Information on Result #1749483
Digital (56, 75, 137)-net over F2, using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(275, 137, F2, 2, 19) (dual of [(137, 2), 199, 20]-NRT-code), using
- OOA 2-folding [i] based on linear OA(275, 274, F2, 19) (dual of [274, 199, 20]-code), using
- construction X applied to Ce(18) ⊂ Ce(14) [i] based on
- linear OA(269, 256, F2, 19) (dual of [256, 187, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 255 = 28−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(257, 256, F2, 15) (dual of [256, 199, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 255 = 28−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(26, 18, F2, 3) (dual of [18, 12, 4]-code or 18-cap in PG(5,2)), using
- discarding factors / shortening the dual code based on linear OA(26, 32, F2, 3) (dual of [32, 26, 4]-code or 32-cap in PG(5,2)), using
- construction X applied to Ce(18) ⊂ Ce(14) [i] based on
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 (57, 76, 137)-net over F2 | [i] | Net Duplication | |