Information on Result #1824492
(12, 21, 4097)-net in base 64, using base change based on digital (9, 18, 4097)-net over F128, using
- net defined by OOA [i] based on linear OOA(12818, 4097, F128, 9, 9) (dual of [(4097, 9), 36855, 10]-NRT-code), using
- OOA 4-folding and stacking with additional row [i] based on linear OA(12818, 16389, F128, 9) (dual of [16389, 16371, 10]-code), using
- discarding factors / shortening the dual code based on linear OA(12818, 16390, F128, 9) (dual of [16390, 16372, 10]-code), using
- construction X applied to C([0,4]) ⊂ C([0,3]) [i] based on
- linear OA(12817, 16385, F128, 9) (dual of [16385, 16368, 10]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385 | 1284−1, defining interval I = [0,4], and minimum distance d ≥ |{−4,−3,…,4}|+1 = 10 (BCH-bound) [i]
- linear OA(12813, 16385, F128, 7) (dual of [16385, 16372, 8]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385 | 1284−1, defining interval I = [0,3], and minimum distance d ≥ |{−3,−2,…,3}|+1 = 8 (BCH-bound) [i]
- linear OA(1281, 5, F128, 1) (dual of [5, 4, 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([0,4]) ⊂ C([0,3]) [i] based on
- discarding factors / shortening the dual code based on linear OA(12818, 16390, F128, 9) (dual of [16390, 16372, 10]-code), using
- OOA 4-folding and stacking with additional row [i] based on linear OA(12818, 16389, F128, 9) (dual of [16389, 16371, 10]-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 | (13, 22, 4097)-net in base 64 | [i] | Net Duplication | |
| 2 | (72, 90, 936164)-net in base 64 | [i] | (u, u+v)-Construction for Nets | |