Information on Result #1758160
Digital (198, 237, 1376)-net over F2, using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(2237, 1376, F2, 3, 39) (dual of [(1376, 3), 3891, 40]-NRT-code), using
- OOA 3-folding [i] based on linear OA(2237, 4128, F2, 39) (dual of [4128, 3891, 40]-code), using
- 2 times code embedding in larger space [i] based on linear OA(2235, 4126, F2, 39) (dual of [4126, 3891, 40]-code), using
- construction X applied to Ce(38) ⊂ Ce(34) [i] based on
- linear OA(2229, 4096, F2, 39) (dual of [4096, 3867, 40]-code), using an extension Ce(38) of the primitive narrow-sense BCH-code C(I) with length 4095 = 212−1, defining interval I = [1,38], and designed minimum distance d ≥ |I|+1 = 39 [i]
- linear OA(2205, 4096, F2, 35) (dual of [4096, 3891, 36]-code), using an extension Ce(34) of the primitive narrow-sense BCH-code C(I) with length 4095 = 212−1, defining interval I = [1,34], and designed minimum distance d ≥ |I|+1 = 35 [i]
- linear OA(26, 30, F2, 3) (dual of [30, 24, 4]-code or 30-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(38) ⊂ Ce(34) [i] based on
- 2 times code embedding in larger space [i] based on linear OA(2235, 4126, F2, 39) (dual of [4126, 3891, 40]-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 (199, 238, 1376)-net over F2 | [i] | Net Duplication | |
| 2 | Digital (200, 239, 1376)-net over F2 | [i] | ||