Information on Result #1224781
Digital (40, 52, 174807)-net over F32, using (u, u+v)-construction based on
- digital (1, 7, 44)-net over F32, using
- net from sequence [i] based on digital (1, 43)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 1 and N(F) ≥ 44, using
- net from sequence [i] based on digital (1, 43)-sequence over F32, using
- digital (33, 45, 174763)-net over F32, using
- net defined by OOA [i] based on linear OOA(3245, 174763, F32, 12, 12) (dual of [(174763, 12), 2097111, 13]-NRT-code), using
- OA 6-folding and stacking [i] based on linear OA(3245, 1048578, F32, 12) (dual of [1048578, 1048533, 13]-code), using
- discarding factors / shortening the dual code based on linear OA(3245, 1048580, F32, 12) (dual of [1048580, 1048535, 13]-code), using
- construction X applied to Ce(11) ⊂ Ce(10) [i] based on
- linear OA(3245, 1048576, F32, 12) (dual of [1048576, 1048531, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 324−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(3241, 1048576, F32, 11) (dual of [1048576, 1048535, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 324−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [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(11) ⊂ Ce(10) [i] based on
- discarding factors / shortening the dual code based on linear OA(3245, 1048580, F32, 12) (dual of [1048580, 1048535, 13]-code), using
- OA 6-folding and stacking [i] based on linear OA(3245, 1048578, F32, 12) (dual of [1048578, 1048533, 13]-code), using
- net defined by OOA [i] based on linear OOA(3245, 174763, F32, 12, 12) (dual of [(174763, 12), 2097111, 13]-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 (97, 109, 5593824)-net over F32 | [i] | Generalized (u, u+v)-Construction for Nets | |
| 2 | (53, 65, 174807)-net in base 16 | [i] | Base Change | |