Information on Result #1760113
Digital (231, 258, 74905)-net over F2, using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(2258, 74905, F2, 7, 27) (dual of [(74905, 7), 524077, 28]-NRT-code), using
- 21 times duplication [i] based on linear OOA(2257, 74905, F2, 7, 27) (dual of [(74905, 7), 524078, 28]-NRT-code), using
- OOA 7-folding [i] based on linear OA(2257, 524335, F2, 27) (dual of [524335, 524078, 28]-code), using
- 2 times code embedding in larger space [i] based on linear OA(2255, 524333, F2, 27) (dual of [524333, 524078, 28]-code), using
- construction X applied to Ce(26) ⊂ Ce(22) [i] based on
- linear OA(2248, 524288, F2, 27) (dual of [524288, 524040, 28]-code), using an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 524287 = 219−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [i]
- linear OA(2210, 524288, F2, 23) (dual of [524288, 524078, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 524287 = 219−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(27, 45, F2, 3) (dual of [45, 38, 4]-code or 45-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 Ce(26) ⊂ Ce(22) [i] based on
- 2 times code embedding in larger space [i] based on linear OA(2255, 524333, F2, 27) (dual of [524333, 524078, 28]-code), using
- OOA 7-folding [i] based on linear OA(2257, 524335, F2, 27) (dual of [524335, 524078, 28]-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 (232, 259, 74905)-net over F2 | [i] | Net Duplication | |
| 2 | Digital (233, 260, 74905)-net over F2 | [i] | ||