Information on Result #1209917
Digital (48, 55, 349545)-net over F4, using (u, u+v)-construction based on
- digital (1, 4, 17)-net over F4, using
- net defined by OOA [i] based on linear OOA(44, 17, F4, 3, 3) (dual of [(17, 3), 47, 4]-NRT-code), using
- digital (44, 51, 349528)-net over F4, using
- net defined by OOA [i] based on linear OOA(451, 349528, F4, 7, 7) (dual of [(349528, 7), 2446645, 8]-NRT-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OA(451, 1048585, F4, 7) (dual of [1048585, 1048534, 8]-code), using
- discarding factors / shortening the dual code based on linear OA(451, 1048586, F4, 7) (dual of [1048586, 1048535, 8]-code), using
- construction X applied to Ce(6) ⊂ Ce(5) [i] based on
- linear OA(451, 1048576, F4, 7) (dual of [1048576, 1048525, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 410−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(441, 1048576, F4, 6) (dual of [1048576, 1048535, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 410−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(40, 10, F4, 0) (dual of [10, 10, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(40, s, F4, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- construction X applied to Ce(6) ⊂ Ce(5) [i] based on
- discarding factors / shortening the dual code based on linear OA(451, 1048586, F4, 7) (dual of [1048586, 1048535, 8]-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OA(451, 1048585, F4, 7) (dual of [1048585, 1048534, 8]-code), using
- net defined by OOA [i] based on linear OOA(451, 349528, F4, 7, 7) (dual of [(349528, 7), 2446645, 8]-NRT-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 (201, 215, 5143029)-net over F4 | [i] | (u, u+v)-Construction for Nets | |
| 2 | Digital (212, 227, 5143029)-net over F4 | [i] | ||