Information on Result #1224853
Digital (62, 75, 1398627)-net over F32, using (u, u+v)-construction based on
- digital (8, 14, 527)-net over F32, using
- net defined by OOA [i] based on linear OOA(3214, 527, F32, 10, 6) (dual of [(527, 10), 5256, 7]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OOA(3214, 1055, F32, 2, 6) (dual of [(1055, 2), 2096, 7]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3214, 1056, F32, 2, 6) (dual of [(1056, 2), 2098, 7]-NRT-code), using
- generalized (u, u+v)-construction [i] based on
- linear OOA(320, 33, F32, 2, 0) (dual of [(33, 2), 66, 1]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(320, s, F32, 2, 0) for arbitrarily large s, using
- linear OOA(320, 33, F32, 2, 0) (dual of [(33, 2), 66, 1]-NRT-code) (see above)
- linear OOA(320, 33, F32, 2, 0) (dual of [(33, 2), 66, 1]-NRT-code) (see above)
- linear OOA(320, 33, F32, 2, 0) (dual of [(33, 2), 66, 1]-NRT-code) (see above)
- linear OOA(320, 33, F32, 2, 0) (dual of [(33, 2), 66, 1]-NRT-code) (see above)
- linear OOA(320, 33, F32, 2, 0) (dual of [(33, 2), 66, 1]-NRT-code) (see above)
- linear OOA(320, 33, F32, 2, 0) (dual of [(33, 2), 66, 1]-NRT-code) (see above)
- linear OOA(320, 33, F32, 2, 0) (dual of [(33, 2), 66, 1]-NRT-code) (see above)
- linear OOA(320, 33, F32, 2, 0) (dual of [(33, 2), 66, 1]-NRT-code) (see above)
- linear OOA(320, 33, F32, 2, 0) (dual of [(33, 2), 66, 1]-NRT-code) (see above)
- linear OOA(320, 33, F32, 2, 0) (dual of [(33, 2), 66, 1]-NRT-code) (see above)
- linear OOA(320, 33, F32, 2, 0) (dual of [(33, 2), 66, 1]-NRT-code) (see above)
- linear OOA(320, 33, F32, 2, 0) (dual of [(33, 2), 66, 1]-NRT-code) (see above)
- linear OOA(320, 33, F32, 2, 0) (dual of [(33, 2), 66, 1]-NRT-code) (see above)
- linear OOA(320, 33, F32, 2, 0) (dual of [(33, 2), 66, 1]-NRT-code) (see above)
- linear OOA(320, 33, F32, 2, 0) (dual of [(33, 2), 66, 1]-NRT-code) (see above)
- linear OOA(320, 33, F32, 2, 0) (dual of [(33, 2), 66, 1]-NRT-code) (see above)
- linear OOA(320, 33, F32, 2, 0) (dual of [(33, 2), 66, 1]-NRT-code) (see above)
- linear OOA(320, 33, F32, 2, 0) (dual of [(33, 2), 66, 1]-NRT-code) (see above)
- linear OOA(320, 33, F32, 2, 0) (dual of [(33, 2), 66, 1]-NRT-code) (see above)
- linear OOA(320, 33, F32, 2, 0) (dual of [(33, 2), 66, 1]-NRT-code) (see above)
- linear OOA(320, 33, F32, 2, 0) (dual of [(33, 2), 66, 1]-NRT-code) (see above)
- linear OOA(320, 33, F32, 2, 0) (dual of [(33, 2), 66, 1]-NRT-code) (see above)
- linear OOA(320, 33, F32, 2, 0) (dual of [(33, 2), 66, 1]-NRT-code) (see above)
- linear OOA(320, 33, F32, 2, 0) (dual of [(33, 2), 66, 1]-NRT-code) (see above)
- linear OOA(320, 33, F32, 2, 0) (dual of [(33, 2), 66, 1]-NRT-code) (see above)
- linear OOA(321, 33, F32, 2, 1) (dual of [(33, 2), 65, 2]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(321, s, F32, 2, 1) for arbitrarily large s, using
- appending 1 arbitrary column [i] based on linear OA(321, s, F32, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- discarding factors / shortening the dual code based on linear OOA(321, s, F32, 2, 1) for arbitrarily large s, using
- linear OOA(321, 33, F32, 2, 1) (dual of [(33, 2), 65, 2]-NRT-code) (see above)
- linear OOA(321, 33, F32, 2, 1) (dual of [(33, 2), 65, 2]-NRT-code) (see above)
- linear OOA(322, 33, F32, 2, 2) (dual of [(33, 2), 64, 3]-NRT-code), using
- extended Reed–Solomon NRT-code RSe(2;64,32) [i]
- linear OOA(323, 33, F32, 2, 3) (dual of [(33, 2), 63, 4]-NRT-code), using
- extended Reed–Solomon NRT-code RSe(2;63,32) [i]
- linear OOA(326, 33, F32, 2, 6) (dual of [(33, 2), 60, 7]-NRT-code), using
- extended Reed–Solomon NRT-code RSe(2;60,32) [i]
- linear OOA(320, 33, F32, 2, 0) (dual of [(33, 2), 66, 1]-NRT-code), using
- generalized (u, u+v)-construction [i] based on
- discarding factors / shortening the dual code based on linear OOA(3214, 1056, F32, 2, 6) (dual of [(1056, 2), 2098, 7]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OOA(3214, 1055, F32, 2, 6) (dual of [(1055, 2), 2096, 7]-NRT-code), using
- net defined by OOA [i] based on linear OOA(3214, 527, F32, 10, 6) (dual of [(527, 10), 5256, 7]-NRT-code), using
- digital (48, 61, 1398100)-net over F32, using
- net defined by OOA [i] based on linear OOA(3261, 1398100, F32, 13, 13) (dual of [(1398100, 13), 18175239, 14]-NRT-code), using
- OOA 6-folding and stacking with additional row [i] based on linear OA(3261, 8388601, F32, 13) (dual of [8388601, 8388540, 14]-code), using
- discarding factors / shortening the dual code based on linear OA(3261, large, F32, 13) (dual of [large, large−61, 14]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 33554433 | 3210−1, defining interval I = [0,6], and minimum distance d ≥ |{−6,−5,…,6}|+1 = 14 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(3261, large, F32, 13) (dual of [large, large−61, 14]-code), using
- OOA 6-folding and stacking with additional row [i] based on linear OA(3261, 8388601, F32, 13) (dual of [8388601, 8388540, 14]-code), using
- net defined by OOA [i] based on linear OOA(3261, 1398100, F32, 13, 13) (dual of [(1398100, 13), 18175239, 14]-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 (88, 101, 2797254)-net over F32 | [i] | (u, u+v)-Construction for Nets | |