Information on Result #1022020
Linear OOA(923, 510, F9, 3, 7) (dual of [(510, 3), 1507, 8]-NRT-code), using generalized (u, u+v)-construction based on
- linear OOA(91, 91, F9, 3, 1) (dual of [(91, 3), 272, 2]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(91, s, F9, 3, 1) for arbitrarily large s, using
- appending 2 arbitrary columns [i] based on linear OA(91, s, F9, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- discarding factors / shortening the dual code based on linear OOA(91, s, F9, 3, 1) for arbitrarily large s, using
- linear OOA(93, 91, F9, 3, 2) (dual of [(91, 3), 270, 3]-NRT-code), using
- appending 1 arbitrary column [i] based on linear OOA(93, 91, F9, 2, 2) (dual of [(91, 2), 179, 3]-NRT-code), using
- appending kth column [i] based on linear OA(93, 91, F9, 2) (dual of [91, 88, 3]-code), using
- Hamming code H(3,9) [i]
- appending kth column [i] based on linear OA(93, 91, F9, 2) (dual of [91, 88, 3]-code), using
- appending 1 arbitrary column [i] based on linear OOA(93, 91, F9, 2, 2) (dual of [(91, 2), 179, 3]-NRT-code), using
- linear OOA(95, 164, F9, 3, 3) (dual of [(164, 3), 487, 4]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(95, 211, F9, 3, 3) (dual of [(211, 3), 628, 4]-NRT-code), using
- linear OOA(914, 164, F9, 3, 7) (dual of [(164, 3), 478, 8]-NRT-code), using
- extracting embedded OOA [i] based on digital (7, 14, 164)-net over F9, using
- trace code for nets [i] based on digital (0, 7, 82)-net over F81, using
- net from sequence [i] based on digital (0, 81)-sequence over F81, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 0 and N(F) ≥ 82, using
- the rational function field F81(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 81)-sequence over F81, using
- trace code for nets [i] based on digital (0, 7, 82)-net over F81, using
- extracting embedded OOA [i] based on digital (7, 14, 164)-net over F9, using
Mode: Constructive and linear.
Optimality
Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OOA(9137, 5592912, F9, 3, 15) (dual of [(5592912, 3), 16778599, 16]-NRT-code) | [i] | (u, u+v)-Construction for OOAs | |
| 2 | Linear OOA(9129, 5592912, F9, 3, 14) (dual of [(5592912, 3), 16778607, 15]-NRT-code) | [i] | ||
| 3 | Linear OOA(923, 509, F9, 9, 7) (dual of [(509, 9), 4558, 8]-NRT-code) | [i] | OOA Stacking with Additional Row | |