Information on Result #1186708
Digital (165, 182, 2097150)-net over F4, using net defined by OOA based on linear OOA(4182, 2097150, F4, 18, 17) (dual of [(2097150, 18), 37748518, 18]-NRT-code), using
- OOA 4-folding and stacking with additional row [i] based on linear OOA(4182, 8388601, F4, 2, 17) (dual of [(8388601, 2), 16777020, 18]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(4182, 8388602, F4, 2, 17) (dual of [(8388602, 2), 16777022, 18]-NRT-code), using
- trace code [i] based on linear OOA(1691, 4194301, F16, 2, 17) (dual of [(4194301, 2), 8388511, 18]-NRT-code), using
- OOA 2-folding [i] based on linear OA(1691, 8388602, F16, 17) (dual of [8388602, 8388511, 18]-code), using
- discarding factors / shortening the dual code based on linear OA(1691, large, F16, 17) (dual of [large, large−91, 18]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 166−1, defining interval I = [0,16], and designed minimum distance d ≥ |I|+1 = 18 [i]
- discarding factors / shortening the dual code based on linear OA(1691, large, F16, 17) (dual of [large, large−91, 18]-code), using
- OOA 2-folding [i] based on linear OA(1691, 8388602, F16, 17) (dual of [8388602, 8388511, 18]-code), using
- trace code [i] based on linear OOA(1691, 4194301, F16, 2, 17) (dual of [(4194301, 2), 8388511, 18]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(4182, 8388602, F4, 2, 17) (dual of [(8388602, 2), 16777022, 18]-NRT-code), 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 | Digital (166, 182, 2097150)-net over F4 | [i] | t-Expansion | |
| 2 | Digital (166, 183, 2097150)-net over F4 | [i] | Net Duplication | |
| 3 | Digital (167, 184, 2097150)-net over F4 | [i] | ||
| 4 | Digital (168, 185, 2097150)-net over F4 | [i] | ||
| 5 | Digital (169, 186, 2097150)-net over F4 | [i] | ||
| 6 | Digital (170, 187, 2097150)-net over F4 | [i] | ||
| 7 | Digital (171, 188, 2097150)-net over F4 | [i] | ||
| 8 | Digital (172, 189, 2097150)-net over F4 | [i] | ||
| 9 | Digital (165, 181, 2097150)-net over F4 | [i] | m-Reduction | |
| 10 | Digital (173, 190, 2097155)-net over F4 | [i] | (u, u+v)-Construction for Nets | |
| 11 | Digital (174, 191, 2097159)-net over F4 | [i] | ||
| 12 | Digital (175, 192, 2097160)-net over F4 | [i] | ||
| 13 | Digital (176, 193, 2097164)-net over F4 | [i] | ||
| 14 | Digital (177, 194, 2097167)-net over F4 | [i] | ||