Information on Result #1203602
Digital (29, 44, 299594)-net over F128, using net defined by OOA based on linear OOA(12844, 299594, F128, 15, 15) (dual of [(299594, 15), 4493866, 16]-NRT-code), using
- OOA 7-folding and stacking with additional row [i] based on linear OA(12844, 2097159, F128, 15) (dual of [2097159, 2097115, 16]-code), using
- discarding factors / shortening the dual code based on linear OA(12844, 2097160, F128, 15) (dual of [2097160, 2097116, 16]-code), using
- construction X applied to C([0,7]) ⊂ C([0,6]) [i] based on
- linear OA(12843, 2097153, F128, 15) (dual of [2097153, 2097110, 16]-code), using the expurgated narrow-sense BCH-code C(I) with length 2097153 | 1286−1, defining interval I = [0,7], and minimum distance d ≥ |{−7,−6,…,7}|+1 = 16 (BCH-bound) [i]
- linear OA(12837, 2097153, F128, 13) (dual of [2097153, 2097116, 14]-code), using the expurgated narrow-sense BCH-code C(I) with length 2097153 | 1286−1, defining interval I = [0,6], and minimum distance d ≥ |{−6,−5,…,6}|+1 = 14 (BCH-bound) [i]
- linear OA(1281, 7, F128, 1) (dual of [7, 6, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(1281, s, F128, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- construction X applied to C([0,7]) ⊂ C([0,6]) [i] based on
- discarding factors / shortening the dual code based on linear OA(12844, 2097160, F128, 15) (dual of [2097160, 2097116, 16]-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 (30, 45, 299594)-net over F128 | [i] | Net Duplication | |
| 2 | Digital (37, 52, 299744)-net over F128 | [i] | (u, u+v)-Construction for Nets | |
| 3 | (62, 77, 299594)-net in base 16 | [i] | Base Change | |