Information on Result #1209938
Digital (84, 92, large)-net over F4, using (u, u+v)-construction based on
- digital (0, 4, 5)-net over F4, using
- net from sequence [i] based on digital (0, 4)-sequence over F4, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 0 and N(F) ≥ 5, using
- the rational function field F4(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 4)-sequence over F4, using
- digital (80, 88, 8388600)-net over F4, using
- trace code for nets [i] based on digital (36, 44, 4194300)-net over F16, using
- net defined by OOA [i] based on linear OOA(1644, 4194300, F16, 10, 8) (dual of [(4194300, 10), 41942956, 9]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OOA(1644, 8388601, F16, 2, 8) (dual of [(8388601, 2), 16777158, 9]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(1644, 8388602, F16, 2, 8) (dual of [(8388602, 2), 16777160, 9]-NRT-code), using
- trace code [i] based on linear OOA(25622, 4194301, F256, 2, 8) (dual of [(4194301, 2), 8388580, 9]-NRT-code), using
- OOA 2-folding [i] based on linear OA(25622, 8388602, F256, 8) (dual of [8388602, 8388580, 9]-code), using
- discarding factors / shortening the dual code based on linear OA(25622, large, F256, 8) (dual of [large, large−22, 9]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 2563−1, defining interval I = [0,7], and designed minimum distance d ≥ |I|+1 = 9 [i]
- discarding factors / shortening the dual code based on linear OA(25622, large, F256, 8) (dual of [large, large−22, 9]-code), using
- OOA 2-folding [i] based on linear OA(25622, 8388602, F256, 8) (dual of [8388602, 8388580, 9]-code), using
- trace code [i] based on linear OOA(25622, 4194301, F256, 2, 8) (dual of [(4194301, 2), 8388580, 9]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(1644, 8388602, F16, 2, 8) (dual of [(8388602, 2), 16777160, 9]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OOA(1644, 8388601, F16, 2, 8) (dual of [(8388601, 2), 16777158, 9]-NRT-code), using
- net defined by OOA [i] based on linear OOA(1644, 4194300, F16, 10, 8) (dual of [(4194300, 10), 41942956, 9]-NRT-code), using
- trace code for nets [i] based on digital (36, 44, 4194300)-net over F16, using
Mode: Constructive and linear.
Optimality
Show details for fixed k and m, k and t, m and t.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Digital (85, 92, large)-net over F4 | [i] | t-Expansion | |
| 2 | Digital (86, 92, large)-net over F4 | [i] | ||
| 3 | Digital (87, 92, large)-net over F4 | [i] | ||
| 4 | Digital (88, 92, large)-net over F4 | [i] | ||
| 5 | Digital (89, 92, large)-net over F4 | [i] | ||
| 6 | Digital (85, 93, large)-net over F4 | [i] | Net Duplication | |
| 7 | Digital (86, 94, large)-net over F4 | [i] | ||
| 8 | Digital (87, 95, large)-net over F4 | [i] | ||
| 9 | Digital (88, 96, large)-net over F4 | [i] | ||
| 10 | Digital (89, 97, large)-net over F4 | [i] | ||
| 11 | Digital (90, 98, large)-net over F4 | [i] | ||
| 12 | Digital (91, 99, large)-net over F4 | [i] | ||
| 13 | Digital (92, 100, large)-net over F4 | [i] | ||
| 14 | Digital (93, 101, large)-net over F4 | [i] | ||
| 15 | Digital (94, 102, large)-net over F4 | [i] | ||
| 16 | Digital (84, 91, large)-net over F4 | [i] | m-Reduction | |
| 17 | Digital (84, 90, large)-net over F4 | [i] | ||
| 18 | Digital (84, 89, large)-net over F4 | [i] | ||
| 19 | Digital (84, 88, large)-net over F4 | [i] | ||
| 20 | Digital (84, 87, large)-net over F4 | [i] | ||