Information on Result #1757103
Digital (199, 224, 37455)-net over F2, using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(2224, 37455, F2, 7, 25) (dual of [(37455, 7), 261961, 26]-NRT-code), using
- OOA 7-folding [i] based on linear OA(2224, 262185, F2, 25) (dual of [262185, 261961, 26]-code), using
- discarding factors / shortening the dual code based on linear OA(2224, 262188, F2, 25) (dual of [262188, 261964, 26]-code), using
- construction X applied to C([0,12]) ⊂ C([0,10]) [i] based on
- linear OA(2217, 262145, F2, 25) (dual of [262145, 261928, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 262145 | 236−1, defining interval I = [0,12], and minimum distance d ≥ |{−12,−11,…,12}|+1 = 26 (BCH-bound) [i]
- linear OA(2181, 262145, F2, 21) (dual of [262145, 261964, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 262145 | 236−1, defining interval I = [0,10], and minimum distance d ≥ |{−10,−9,…,10}|+1 = 22 (BCH-bound) [i]
- linear OA(27, 43, F2, 3) (dual of [43, 36, 4]-code or 43-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([0,12]) ⊂ C([0,10]) [i] based on
- discarding factors / shortening the dual code based on linear OA(2224, 262188, F2, 25) (dual of [262188, 261964, 26]-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 (200, 225, 37455)-net over F2 | [i] | Net Duplication | |
| 2 | Digital (201, 226, 37455)-net over F2 | [i] | ||