Information on Result #1191036
Digital (27, 33, 174765)-net over F8, using net defined by OOA based on linear OOA(833, 174765, F8, 6, 6) (dual of [(174765, 6), 1048557, 7]-NRT-code), using
- OA 3-folding and stacking [i] based on linear OA(833, 524295, F8, 6) (dual of [524295, 524262, 7]-code), using
- 1 times code embedding in larger space [i] based on linear OA(832, 524294, F8, 6) (dual of [524294, 524262, 7]-code), using
- trace code [i] based on linear OA(6416, 262147, F64, 6) (dual of [262147, 262131, 7]-code), using
- construction X applied to Ce(5) ⊂ Ce(4) [i] based on
- linear OA(6416, 262144, F64, 6) (dual of [262144, 262128, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(6413, 262144, F64, 5) (dual of [262144, 262131, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [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(5) ⊂ Ce(4) [i] based on
- trace code [i] based on linear OA(6416, 262147, F64, 6) (dual of [262147, 262131, 7]-code), using
- 1 times code embedding in larger space [i] based on linear OA(832, 524294, F8, 6) (dual of [524294, 524262, 7]-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 | Digital (111, 123, 2970965)-net over F8 | [i] | (u, u+v)-Construction for Nets | |
| 2 | Digital (118, 131, 2970965)-net over F8 | [i] | ||