Information on Result #1757430
Digital (210, 228, 1677749)-net over F2, using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(2228, 1677749, F2, 5, 18) (dual of [(1677749, 5), 8388517, 19]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(221, 29, F2, 5, 9) (dual of [(29, 5), 124, 10]-NRT-code), using
- extracting embedded OOA [i] based on digital (12, 21, 29)-net over F2, using
- linear OOA(2207, 1677720, F2, 5, 18) (dual of [(1677720, 5), 8388393, 19]-NRT-code), using
- OOA 5-folding [i] based on linear OA(2207, 8388600, F2, 18) (dual of [8388600, 8388393, 19]-code), using
- discarding factors / shortening the dual code based on linear OA(2207, large, F2, 18) (dual of [large, large−207, 19]-code), using
- the primitive narrow-sense BCH-code C(I) with length 8388607 = 223−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- discarding factors / shortening the dual code based on linear OA(2207, large, F2, 18) (dual of [large, large−207, 19]-code), using
- OOA 5-folding [i] based on linear OA(2207, 8388600, F2, 18) (dual of [8388600, 8388393, 19]-code), using
- linear OOA(221, 29, F2, 5, 9) (dual of [(29, 5), 124, 10]-NRT-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 (211, 229, 1677749)-net over F2 | [i] | Net Duplication | |
| 2 | Digital (212, 230, 1677749)-net over F2 | [i] | ||