Information on Result #1841975
(27, 44, 8194)-net in base 128, using net defined by OOA based on OOA(12844, 8194, S128, 17, 17), using
- OOA 8-folding and stacking with additional row [i] based on OA(12844, 65553, S128, 17), using
- discarding factors based on OA(12844, 65554, S128, 17), using
- discarding parts of the base [i] based on linear OA(25638, 65554, F256, 17) (dual of [65554, 65516, 18]-code), using
- construction X applied to C([0,8]) ⊂ C([0,5]) [i] based on
- linear OA(25633, 65537, F256, 17) (dual of [65537, 65504, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 2564−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
- linear OA(25621, 65537, F256, 11) (dual of [65537, 65516, 12]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 2564−1, defining interval I = [0,5], and minimum distance d ≥ |{−5,−4,…,5}|+1 = 12 (BCH-bound) [i]
- linear OA(2565, 17, F256, 5) (dual of [17, 12, 6]-code or 17-arc in PG(4,256)), using
- discarding factors / shortening the dual code based on linear OA(2565, 256, F256, 5) (dual of [256, 251, 6]-code or 256-arc in PG(4,256)), using
- Reed–Solomon code RS(251,256) [i]
- discarding factors / shortening the dual code based on linear OA(2565, 256, F256, 5) (dual of [256, 251, 6]-code or 256-arc in PG(4,256)), using
- construction X applied to C([0,8]) ⊂ C([0,5]) [i] based on
- discarding parts of the base [i] based on linear OA(25638, 65554, F256, 17) (dual of [65554, 65516, 18]-code), using
- discarding factors based on OA(12844, 65554, S128, 17), using
Mode: Constructive.
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 | (28, 45, 8194)-net in base 128 | [i] | Net Duplication | |
| 2 | (27, 43, 8194)-net in base 128 | [i] | m-Reduction | |