Information on Result #1182814
Digital (48, 55, 531446)-net over F3, using net defined by OOA based on linear OOA(355, 531446, F3, 7, 7) (dual of [(531446, 7), 3720067, 8]-NRT-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OA(355, 1594339, F3, 7) (dual of [1594339, 1594284, 8]-code), using
- 1 times code embedding in larger space [i] based on linear OA(354, 1594338, F3, 7) (dual of [1594338, 1594284, 8]-code), using
- construction X4 applied to Ce(6) ⊂ Ce(4) [i] based on
- linear OA(353, 1594323, F3, 7) (dual of [1594323, 1594270, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 1594322 = 313−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(340, 1594323, F3, 5) (dual of [1594323, 1594283, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 1594322 = 313−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(314, 15, F3, 14) (dual of [15, 1, 15]-code or 15-arc in PG(13,3)), using
- dual of repetition code with length 15 [i]
- linear OA(31, 15, F3, 1) (dual of [15, 14, 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(6) ⊂ Ce(4) [i] based on
- 1 times code embedding in larger space [i] based on linear OA(354, 1594338, F3, 7) (dual of [1594338, 1594284, 8]-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 (49, 56, 531446)-net over F3 | [i] | Net Duplication | |
| 2 | Digital (177, 191, 1729817)-net over F3 | [i] | (u, u+v)-Construction for Nets | |
| 3 | Digital (190, 205, 1729817)-net over F3 | [i] | ||