Information on Result #1224749
Digital (77, 88, 3423022)-net over F32, using (u, u+v)-construction based on
- digital (16, 21, 4194301)-net over F32, using
- net defined by OOA [i] based on linear OOA(3221, 4194301, F32, 5, 5) (dual of [(4194301, 5), 20971484, 6]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OA(3221, large, F32, 5) (dual of [large, large−21, 6]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 33554433 | 3210−1, defining interval I = [0,2], and minimum distance d ≥ |{−2,−1,0,1,2}|+1 = 6 (BCH-bound) [i]
- OOA 2-folding and stacking with additional row [i] based on linear OA(3221, large, F32, 5) (dual of [large, large−21, 6]-code), using
- net defined by OOA [i] based on linear OOA(3221, 4194301, F32, 5, 5) (dual of [(4194301, 5), 20971484, 6]-NRT-code), using
- digital (56, 67, 1711511)-net over F32, using
- (u, u+v)-construction [i] based on
- digital (11, 16, 33791)-net over F32, using
- net defined by OOA [i] based on linear OOA(3216, 33791, F32, 6, 5) (dual of [(33791, 6), 202730, 6]-NRT-code), using
- OOA stacking with additional row [i] based on linear OOA(3216, 33792, F32, 2, 5) (dual of [(33792, 2), 67568, 6]-NRT-code), using
- generalized (u, u+v)-construction [i] based on
- linear OOA(320, 1056, F32, 2, 0) (dual of [(1056, 2), 2112, 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, 1056, F32, 2, 0) (dual of [(1056, 2), 2112, 1]-NRT-code) (see above)
- linear OOA(320, 1056, F32, 2, 0) (dual of [(1056, 2), 2112, 1]-NRT-code) (see above)
- linear OOA(320, 1056, F32, 2, 0) (dual of [(1056, 2), 2112, 1]-NRT-code) (see above)
- linear OOA(320, 1056, F32, 2, 0) (dual of [(1056, 2), 2112, 1]-NRT-code) (see above)
- linear OOA(320, 1056, F32, 2, 0) (dual of [(1056, 2), 2112, 1]-NRT-code) (see above)
- linear OOA(320, 1056, F32, 2, 0) (dual of [(1056, 2), 2112, 1]-NRT-code) (see above)
- linear OOA(320, 1056, F32, 2, 0) (dual of [(1056, 2), 2112, 1]-NRT-code) (see above)
- linear OOA(320, 1056, F32, 2, 0) (dual of [(1056, 2), 2112, 1]-NRT-code) (see above)
- linear OOA(320, 1056, F32, 2, 0) (dual of [(1056, 2), 2112, 1]-NRT-code) (see above)
- linear OOA(320, 1056, F32, 2, 0) (dual of [(1056, 2), 2112, 1]-NRT-code) (see above)
- linear OOA(320, 1056, F32, 2, 0) (dual of [(1056, 2), 2112, 1]-NRT-code) (see above)
- linear OOA(320, 1056, F32, 2, 0) (dual of [(1056, 2), 2112, 1]-NRT-code) (see above)
- linear OOA(320, 1056, F32, 2, 0) (dual of [(1056, 2), 2112, 1]-NRT-code) (see above)
- linear OOA(320, 1056, F32, 2, 0) (dual of [(1056, 2), 2112, 1]-NRT-code) (see above)
- linear OOA(320, 1056, F32, 2, 0) (dual of [(1056, 2), 2112, 1]-NRT-code) (see above)
- linear OOA(320, 1056, F32, 2, 0) (dual of [(1056, 2), 2112, 1]-NRT-code) (see above)
- linear OOA(320, 1056, F32, 2, 0) (dual of [(1056, 2), 2112, 1]-NRT-code) (see above)
- linear OOA(320, 1056, F32, 2, 0) (dual of [(1056, 2), 2112, 1]-NRT-code) (see above)
- linear OOA(320, 1056, F32, 2, 0) (dual of [(1056, 2), 2112, 1]-NRT-code) (see above)
- linear OOA(320, 1056, F32, 2, 0) (dual of [(1056, 2), 2112, 1]-NRT-code) (see above)
- linear OOA(320, 1056, F32, 2, 0) (dual of [(1056, 2), 2112, 1]-NRT-code) (see above)
- linear OOA(320, 1056, F32, 2, 0) (dual of [(1056, 2), 2112, 1]-NRT-code) (see above)
