Information on Result #1221987
Digital (69, 79, 3358250)-net over F27, using (u, u+v)-construction based on
- digital (16, 21, 4194301)-net over F27, using
- net defined by OOA [i] based on linear OOA(2721, 4194301, F27, 5, 5) (dual of [(4194301, 5), 20971484, 6]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OA(2721, large, F27, 5) (dual of [large, large−21, 6]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 14348908 | 2710−1, 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(2721, large, F27, 5) (dual of [large, large−21, 6]-code), using
- net defined by OOA [i] based on linear OOA(2721, 4194301, F27, 5, 5) (dual of [(4194301, 5), 20971484, 6]-NRT-code), using
- digital (48, 58, 1679125)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (7, 12, 1405)-net over F27, using
- net defined by OOA [i] based on linear OOA(2712, 1405, F27, 5, 5) (dual of [(1405, 5), 7013, 6]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OA(2712, 2811, F27, 5) (dual of [2811, 2799, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(2712, 2812, F27, 5) (dual of [2812, 2800, 6]-code), using
- generalized (u, u+v)-construction [i] based on
- linear OA(271, 703, F27, 1) (dual of [703, 702, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(271, s, F27, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- linear OA(271, 703, F27, 1) (dual of [703, 702, 2]-code) (see above)
- linear OA(273, 703, F27, 2) (dual of [703, 700, 3]-code), using
- discarding factors / shortening the dual code based on linear OA(273, 728, F27, 2) (dual of [728, 725, 3]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 272−1, defining interval I = [0,1], and designed minimum distance d ≥ |I|+1 = 3 [i]
- discarding factors / shortening the dual code based on linear OA(273, 728, F27, 2) (dual of [728, 725, 3]-code), using
- linear OA(277, 703, F27, 5) (dual of [703, 696, 6]-code), using
- linear OA(271, 703, F27, 1) (dual of [703, 702, 2]-code), using
- generalized (u, u+v)-construction [i] based on
- discarding factors / shortening the dual code based on linear OA(2712, 2812, F27, 5) (dual of [2812, 2800, 6]-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OA(2712, 2811, F27, 5) (dual of [2811, 2799, 6]-code), using
- net defined by OOA [i] based on linear OOA(2712, 1405, F27, 5, 5) (dual of [(1405, 5), 7013, 6]-NRT-code), using
- digital (36, 46, 1677720)-net over F27, using
- net defined by OOA [i] based on linear OOA(2746, 1677720, F27, 10, 10) (dual of [(1677720, 10), 16777154, 11]-NRT-code), using
- OA 5-folding and stacking [i] based on linear OA(2746, 8388600, F27, 10) (dual of [8388600, 8388554, 11]-code), using
- discarding factors / shortening the dual code based on linear OA(2746, large, F27, 10) (dual of [large, large−46, 11]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 14348906 = 275−1, defining interval I = [0,9], and designed minimum distance d ≥ |I|+1 = 11 [i]
- discarding factors / shortening the dual code based on linear OA(2746, large, F27, 10) (dual of [large, large−46, 11]-code), using
- OA 5-folding and stacking [i] based on linear OA(2746, 8388600, F27, 10) (dual of [8388600, 8388554, 11]-code), using
- net defined by OOA [i] based on linear OOA(2746, 1677720, F27, 10, 10) (dual of [(1677720, 10), 16777154, 11]-NRT-code), using
- digital (7, 12, 1405)-net over F27, 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 (90, 100, 6716500)-net over F27 | [i] | (u, u+v)-Construction for Nets | |