Information on Result #1224674
Digital (54, 64, 2202013)-net over F32, using (u, u+v)-construction based on
- digital (13, 18, 524293)-net over F32, using
- net defined by OOA [i] based on linear OOA(3218, 524293, F32, 5, 5) (dual of [(524293, 5), 2621447, 6]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OA(3218, 1048587, F32, 5) (dual of [1048587, 1048569, 6]-code), using
- construction X4 applied to C([0,2]) ⊂ C([0,1]) [i] based on
- linear OA(3217, 1048577, F32, 5) (dual of [1048577, 1048560, 6]-code), using the expurgated narrow-sense BCH-code C(I) with length 1048577 | 328−1, defining interval I = [0,2], and minimum distance d ≥ |{−2,−1,0,1,2}|+1 = 6 (BCH-bound) [i]
- linear OA(329, 1048577, F32, 3) (dual of [1048577, 1048568, 4]-code or 1048577-cap in PG(8,32)), using the expurgated narrow-sense BCH-code C(I) with length 1048577 | 328−1, defining interval I = [0,1], and minimum distance d ≥ |{−1,0,1}|+1 = 4 (BCH-bound) [i]
- linear OA(329, 10, F32, 9) (dual of [10, 1, 10]-code or 10-arc in PG(8,32)), using
- dual of repetition code with length 10 [i]
- linear OA(321, 10, F32, 1) (dual of [10, 9, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(321, 32, F32, 1) (dual of [32, 31, 2]-code), using
- Reed–Solomon code RS(31,32) [i]
- discarding factors / shortening the dual code based on linear OA(321, 32, F32, 1) (dual of [32, 31, 2]-code), using
- construction X4 applied to C([0,2]) ⊂ C([0,1]) [i] based on
- OOA 2-folding and stacking with additional row [i] based on linear OA(3218, 1048587, F32, 5) (dual of [1048587, 1048569, 6]-code), using
- net defined by OOA [i] based on linear OOA(3218, 524293, F32, 5, 5) (dual of [(524293, 5), 2621447, 6]-NRT-code), using
- digital (36, 46, 1677720)-net over F32, using
- net defined by OOA [i] based on linear OOA(3246, 1677720, F32, 10, 10) (dual of [(1677720, 10), 16777154, 11]-NRT-code), using
- OA 5-folding and stacking [i] based on linear OA(3246, 8388600, F32, 10) (dual of [8388600, 8388554, 11]-code), using
- discarding factors / shortening the dual code based on linear OA(3246, large, F32, 10) (dual of [large, large−46, 11]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 33554431 = 325−1, defining interval I = [0,9], and designed minimum distance d ≥ |I|+1 = 11 [i]
- discarding factors / shortening the dual code based on linear OA(3246, large, F32, 10) (dual of [large, large−46, 11]-code), using
- OA 5-folding and stacking [i] based on linear OA(3246, 8388600, F32, 10) (dual of [8388600, 8388554, 11]-code), using
- net defined by OOA [i] based on linear OOA(3246, 1677720, F32, 10, 10) (dual of [(1677720, 10), 16777154, 11]-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 (75, 85, 4404026)-net over F32 | [i] | (u, u+v)-Construction for Nets | |