Information on Result #1201028
Digital (17, 26, 65537)-net over F64, using net defined by OOA based on linear OOA(6426, 65537, F64, 9, 9) (dual of [(65537, 9), 589807, 10]-NRT-code), using
- OOA 4-folding and stacking with additional row [i] based on linear OA(6426, 262149, F64, 9) (dual of [262149, 262123, 10]-code), using
- discarding factors / shortening the dual code based on linear OA(6426, 262152, F64, 9) (dual of [262152, 262126, 10]-code), using
- construction X applied to C([0,4]) ⊂ C([0,3]) [i] based on
- linear OA(6425, 262145, F64, 9) (dual of [262145, 262120, 10]-code), using the expurgated narrow-sense BCH-code C(I) with length 262145 | 646−1, defining interval I = [0,4], and minimum distance d ≥ |{−4,−3,…,4}|+1 = 10 (BCH-bound) [i]
- linear OA(6419, 262145, F64, 7) (dual of [262145, 262126, 8]-code), using the expurgated narrow-sense BCH-code C(I) with length 262145 | 646−1, defining interval I = [0,3], and minimum distance d ≥ |{−3,−2,…,3}|+1 = 8 (BCH-bound) [i]
- linear OA(641, 7, F64, 1) (dual of [7, 6, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(641, s, F64, 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(6426, 262152, F64, 9) (dual of [262152, 262126, 10]-code), using
Mode: Constructive and linear.
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 | (30, 39, 65537)-net in base 16 | [i] | Base Change | |