Information on Result #1182900
Digital (35, 43, 1643)-net over F3, using net defined by OOA based on linear OOA(343, 1643, F3, 8, 8) (dual of [(1643, 8), 13101, 9]-NRT-code), using
- OA 4-folding and stacking [i] based on linear OA(343, 6572, F3, 8) (dual of [6572, 6529, 9]-code), using
- 1 times code embedding in larger space [i] based on linear OA(342, 6571, F3, 8) (dual of [6571, 6529, 9]-code), using
- construction X4 applied to Ce(7) ⊂ Ce(6) [i] based on
- linear OA(341, 6561, F3, 8) (dual of [6561, 6520, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 6560 = 38−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(333, 6561, F3, 7) (dual of [6561, 6528, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 6560 = 38−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(39, 10, F3, 9) (dual of [10, 1, 10]-code or 10-arc in PG(8,3)), using
- dual of repetition code with length 10 [i]
- linear OA(31, 10, F3, 1) (dual of [10, 9, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(31, s, F3, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- construction X4 applied to Ce(7) ⊂ Ce(6) [i] based on
- 1 times code embedding in larger space [i] based on linear OA(342, 6571, F3, 8) (dual of [6571, 6529, 9]-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 (36, 44, 1643)-net over F3 | [i] | Net Duplication | |
| 2 | Digital (178, 194, 1050218)-net over F3 | [i] | (u, u+v)-Construction for Nets | |
| 3 | Digital (192, 209, 1050218)-net over F3 | [i] | ||