Information on Result #1224533
Digital (18, 24, 349559)-net over F32, using (u, u+v)-construction based on
- digital (0, 3, 33)-net over F32, using
- net from sequence [i] based on digital (0, 32)-sequence over F32, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 0 and N(F) ≥ 33, using
- the rational function field F32(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 32)-sequence over F32, using
- digital (15, 21, 349526)-net over F32, using
- net defined by OOA [i] based on linear OOA(3221, 349526, F32, 6, 6) (dual of [(349526, 6), 2097135, 7]-NRT-code), using
- OA 3-folding and stacking [i] based on linear OA(3221, 1048578, F32, 6) (dual of [1048578, 1048557, 7]-code), using
- discarding factors / shortening the dual code based on linear OA(3221, 1048580, F32, 6) (dual of [1048580, 1048559, 7]-code), using
- construction X applied to Ce(5) ⊂ Ce(4) [i] based on
- linear OA(3221, 1048576, F32, 6) (dual of [1048576, 1048555, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 324−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(3217, 1048576, F32, 5) (dual of [1048576, 1048559, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 324−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(320, 4, F32, 0) (dual of [4, 4, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(320, s, F32, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- construction X applied to Ce(5) ⊂ Ce(4) [i] based on
- discarding factors / shortening the dual code based on linear OA(3221, 1048580, F32, 6) (dual of [1048580, 1048559, 7]-code), using
- OA 3-folding and stacking [i] based on linear OA(3221, 1048578, F32, 6) (dual of [1048578, 1048557, 7]-code), using
- net defined by OOA [i] based on linear OOA(3221, 349526, F32, 6, 6) (dual of [(349526, 6), 2097135, 7]-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 (68, 80, 1747659)-net over F32 | [i] | (u, u+v)-Construction for Nets | |
| 2 | Digital (72, 85, 1747659)-net over F32 | [i] | ||