Information on Result #1840997
(54, 71, 262145)-net in base 32, using net defined by OOA based on OOA(3271, 262145, S32, 17, 17), using
- OOA 8-folding and stacking with additional row [i] based on OA(3271, 2097161, S32, 17), using
- 1 times code embedding in larger space [i] based on OA(3270, 2097160, S32, 17), using
- discarding parts of the base [i] based on linear OA(12850, 2097160, F128, 17) (dual of [2097160, 2097110, 18]-code), using
- construction X applied to C([0,8]) ⊂ C([0,7]) [i] based on
- linear OA(12849, 2097153, F128, 17) (dual of [2097153, 2097104, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 2097153 | 1286−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
- linear OA(12843, 2097153, F128, 15) (dual of [2097153, 2097110, 16]-code), using the expurgated narrow-sense BCH-code C(I) with length 2097153 | 1286−1, defining interval I = [0,7], and minimum distance d ≥ |{−7,−6,…,7}|+1 = 16 (BCH-bound) [i]
- linear OA(1281, 7, F128, 1) (dual of [7, 6, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(1281, s, F128, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- construction X applied to C([0,8]) ⊂ C([0,7]) [i] based on
- discarding parts of the base [i] based on linear OA(12850, 2097160, F128, 17) (dual of [2097160, 2097110, 18]-code), using
- 1 times code embedding in larger space [i] based on OA(3270, 2097160, S32, 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 | (55, 72, 262145)-net in base 32 | [i] | Net Duplication | |
| 2 | (56, 73, 262145)-net in base 32 | [i] | ||