Information on Result #1841057
(42, 61, 7282)-net in base 32, using net defined by OOA based on OOA(3261, 7282, S32, 19, 19), using
- OOA 9-folding and stacking with additional row [i] based on OA(3261, 65539, S32, 19), using
- discarding factors based on OA(3261, 65542, S32, 19), using
- discarding parts of the base [i] based on linear OA(25638, 65542, F256, 19) (dual of [65542, 65504, 20]-code), using
- construction X applied to C([0,9]) ⊂ C([0,8]) [i] based on
- 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(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(2561, 5, F256, 1) (dual of [5, 4, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(2561, s, F256, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- construction X applied to C([0,9]) ⊂ C([0,8]) [i] based on
- discarding parts of the base [i] based on linear OA(25638, 65542, F256, 19) (dual of [65542, 65504, 20]-code), using
- discarding factors based on OA(3261, 65542, S32, 19), 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, 62, 7282)-net in base 32 | [i] | Net Duplication | |
| 2 | (44, 63, 7282)-net in base 32 | [i] | ||
| 3 | (42, 60, 7282)-net in base 32 | [i] | m-Reduction | |