Information on Result #1757508
Digital (210, 229, 1398129)-net over F2, using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(2229, 1398129, F2, 6, 19) (dual of [(1398129, 6), 8388545, 20]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(221, 29, F2, 6, 9) (dual of [(29, 6), 153, 10]-NRT-code), using
- extracting embedded OOA [i] based on digital (12, 21, 29)-net over F2, using
- linear OOA(2208, 1398100, F2, 6, 19) (dual of [(1398100, 6), 8388392, 20]-NRT-code), using
- OOA 6-folding [i] based on linear OA(2208, 8388600, F2, 19) (dual of [8388600, 8388392, 20]-code), using
- discarding factors / shortening the dual code based on linear OA(2208, large, F2, 19) (dual of [large, large−208, 20]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 8388607 = 223−1, defining interval I = [0,18], and designed minimum distance d ≥ |I|+1 = 20 [i]
- discarding factors / shortening the dual code based on linear OA(2208, large, F2, 19) (dual of [large, large−208, 20]-code), using
- OOA 6-folding [i] based on linear OA(2208, 8388600, F2, 19) (dual of [8388600, 8388392, 20]-code), using
- linear OOA(221, 29, F2, 6, 9) (dual of [(29, 6), 153, 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, 230, 1398129)-net over F2 | [i] | Net Duplication | |
| 2 | Digital (212, 231, 1398129)-net over F2 | [i] | ||