Information on Result #1755865
Digital (187, 208, 149803)-net over F2, using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(2208, 149803, F2, 7, 21) (dual of [(149803, 7), 1048413, 22]-NRT-code), using
- OOA 7-folding [i] based on linear OA(2208, 1048621, F2, 21) (dual of [1048621, 1048413, 22]-code), using
- discarding factors / shortening the dual code based on linear OA(2208, 1048624, F2, 21) (dual of [1048624, 1048416, 22]-code), using
- construction X applied to C([0,10]) ⊂ C([0,8]) [i] based on
- linear OA(2201, 1048577, F2, 21) (dual of [1048577, 1048376, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 1048577 | 240−1, defining interval I = [0,10], and minimum distance d ≥ |{−10,−9,…,10}|+1 = 22 (BCH-bound) [i]
- linear OA(2161, 1048577, F2, 17) (dual of [1048577, 1048416, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 1048577 | 240−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
- linear OA(27, 47, F2, 3) (dual of [47, 40, 4]-code or 47-cap in PG(6,2)), using
- discarding factors / shortening the dual code based on linear OA(27, 63, F2, 3) (dual of [63, 56, 4]-code or 63-cap in PG(6,2)), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 26−1, defining interval I = [0,1], and designed minimum distance d ≥ |I|+1 = 4 [i]
- discarding factors / shortening the dual code based on linear OA(27, 63, F2, 3) (dual of [63, 56, 4]-code or 63-cap in PG(6,2)), using
- construction X applied to C([0,10]) ⊂ C([0,8]) [i] based on
- discarding factors / shortening the dual code based on linear OA(2208, 1048624, F2, 21) (dual of [1048624, 1048416, 22]-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 (188, 209, 149803)-net over F2 | [i] | Net Duplication | |
| 2 | Digital (189, 210, 149803)-net over F2 | [i] | ||