32]-code), using
Mode: 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 (138, 169, 687)-net over F2 | [i] | Net Duplication | |
| 2 | Digital (139, 170, 687)-net over F2 | [i] | ||