Information on Result #1222170
Digital (62, 75, 1398477)-net over F27, using (u, u+v)-construction based on
- digital (8, 14, 377)-net over F27, using
- net defined by OOA [i] based on linear OOA(2714, 377, F27, 10, 6) (dual of [(377, 10), 3756, 7]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OOA(2714, 755, F27, 2, 6) (dual of [(755, 2), 1496, 7]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2714, 756, F27, 2, 6) (dual of [(756, 2), 1498, 7]-NRT-code), using
- generalized (u, u+v)-construction [i] based on
- linear OOA(270, 28, F27, 2, 0) (dual of [(28, 2), 56, 1]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(270, s, F27, 2, 0) for arbitrarily large s, using
- linear OOA(270, 28, F27, 2, 0) (dual of [(28, 2), 56, 1]-NRT-code) (see above)
- linear OOA(270, 28, F27, 2, 0) (dual of [(28, 2), 56, 1]-NRT-code) (see above)
- linear OOA(270, 28, F27, 2, 0) (dual of [(28, 2), 56, 1]-NRT-code) (see above)
- linear OOA(270, 28, F27, 2, 0) (dual of [(28, 2), 56, 1]-NRT-code) (see above)
- linear OOA(270, 28, F27, 2, 0) (dual of [(28, 2), 56, 1]-NRT-code) (see above)
- linear OOA(270, 28, F27, 2, 0) (dual of [(28, 2), 56, 1]-NRT-code) (see above)
- linear OOA(270, 28, F27, 2, 0) (dual of [(28, 2), 56, 1]-NRT-code) (see above)
- linear OOA(270, 28, F27, 2, 0) (dual of [(28, 2), 56, 1]-NRT-code) (see above)
- linear OOA(270, 28, F27, 2, 0) (dual of [(28, 2), 56, 1]-NRT-code) (see above)
- linear OOA(270, 28, F27, 2, 0) (dual of [(28, 2), 56, 1]-NRT-code) (see above)
- linear OOA(270, 28, F27, 2, 0) (dual of [(28, 2), 56, 1]-NRT-code) (see above)
- linear OOA(270, 28, F27, 2, 0) (dual of [(28, 2), 56, 1]-NRT-code) (see above)
- linear OOA(270, 28, F27, 2, 0) (dual of [(28, 2), 56, 1]-NRT-code) (see above)
- linear OOA(270, 28, F27, 2, 0) (dual of [(28, 2), 56, 1]-NRT-code) (see above)
- linear OOA(270, 28, F27, 2, 0) (dual of [(28, 2), 56, 1]-NRT-code) (see above)
- linear OOA(270, 28, F27, 2, 0) (dual of [(28, 2), 56, 1]-NRT-code) (see above)
- linear OOA(270, 28, F27, 2, 0) (dual of [(28, 2), 56, 1]-NRT-code) (see above)
- linear OOA(270, 28, F27, 2, 0) (dual of [(28, 2), 56, 1]-NRT-code) (see above)
- linear OOA(270, 28, F27, 2, 0) (dual of [(28, 2), 56, 1]-NRT-code) (see above)
- linear OOA(270, 28, F27, 2, 0) (dual of [(28, 2), 56, 1]-NRT-code) (see above)
- linear OOA(271, 28, F27, 2, 1) (dual of [(28, 2), 55, 2]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(271, s, F27, 2, 1) for arbitrarily large s, using
- appending 1 arbitrary column [i] based on linear OA(271, s, F27, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- discarding factors / shortening the dual code based on linear OOA(271, s, F27, 2, 1) for arbitrarily large s, using
- linear OOA(271, 28, F27, 2, 1) (dual of [(28, 2), 55, 2]-NRT-code) (see above)
- linear OOA(271, 28, F27, 2, 1) (dual of [(28, 2), 55, 2]-NRT-code) (see above)
- linear OOA(272, 28, F27, 2, 2) (dual of [(28, 2), 54, 3]-NRT-code), using
- extended Reed–Solomon NRT-code RSe(2;54,27) [i]
- linear OOA(273, 28, F27, 2, 3) (dual of [(28, 2), 53, 4]-NRT-code), using
- extended Reed–Solomon NRT-code RSe(2;53,27) [i]
- linear OOA(276, 28, F27, 2, 6) (dual of [(28, 2), 50, 7]-NRT-code), using
- extended Reed–Solomon NRT-code RSe(2;50,27) [i]
- linear OOA(270, 28, F27, 2, 0) (dual of [(28, 2), 56, 1]-NRT-code), using
- generalized (u, u+v)-construction [i] based on
- discarding factors / shortening the dual code based on linear OOA(2714, 756, F27, 2, 6) (dual of [(756, 2), 1498, 7]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OOA(2714, 755, F27, 2, 6) (dual of [(755, 2), 1496, 7]-NRT-code), using
- net defined by OOA [i] based on linear OOA(2714, 377, F27, 10, 6) (dual of [(377, 10), 3756, 7]-NRT-code), using
- digital (48, 61, 1398100)-net over F27, using
- net defined by OOA [i] based on linear OOA(2761, 1398100, F27, 13, 13) (dual of [(1398100, 13), 18175239, 14]-NRT-code), using
- OOA 6-folding and stacking with additional row [i] based on linear OA(2761, 8388601, F27, 13) (dual of [8388601, 8388540, 14]-code), using
- discarding factors / shortening the dual code based on linear OA(2761, large, F27, 13) (dual of [large, large−61, 14]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 14348908 | 2710−1, 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(2761, large, F27, 13) (dual of [large, large−61, 14]-code), using
- OOA 6-folding and stacking with additional row [i] based on linear OA(2761, 8388601, F27, 13) (dual of [8388601, 8388540, 14]-code), using
- net defined by OOA [i] based on linear OOA(2761, 1398100, F27, 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, 2796954)-net over F27 | [i] | (u, u+v)-Construction for Nets | |