Information on Result #1758529
Digital (211, 241, 10925)-net over F2, using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(2241, 10925, F2, 6, 30) (dual of [(10925, 6), 65309, 31]-NRT-code), using
- OOA 6-folding [i] based on linear OA(2241, 65550, F2, 30) (dual of [65550, 65309, 31]-code), using
- discarding factors / shortening the dual code based on linear OA(2241, 65552, F2, 30) (dual of [65552, 65311, 31]-code), using
- 1 times truncation [i] based on linear OA(2242, 65553, F2, 31) (dual of [65553, 65311, 32]-code), using
- construction X applied to Ce(30) ⊂ Ce(28) [i] based on
- linear OA(2241, 65536, F2, 31) (dual of [65536, 65295, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 65535 = 216−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(2225, 65536, F2, 29) (dual of [65536, 65311, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 65535 = 216−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(21, 17, F2, 1) (dual of [17, 16, 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 truncation [i] based on linear OA(2242, 65553, F2, 31) (dual of [65553, 65311, 32]-code), using
- discarding factors / shortening the dual code based on linear OA(2241, 65552, F2, 30) (dual of [65552, 65311, 31]-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 (212, 242, 10925)-net over F2 | [i] | Net Duplication | |
| 2 | Digital (213, 243, 10925)-net over F2 | [i] | ||
| 3 | Digital (214, 244, 10925)-net over F2 | [i] | ||