Information on Result #1840329
(26, 34, 65537)-net in base 16, using net defined by OOA based on OOA(1634, 65537, S16, 8, 8), using
- OA 4-folding and stacking [i] based on OA(1634, 262148, S16, 8), using
- 1 times code embedding in larger space [i] based on OA(1633, 262147, S16, 8), using
- discarding parts of the base [i] based on linear OA(6422, 262147, F64, 8) (dual of [262147, 262125, 9]-code), using
- construction X applied to Ce(7) ⊂ Ce(6) [i] based on
- linear OA(6422, 262144, F64, 8) (dual of [262144, 262122, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(6419, 262144, F64, 7) (dual of [262144, 262125, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(640, 3, F64, 0) (dual of [3, 3, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(640, s, F64, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- construction X applied to Ce(7) ⊂ Ce(6) [i] based on
- discarding parts of the base [i] based on linear OA(6422, 262147, F64, 8) (dual of [262147, 262125, 9]-code), using
- 1 times code embedding in larger space [i] based on OA(1633, 262147, S16, 8), 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 | (27, 35, 65537)-net in base 16 | [i] | Net Duplication | |
| 2 | (110, 126, 2162687)-net in base 16 | [i] | (u, u+v)-Construction for Nets | |