Information on Result #1823561
(32, 40, 32769)-net in base 8, using base change based on digital (22, 30, 32769)-net over F16, using
- net defined by OOA [i] based on linear OOA(1630, 32769, F16, 8, 8) (dual of [(32769, 8), 262122, 9]-NRT-code), using
- OA 4-folding and stacking [i] based on linear OA(1630, 131076, F16, 8) (dual of [131076, 131046, 9]-code), using
- trace code [i] based on linear OA(25615, 65538, F256, 8) (dual of [65538, 65523, 9]-code), using
- construction X applied to Ce(7) ⊂ Ce(6) [i] based on
- linear OA(25615, 65536, F256, 8) (dual of [65536, 65521, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(25613, 65536, F256, 7) (dual of [65536, 65523, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(2560, 2, F256, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(2560, s, F256, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- construction X applied to Ce(7) ⊂ Ce(6) [i] based on
- trace code [i] based on linear OA(25615, 65538, F256, 8) (dual of [65538, 65523, 9]-code), using
- OA 4-folding and stacking [i] based on linear OA(1630, 131076, F16, 8) (dual of [131076, 131046, 9]-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 | (33, 41, 32769)-net in base 8 | [i] | Net Duplication | |
| 2 | (146, 162, 2129919)-net in base 8 | [i] | (u, u+v)-Construction for Nets | |
| 3 | (153, 170, 2129919)-net in base 8 | [i] | ||