Information on Result #1198450
Digital (50, 75, 1641)-net over F27, using net defined by OOA based on linear OOA(2775, 1641, F27, 25, 25) (dual of [(1641, 25), 40950, 26]-NRT-code), using
- OOA 12-folding and stacking with additional row [i] based on linear OA(2775, 19693, F27, 25) (dual of [19693, 19618, 26]-code), using
- discarding factors / shortening the dual code based on linear OA(2775, 19694, F27, 25) (dual of [19694, 19619, 26]-code), using
- construction X applied to Ce(24) ⊂ Ce(21) [i] based on
- linear OA(2773, 19683, F27, 25) (dual of [19683, 19610, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 19682 = 273−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(2764, 19683, F27, 22) (dual of [19683, 19619, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 19682 = 273−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(272, 11, F27, 2) (dual of [11, 9, 3]-code or 11-arc in PG(1,27)), using
- discarding factors / shortening the dual code based on linear OA(272, 27, F27, 2) (dual of [27, 25, 3]-code or 27-arc in PG(1,27)), using
- Reed–Solomon code RS(25,27) [i]
- discarding factors / shortening the dual code based on linear OA(272, 27, F27, 2) (dual of [27, 25, 3]-code or 27-arc in PG(1,27)), using
- construction X applied to Ce(24) ⊂ Ce(21) [i] based on
- discarding factors / shortening the dual code based on linear OA(2775, 19694, F27, 25) (dual of [19694, 19619, 26]-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 (51, 76, 1641)-net over F27 | [i] | Net Duplication | |
| 2 | Digital (52, 77, 1641)-net over F27 | [i] | ||
| 3 | Digital (50, 74, 1641)-net over F27 | [i] | m-Reduction | |
| 4 | (69, 94, 1757)-net in base 27 | [i] | (u, u+v)-Construction for Nets | |