Information on Result #1207941
Digital (162, 172, 6711980)-net over F3, using (u, u+v)-construction based on
- digital (19, 24, 1100)-net over F3, using
- net defined by OOA [i] based on linear OOA(324, 1100, F3, 5, 5) (dual of [(1100, 5), 5476, 6]-NRT-code), using
- OOA stacking with additional row [i] based on linear OOA(324, 1101, F3, 2, 5) (dual of [(1101, 2), 2178, 6]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(32, 4, F3, 2, 2) (dual of [(4, 2), 6, 3]-NRT-code), using
- extended Reed–Solomon NRT-code RSe(2;6,3) [i]
- linear OOA(322, 1097, F3, 2, 5) (dual of [(1097, 2), 2172, 6]-NRT-code), using
- OOA 2-folding [i] based on linear OA(322, 2194, F3, 5) (dual of [2194, 2172, 6]-code), using
- construction X applied to Ce(4) ⊂ Ce(3) [i] based on
- linear OA(322, 2187, F3, 5) (dual of [2187, 2165, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 2186 = 37−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(315, 2187, F3, 4) (dual of [2187, 2172, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 2186 = 37−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [i]
- linear OA(30, 7, F3, 0) (dual of [7, 7, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(30, s, F3, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- construction X applied to Ce(4) ⊂ Ce(3) [i] based on
- OOA 2-folding [i] based on linear OA(322, 2194, F3, 5) (dual of [2194, 2172, 6]-code), using
- linear OOA(32, 4, F3, 2, 2) (dual of [(4, 2), 6, 3]-NRT-code), using
- (u, u+v)-construction [i] based on
- OOA stacking with additional row [i] based on linear OOA(324, 1101, F3, 2, 5) (dual of [(1101, 2), 2178, 6]-NRT-code), using
- net defined by OOA [i] based on linear OOA(324, 1100, F3, 5, 5) (dual of [(1100, 5), 5476, 6]-NRT-code), using
- digital (138, 148, 6710880)-net over F3, using
- trace code for nets [i] based on digital (27, 37, 1677720)-net over F81, using
- net defined by OOA [i] based on linear OOA(8137, 1677720, F81, 10, 10) (dual of [(1677720, 10), 16777163, 11]-NRT-code), using
- OA 5-folding and stacking [i] based on linear OA(8137, 8388600, F81, 10) (dual of [8388600, 8388563, 11]-code), using
- discarding factors / shortening the dual code based on linear OA(8137, large, F81, 10) (dual of [large, large−37, 11]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 21523360 | 814−1, defining interval I = [0,9], and designed minimum distance d ≥ |I|+1 = 11 [i]
- discarding factors / shortening the dual code based on linear OA(8137, large, F81, 10) (dual of [large, large−37, 11]-code), using
- OA 5-folding and stacking [i] based on linear OA(8137, 8388600, F81, 10) (dual of [8388600, 8388563, 11]-code), using
- net defined by OOA [i] based on linear OOA(8137, 1677720, F81, 10, 10) (dual of [(1677720, 10), 16777163, 11]-NRT-code), using
- trace code for nets [i] based on digital (27, 37, 1677720)-net over F81, 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 | Linear OOA(3172, 6711980, F3, 5, 10) (dual of [(6711980, 5), 33559728, 11]-NRT-code) | [i] | Extracting Embedded OOA | |