Information on Result #1842137
(42, 69, 5043)-net in base 128, using net defined by OOA based on OOA(12869, 5043, S128, 27, 27), using
- OOA 13-folding and stacking with additional row [i] based on OA(12869, 65560, S128, 27), using
- discarding parts of the base [i] based on linear OA(25660, 65560, F256, 27) (dual of [65560, 65500, 28]-code), using
- construction X applied to C([0,13]) ⊂ C([0,9]) [i] based on
- linear OA(25653, 65537, F256, 27) (dual of [65537, 65484, 28]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 2564−1, defining interval I = [0,13], and minimum distance d ≥ |{−13,−12,…,13}|+1 = 28 (BCH-bound) [i]
- linear OA(25637, 65537, F256, 19) (dual of [65537, 65500, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 2564−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (BCH-bound) [i]
- linear OA(2567, 23, F256, 7) (dual of [23, 16, 8]-code or 23-arc in PG(6,256)), using
- discarding factors / shortening the dual code based on linear OA(2567, 256, F256, 7) (dual of [256, 249, 8]-code or 256-arc in PG(6,256)), using
- Reed–Solomon code RS(249,256) [i]
- discarding factors / shortening the dual code based on linear OA(2567, 256, F256, 7) (dual of [256, 249, 8]-code or 256-arc in PG(6,256)), using
- construction X applied to C([0,13]) ⊂ C([0,9]) [i] based on
- discarding parts of the base [i] based on linear OA(25660, 65560, F256, 27) (dual of [65560, 65500, 28]-code), 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 | (43, 69, 5043)-net in base 128 | [i] | t-Expansion | |
| 2 | (43, 70, 5043)-net in base 128 | [i] | Net Duplication | |
| 3 | (44, 71, 5043)-net in base 128 | [i] | ||
| 4 | (42, 68, 5043)-net in base 128 | [i] | m-Reduction | |