Information on Result #1207937
Digital (158, 168, 6711250)-net over F3, using (u, u+v)-construction based on
- digital (15, 20, 370)-net over F3, using
- net defined by OOA [i] based on linear OOA(320, 370, F3, 5, 5) (dual of [(370, 5), 1830, 6]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OA(320, 741, F3, 5) (dual of [741, 721, 6]-code), using
- construction XX applied to C1 = C([361,364]), C2 = C([363,365]), C3 = C1 + C2 = C([363,364]), and C∩ = C1 ∩ C2 = C([361,365]) [i] based on
- linear OA(313, 728, F3, 4) (dual of [728, 715, 5]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {361,362,363,364}, and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(313, 728, F3, 3) (dual of [728, 715, 4]-code or 728-cap in PG(12,3)), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {363,364,365}, and designed minimum distance d ≥ |I|+1 = 4 [i]
- linear OA(319, 728, F3, 5) (dual of [728, 709, 6]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {361,362,363,364,365}, and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(37, 728, F3, 2) (dual of [728, 721, 3]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {363,364}, and designed minimum distance d ≥ |I|+1 = 3 [i]
- linear OA(31, 7, F3, 1) (dual of [7, 6, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(31, s, F3, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- linear OA(30, 6, F3, 0) (dual of [6, 6, 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 XX applied to C1 = C([361,364]), C2 = C([363,365]), C3 = C1 + C2 = C([363,364]), and C∩ = C1 ∩ C2 = C([361,365]) [i] based on
- OOA 2-folding and stacking with additional row [i] based on linear OA(320, 741, F3, 5) (dual of [741, 721, 6]-code), using
- net defined by OOA [i] based on linear OOA(320, 370, F3, 5, 5) (dual of [(370, 5), 1830, 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(3168, 6711250, F3, 5, 10) (dual of [(6711250, 5), 33556082, 11]-NRT-code) | [i] | Extracting Embedded OOA | |