Information on Result #1180034
Digital (76, 87, 26218)-net over F2, using net defined by OOA based on linear OOA(287, 26218, F2, 11, 11) (dual of [(26218, 11), 288311, 12]-NRT-code), using
- OOA 5-folding and stacking with additional row [i] based on linear OA(287, 131091, F2, 11) (dual of [131091, 131004, 12]-code), using
- construction X4 applied to Ce(10) ⊂ Ce(8) [i] based on
- linear OA(286, 131072, F2, 11) (dual of [131072, 130986, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 131071 = 217−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(269, 131072, F2, 9) (dual of [131072, 131003, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 131071 = 217−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(218, 19, F2, 17) (dual of [19, 1, 18]-code), using
- strength reduction [i] based on linear OA(218, 19, F2, 18) (dual of [19, 1, 19]-code or 19-arc in PG(17,2)), using
- dual of repetition code with length 19 [i]
- strength reduction [i] based on linear OA(218, 19, F2, 18) (dual of [19, 1, 19]-code or 19-arc in PG(17,2)), using
- linear OA(21, 19, F2, 1) (dual of [19, 18, 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(10) ⊂ Ce(8) [i] based on
Mode: Constructive and 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 (77, 87, 26218)-net over F2 | [i] | t-Expansion | |
| 2 | Digital (77, 88, 26218)-net over F2 | [i] | Net Duplication | |
| 3 | Digital (78, 89, 26218)-net over F2 | [i] | ||
| 4 | Digital (79, 90, 26218)-net over F2 | [i] | ||