Information on Result #1215282
Digital (97, 110, 2796330)-net over F8, using (u, u+v)-construction based on
- digital (6, 12, 130)-net over F8, using
- trace code for nets [i] based on digital (0, 6, 65)-net over F64, using
- net from sequence [i] based on digital (0, 64)-sequence over F64, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 0 and N(F) ≥ 65, using
- the rational function field F64(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 64)-sequence over F64, using
- trace code for nets [i] based on digital (0, 6, 65)-net over F64, using
- digital (85, 98, 2796200)-net over F8, using
- net defined by OOA [i] based on linear OOA(898, 2796200, F8, 14, 13) (dual of [(2796200, 14), 39146702, 14]-NRT-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OOA(898, 8388601, F8, 2, 13) (dual of [(8388601, 2), 16777104, 14]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(898, 8388602, F8, 2, 13) (dual of [(8388602, 2), 16777106, 14]-NRT-code), using
- trace code [i] based on linear OOA(6449, 4194301, F64, 2, 13) (dual of [(4194301, 2), 8388553, 14]-NRT-code), using
- OOA 2-folding [i] based on linear OA(6449, 8388602, F64, 13) (dual of [8388602, 8388553, 14]-code), using
- discarding factors / shortening the dual code based on linear OA(6449, large, F64, 13) (dual of [large, large−49, 14]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 16777217 | 648−1, defining interval I = [0,6], and minimum distance d ≥ |{−6,−5,…,6}|+1 = 14 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(6449, large, F64, 13) (dual of [large, large−49, 14]-code), using
- OOA 2-folding [i] based on linear OA(6449, 8388602, F64, 13) (dual of [8388602, 8388553, 14]-code), using
- trace code [i] based on linear OOA(6449, 4194301, F64, 2, 13) (dual of [(4194301, 2), 8388553, 14]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(898, 8388602, F8, 2, 13) (dual of [(8388602, 2), 16777106, 14]-NRT-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OOA(898, 8388601, F8, 2, 13) (dual of [(8388601, 2), 16777104, 14]-NRT-code), using
- net defined by OOA [i] based on linear OOA(898, 2796200, F8, 14, 13) (dual of [(2796200, 14), 39146702, 14]-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 (98, 111, 2796330)-net over F8 | [i] | Net Duplication | |
| 2 | Digital (138, 151, 5592531)-net over F8 | [i] | (u, u+v)-Construction for Nets | |