- linear OOA(320, 1056, F32, 2, 0) (dual of [(1056, 2), 2112, 1]-NRT-code) (see above)
- linear OOA(320, 1056, F32, 2, 0) (dual of [(1056, 2), 2112, 1]-NRT-code) (see above)
- linear OOA(320, 1056, F32, 2, 0) (dual of [(1056, 2), 2112, 1]-NRT-code) (see above)
- linear OOA(320, 1056, F32, 2, 0) (dual of [(1056, 2), 2112, 1]-NRT-code) (see above)
- linear OOA(321, 1056, F32, 2, 1) (dual of [(1056, 2), 2111, 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, 1056, F32, 2, 1) (dual of [(1056, 2), 2111, 2]-NRT-code) (see above)
- linear OOA(321, 1056, F32, 2, 1) (dual of [(1056, 2), 2111, 2]-NRT-code) (see above)
- linear OOA(323, 1056, F32, 2, 2) (dual of [(1056, 2), 2109, 3]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(323, 1057, F32, 2, 2) (dual of [(1057, 2), 2111, 3]-NRT-code), using
- appending kth column [i] based on linear OA(323, 1057, F32, 2) (dual of [1057, 1054, 3]-code), using
- Hamming code H(3,32) [i]
- appending kth column [i] based on linear OA(323, 1057, F32, 2) (dual of [1057, 1054, 3]-code), using
- discarding factors / shortening the dual code based on linear OOA(323, 1057, F32, 2, 2) (dual of [(1057, 2), 2111, 3]-NRT-code), using
- linear OOA(3210, 1056, F32, 2, 5) (dual of [(1056, 2), 2102, 6]-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 (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(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 (see above)
- 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(325, 33, F32, 2, 5) (dual of [(33, 2), 61, 6]-NRT-code), using
- extended Reed–Solomon NRT-code RSe(2;61,32) [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
- linear OOA(320, 1056, F32, 2, 0) (dual of [(1056, 2), 2112, 1]-NRT-code), using
- generalized (u, u+v)-construction [i] based on
- OOA stacking with additional row [i] based on linear OOA(3216, 33792, F32, 2, 5) (dual of [(33792, 2), 67568, 6]-NRT-code), using
- net defined by OOA [i] based on linear OOA(3216, 33791, F32, 6, 5) (dual of [(33791, 6), 202730, 6]-NRT-code), using
- digital (40, 51, 1677720)-net over F32, using
- net defined by OOA [i] based on linear OOA(3251, 1677720, F32, 11, 11) (dual of [(1677720, 11), 18454869, 12]-NRT-code), using
- OOA 5-folding and stacking with additional row [i] based on linear OA(3251, 8388601, F32, 11) (dual of [8388601, 8388550, 12]-code), using
- discarding factors / shortening the dual code based on linear OA(3251, large, F32, 11) (dual of [large, large−51, 12]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 33554433 | 3210−1, defining interval I = [0,5], and minimum distance d ≥ |{−5,−4,…,5}|+1 = 12 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(3251, large, F32, 11) (dual of [large, large−51, 12]-code), using
- OOA 5-folding and stacking with additional row [i] based on linear OA(3251, 8388601, F32, 11) (dual of [8388601, 8388550, 12]-code), using
- net defined by OOA [i] based on linear OOA(3251, 1677720, F32, 11, 11) (dual of [(1677720, 11), 18454869, 12]-NRT-code), using
- digital (11, 16, 33791)-net over F32, using
- (u, u+v)-construction [i] based on
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 (98, 109, 6846044)-net over F32 | [i] | (u, u+v)-Construction for Nets | |