Information on Result #1186699
Linear OOA(4175, 1048703, F4, 18, 17) (dual of [(1048703, 18), 18876479, 18]-NRT-code), using OOA 4-folding and stacking with additional row based on linear OOA(4175, 4194813, F4, 2, 17) (dual of [(4194813, 2), 8389451, 18]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(4175, 4194815, F4, 2, 17) (dual of [(4194815, 2), 8389455, 18]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(430, 514, F4, 2, 8) (dual of [(514, 2), 998, 9]-NRT-code), using
- extracting embedded OOA [i] based on digital (22, 30, 514)-net over F4, using
- trace code for nets [i] based on digital (7, 15, 257)-net over F16, using
- base reduction for projective spaces (embedding PG(7,256) in PG(14,16)) for nets [i] based on digital (0, 8, 257)-net over F256, using
- net from sequence [i] based on digital (0, 256)-sequence over F256, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F256 with g(F) = 0 and N(F) ≥ 257, using
- the rational function field F256(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 256)-sequence over F256, using
- base reduction for projective spaces (embedding PG(7,256) in PG(14,16)) for nets [i] based on digital (0, 8, 257)-net over F256, using
- trace code for nets [i] based on digital (7, 15, 257)-net over F16, using
- extracting embedded OOA [i] based on digital (22, 30, 514)-net over F4, using
- linear OOA(4145, 4194301, F4, 2, 17) (dual of [(4194301, 2), 8388457, 18]-NRT-code), using
- OOA 2-folding [i] based on linear OA(4145, 8388602, F4, 17) (dual of [8388602, 8388457, 18]-code), using
- discarding factors / shortening the dual code based on linear OA(4145, large, F4, 17) (dual of [large, large−145, 18]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 16777217 | 424−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(4145, large, F4, 17) (dual of [large, large−145, 18]-code), using
- OOA 2-folding [i] based on linear OA(4145, 8388602, F4, 17) (dual of [8388602, 8388457, 18]-code), using
- linear OOA(430, 514, F4, 2, 8) (dual of [(514, 2), 998, 9]-NRT-code), using
- (u, u+v)-construction [i] based on
Mode: Constructive and linear.
Results with these parameters are outside the parameter range considered by MinT and show only up in construction trees.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Digital (158, 175, 1048703)-net over F4 | [i] | Net Defined by OOA | |