Information on Result #1846581
(41, 56, 1853428)-net in base 64, using base change based on digital (33, 48, 1853428)-net over F128, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(12848, 1853428, F128, 15) (dual of [1853428, 1853380, 16]-code), using
- discarding factors / shortening the dual code based on linear OA(12848, 2097176, F128, 15) (dual of [2097176, 2097128, 16]-code), using
- construction X applied to C([0,7]) ⊂ C([0,4]) [i] based on
- 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(12825, 2097153, F128, 9) (dual of [2097153, 2097128, 10]-code), using the expurgated narrow-sense BCH-code C(I) with length 2097153 | 1286−1, defining interval I = [0,4], and minimum distance d ≥ |{−4,−3,…,4}|+1 = 10 (BCH-bound) [i]
- linear OA(1285, 23, F128, 5) (dual of [23, 18, 6]-code or 23-arc in PG(4,128)), using
- discarding factors / shortening the dual code based on linear OA(1285, 128, F128, 5) (dual of [128, 123, 6]-code or 128-arc in PG(4,128)), using
- Reed–Solomon code RS(123,128) [i]
- discarding factors / shortening the dual code based on linear OA(1285, 128, F128, 5) (dual of [128, 123, 6]-code or 128-arc in PG(4,128)), using
- construction X applied to C([0,7]) ⊂ C([0,4]) [i] based on
- discarding factors / shortening the dual code based on linear OA(12848, 2097176, F128, 15) (dual of [2097176, 2097128, 16]-code), using
Mode: Arbitrary.
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 | OOA(6456, 1853428, S64, 2, 15) | [i] | Extracting Embedded OOA | |
| 2 | OOA(6456, 1853428, S64, 3, 15) | [i] | ||