Information on Result #1221507
Digital (55, 76, 1629)-net over F25, using (u, u+v)-construction based on
- digital (4, 14, 66)-net over F25, using
- net from sequence [i] based on digital (4, 65)-sequence over F25, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 4 and N(F) ≥ 66, using
- net from sequence [i] based on digital (4, 65)-sequence over F25, using
- digital (41, 62, 1563)-net over F25, using
- net defined by OOA [i] based on linear OOA(2562, 1563, F25, 21, 21) (dual of [(1563, 21), 32761, 22]-NRT-code), using
- OOA 10-folding and stacking with additional row [i] based on linear OA(2562, 15631, F25, 21) (dual of [15631, 15569, 22]-code), using
- discarding factors / shortening the dual code based on linear OA(2562, 15633, F25, 21) (dual of [15633, 15571, 22]-code), using
- construction X applied to C([0,10]) ⊂ C([0,9]) [i] based on
- linear OA(2561, 15626, F25, 21) (dual of [15626, 15565, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 15626 | 256−1, defining interval I = [0,10], and minimum distance d ≥ |{−10,−9,…,10}|+1 = 22 (BCH-bound) [i]
- linear OA(2555, 15626, F25, 19) (dual of [15626, 15571, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 15626 | 256−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (BCH-bound) [i]
- linear OA(251, 7, F25, 1) (dual of [7, 6, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(251, s, F25, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- construction X applied to C([0,10]) ⊂ C([0,9]) [i] based on
- discarding factors / shortening the dual code based on linear OA(2562, 15633, F25, 21) (dual of [15633, 15571, 22]-code), using
- OOA 10-folding and stacking with additional row [i] based on linear OA(2562, 15631, F25, 21) (dual of [15631, 15569, 22]-code), using
- net defined by OOA [i] based on linear OOA(2562, 1563, F25, 21, 21) (dual of [(1563, 21), 32761, 22]-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 (56, 77, 1629)-net over F25 | [i] | Net Duplication | |