Information on Result #1193018
Digital (22, 27, 531444)-net over F9, using net defined by OOA based on linear OOA(927, 531444, F9, 5, 5) (dual of [(531444, 5), 2657193, 6]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OA(927, 1062889, F9, 5) (dual of [1062889, 1062862, 6]-code), using
- 1 times code embedding in larger space [i] based on linear OA(926, 1062888, F9, 5) (dual of [1062888, 1062862, 6]-code), using
- trace code [i] based on linear OA(8113, 531444, F81, 5) (dual of [531444, 531431, 6]-code), using
- construction X applied to Ce(4) ⊂ Ce(3) [i] based on
- linear OA(8113, 531441, F81, 5) (dual of [531441, 531428, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 531440 = 813−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(8110, 531441, F81, 4) (dual of [531441, 531431, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 531440 = 813−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [i]
- linear OA(810, 3, F81, 0) (dual of [3, 3, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(810, s, F81, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- construction X applied to Ce(4) ⊂ Ce(3) [i] based on
- trace code [i] based on linear OA(8113, 531444, F81, 5) (dual of [531444, 531431, 6]-code), using
- 1 times code embedding in larger space [i] based on linear OA(926, 1062888, F9, 5) (dual of [1062888, 1062862, 6]-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 (91, 101, 3886884)-net over F9 | [i] | (u, u+v)-Construction for Nets | |
| 2 | Digital (98, 109, 3886884)-net over F9 | [i] | ||