Information on Result #1210612
Digital (148, 165, 1048641)-net over F4, using (u, u+v)-construction based on
- digital (12, 20, 66)-net over F4, using
- trace code for nets [i] based on digital (2, 10, 33)-net over F16, using
- net from sequence [i] based on digital (2, 32)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 2 and N(F) ≥ 33, using
- net from sequence [i] based on digital (2, 32)-sequence over F16, using
- trace code for nets [i] based on digital (2, 10, 33)-net over F16, using
- digital (128, 145, 1048575)-net over F4, using
- net defined by OOA [i] based on linear OOA(4145, 1048575, F4, 17, 17) (dual of [(1048575, 17), 17825630, 18]-NRT-code), using
- OOA 8-folding and stacking with additional row [i] based on linear OA(4145, 8388601, F4, 17) (dual of [8388601, 8388456, 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 8-folding and stacking with additional row [i] based on linear OA(4145, 8388601, F4, 17) (dual of [8388601, 8388456, 18]-code), using
- net defined by OOA [i] based on linear OOA(4145, 1048575, F4, 17, 17) (dual of [(1048575, 17), 17825630, 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 (149, 165, 1048641)-net over F4 | [i] | t-Expansion | |
| 2 | Digital (149, 166, 1048641)-net over F4 | [i] | Net Duplication | |