Information on Result #1224748
Digital (76, 87, 3389294)-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 (55, 66, 1694647)-net over F32, using
- (u, u+v)-construction [i] based on
- digital (10, 15, 16927)-net over F32, using
- net defined by OOA [i] based on linear OOA(3215, 16927, F32, 6, 5) (dual of [(16927, 6), 101547, 6]-NRT-code), using
- OOA stacking with additional row [i] based on linear OOA(3215, 16928, F32, 2, 5) (dual of [(16928, 2), 33841, 6]-NRT-code), using
- generalized (u, u+v)-construction [i] based on
- linear OOA(320, 529, F32, 2, 0) (dual of [(529, 2), 1058, 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, 529, F32, 2, 0) (dual of [(529, 2), 1058, 1]-NRT-code) (see above)
- linear OOA(320, 529, F32, 2, 0) (dual of [(529, 2), 1058, 1]-NRT-code) (see above)
- linear OOA(320, 529, F32, 2, 0) (dual of [(529, 2), 1058, 1]-NRT-code) (see above)
- linear OOA(320, 529, F32, 2, 0) (dual of [(529, 2), 1058, 1]-NRT-code) (see above)
- linear OOA(320, 529, F32, 2, 0) (dual of [(529, 2), 1058, 1]-NRT-code) (see above)
- linear OOA(320, 529, F32, 2, 0) (dual of [(529, 2), 1058, 1]-NRT-code) (see above)
- linear OOA(320, 529, F32, 2, 0) (dual of [(529, 2), 1058, 1]-NRT-code) (see above)
- linear OOA(320, 529, F32, 2, 0) (dual of [(529, 2), 1058, 1]-NRT-code) (see above)
- linear OOA(320, 529, F32, 2, 0) (dual of [(529, 2), 1058, 1]-NRT-code) (see above)
- linear OOA(320, 529, F32, 2, 0) (dual of [(529, 2), 1058, 1]-NRT-code) (see above)
- linear OOA(320, 529, F32, 2, 0) (dual of [(529, 2), 1058, 1]-NRT-code) (see above)
- linear OOA(320, 529, F32, 2, 0) (dual of [(529, 2), 1058, 1]-NRT-code) (see above)
- linear OOA(320, 529, F32, 2, 0) (dual of [(529, 2), 1058, 1]-NRT-code) (see above)
- linear OOA(320, 529, F32, 2, 0) (dual of [(529, 2), 1058, 1]-NRT-code) (see above)
- linear OOA(320, 529, F32, 2, 0) (dual of [(529, 2), 1058, 1]-NRT-code) (see above)
- linear OOA(320, 529, F32, 2, 0) (dual of [(529, 2), 1058, 1]-NRT-code) (see above)
- linear OOA(320, 529, F32, 2, 0) (dual of [(529, 2), 1058, 1]-NRT-code) (see above)
- linear OOA(320, 529, F32, 2, 0) (dual of [(529, 2), 1058, 1]-NRT-code) (see above)
- linear OOA(320, 529, F32, 2, 0) (dual of [(529, 2), 1058, 1]-NRT-code) (see above)
- linear OOA(320, 529, F32, 2, 0) (dual of [(529, 2), 1058, 1]-NRT-code) (see above)
- linear OOA(320, 529, F32, 2, 0) (dual of [(529, 2), 1058, 1]-NRT-code) (see above)
- linear OOA(320, 529, F32, 2, 0) (dual of [(529, 2), 1058, 1]-NRT-code) (see above)
- linear OOA(320, 529, F32, 2, 0) (dual of [(529, 2), 1058, 1]-NRT-code) (see above)
- linear OOA(320, 529, F32, 2, 0) (dual of [(529, 2), 1058, 1]-NRT-code) (see above)
- linear OOA(320, 529, F32, 2, 0) (dual of [(529, 2), 1058, 1]-NRT-code) (see above)
- linear OOA(320, 529, F32, 2, 0) (dual of [(529, 2), 1058, 1]-NRT-code) (see above)
- linear OOA(321, 529, F32, 2, 1) (dual of [(529, 2), 1057, 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, 529, F32, 2, 1) (dual of [(529, 2), 1057, 2]-NRT-code) (see above)
- linear OOA(321, 529, F32, 2, 1) (dual of [(529, 2), 1057, 2]-NRT-code) (see above)
- linear OOA(323, 529, F32, 2, 2) (dual of [(529, 2), 1055, 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(329, 529, F32, 2, 5) (dual of [(529, 2), 1049, 6]-NRT-code), using
- (u, u+v)-construction [i] based on
- 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(327, 496, F32, 2, 5) (dual of [(496, 2), 985, 6]-NRT-code), using
- OOA 2-folding [i] based on linear OA(327, 992, F32, 5) (dual of [992, 985, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(327, 993, F32, 5) (dual of [993, 986, 6]-code), using
- OOA 2-folding [i] based on linear OA(327, 992, F32, 5) (dual of [992, 985, 6]-code), using
- linear OOA(322, 33, F32, 2, 2) (dual of [(33, 2), 64, 3]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(320, 529, F32, 2, 0) (dual of [(529, 2), 1058, 1]-NRT-code), using
- generalized (u, u+v)-construction [i] based on
- OOA stacking with additional row [i] based on linear OOA(3215, 16928, F32, 2, 5) (dual of [(16928, 2), 33841, 6]-NRT-code), using
- net defined by OOA [i] based on linear OOA(3215, 16927, F32, 6, 5) (dual of [(16927, 6), 101547, 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 (10, 15, 16927)-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 (97, 108, 6778588)-net over F32 | [i] | (u, u+v)-Construction for Nets | |