Information on Result #1202922
Digital (27, 50, 598)-net over F81, using net defined by OOA based on linear OOA(8150, 598, F81, 23, 23) (dual of [(598, 23), 13704, 24]-NRT-code), using
- OOA 11-folding and stacking with additional row [i] based on linear OA(8150, 6579, F81, 23) (dual of [6579, 6529, 24]-code), using
- construction X applied to C([0,11]) ⊂ C([0,8]) [i] based on
- linear OA(8145, 6562, F81, 23) (dual of [6562, 6517, 24]-code), using the expurgated narrow-sense BCH-code C(I) with length 6562 | 814−1, defining interval I = [0,11], and minimum distance d ≥ |{−11,−10,…,11}|+1 = 24 (BCH-bound) [i]
- linear OA(8133, 6562, F81, 17) (dual of [6562, 6529, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 6562 | 814−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
- linear OA(815, 17, F81, 5) (dual of [17, 12, 6]-code or 17-arc in PG(4,81)), using
- discarding factors / shortening the dual code based on linear OA(815, 81, F81, 5) (dual of [81, 76, 6]-code or 81-arc in PG(4,81)), using
- Reed–Solomon code RS(76,81) [i]
- discarding factors / shortening the dual code based on linear OA(815, 81, F81, 5) (dual of [81, 76, 6]-code or 81-arc in PG(4,81)), using
- construction X applied to C([0,11]) ⊂ C([0,8]) [i] based on
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 (28, 50, 598)-net over F81 | [i] | t-Expansion | |
| 2 | Digital (28, 51, 598)-net over F81 | [i] | Net Duplication | |
| 3 | Digital (29, 52, 598)-net over F81 | [i] | ||
| 4 | Digital (30, 53, 598)-net over F81 | [i] | ||
| 5 | Digital (27, 49, 598)-net over F81 | [i] | m-Reduction | |