Information on Result #1750956
Digital (111, 124, 209720)-net over F2, using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(2124, 209720, F2, 5, 13) (dual of [(209720, 5), 1048476, 14]-NRT-code), using
- OOA 5-folding [i] based on linear OA(2124, 1048600, F2, 13) (dual of [1048600, 1048476, 14]-code), using
- 2 times code embedding in larger space [i] based on linear OA(2122, 1048598, F2, 13) (dual of [1048598, 1048476, 14]-code), using
- construction X4 applied to Ce(12) ⊂ Ce(10) [i] based on
- linear OA(2121, 1048576, F2, 13) (dual of [1048576, 1048455, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 220−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(2101, 1048576, F2, 11) (dual of [1048576, 1048475, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 220−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(221, 22, F2, 21) (dual of [22, 1, 22]-code or 22-arc in PG(20,2)), using
- dual of repetition code with length 22 [i]
- linear OA(21, 22, F2, 1) (dual of [22, 21, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(21, s, F2, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- construction X4 applied to Ce(12) ⊂ Ce(10) [i] based on
- 2 times code embedding in larger space [i] based on linear OA(2122, 1048598, F2, 13) (dual of [1048598, 1048476, 14]-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 (112, 125, 209720)-net over F2 | [i] | Net Duplication | |
| 2 | Digital (113, 126, 209720)-net over F2 | [i] | ||