Information on Result #1224632
Digital (46, 55, 2621443)-net over F32, using (u, u+v)-construction based on
- digital (10, 14, 524293)-net over F32, using
- net defined by OOA [i] based on linear OOA(3214, 524293, F32, 4, 4) (dual of [(524293, 4), 2097158, 5]-NRT-code), using
- OA 2-folding and stacking [i] based on linear OA(3214, 1048586, F32, 4) (dual of [1048586, 1048572, 5]-code), using
- construction X4 applied to Ce(3) ⊂ Ce(1) [i] based on
- linear OA(3213, 1048576, F32, 4) (dual of [1048576, 1048563, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 324−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [i]
- linear OA(325, 1048576, F32, 2) (dual of [1048576, 1048571, 3]-code), using an extension Ce(1) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 324−1, defining interval I = [1,1], and designed minimum distance d ≥ |I|+1 = 2 [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 Ce(3) ⊂ Ce(1) [i] based on
- OA 2-folding and stacking [i] based on linear OA(3214, 1048586, F32, 4) (dual of [1048586, 1048572, 5]-code), using
- net defined by OOA [i] based on linear OOA(3214, 524293, F32, 4, 4) (dual of [(524293, 4), 2097158, 5]-NRT-code), using
- digital (32, 41, 2097150)-net over F32, using
- net defined by OOA [i] based on linear OOA(3241, 2097150, F32, 9, 9) (dual of [(2097150, 9), 18874309, 10]-NRT-code), using
- OOA 4-folding and stacking with additional row [i] based on linear OA(3241, 8388601, F32, 9) (dual of [8388601, 8388560, 10]-code), using
- discarding factors / shortening the dual code based on linear OA(3241, large, F32, 9) (dual of [large, large−41, 10]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 33554433 | 3210−1, defining interval I = [0,4], and minimum distance d ≥ |{−4,−3,…,4}|+1 = 10 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(3241, large, F32, 9) (dual of [large, large−41, 10]-code), using
- OOA 4-folding and stacking with additional row [i] based on linear OA(3241, 8388601, F32, 9) (dual of [8388601, 8388560, 10]-code), using
- net defined by OOA [i] based on linear OOA(3241, 2097150, F32, 9, 9) (dual of [(2097150, 9), 18874309, 10]-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 (62, 71, 5242886)-net over F32 | [i] | (u, u+v)-Construction for Nets | |