Information on Result #1222174
Digital (66, 79, 1404664)-net over F27, using (u, u+v)-construction based on
- digital (12, 18, 6564)-net over F27, using
- net defined by OOA [i] based on linear OOA(2718, 6564, F27, 6, 6) (dual of [(6564, 6), 39366, 7]-NRT-code), using
- OA 3-folding and stacking [i] based on linear OA(2718, 19692, F27, 6) (dual of [19692, 19674, 7]-code), using
- discarding factors / shortening the dual code based on linear OA(2718, 19694, F27, 6) (dual of [19694, 19676, 7]-code), using
- construction X applied to Ce(5) ⊂ Ce(2) [i] based on
- linear OA(2716, 19683, F27, 6) (dual of [19683, 19667, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 19682 = 273−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(277, 19683, F27, 3) (dual of [19683, 19676, 4]-code or 19683-cap in PG(6,27)), using an extension Ce(2) of the primitive narrow-sense BCH-code C(I) with length 19682 = 273−1, defining interval I = [1,2], and designed minimum distance d ≥ |I|+1 = 3 [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(5) ⊂ Ce(2) [i] based on
- discarding factors / shortening the dual code based on linear OA(2718, 19694, F27, 6) (dual of [19694, 19676, 7]-code), using
- OA 3-folding and stacking [i] based on linear OA(2718, 19692, F27, 6) (dual of [19692, 19674, 7]-code), using
- net defined by OOA [i] based on linear OOA(2718, 6564, F27, 6, 6) (dual of [(6564, 6), 39366, 7]-NRT-code), using
- digital (48, 61, 1398100)-net over F27, using
- net defined by OOA [i] based on linear OOA(2761, 1398100, F27, 13, 13) (dual of [(1398100, 13), 18175239, 14]-NRT-code), using
- OOA 6-folding and stacking with additional row [i] based on linear OA(2761, 8388601, F27, 13) (dual of [8388601, 8388540, 14]-code), using
- discarding factors / shortening the dual code based on linear OA(2761, large, F27, 13) (dual of [large, large−61, 14]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 14348908 | 2710−1, 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(2761, large, F27, 13) (dual of [large, large−61, 14]-code), using
- OOA 6-folding and stacking with additional row [i] based on linear OA(2761, 8388601, F27, 13) (dual of [8388601, 8388540, 14]-code), using
- net defined by OOA [i] based on linear OOA(2761, 1398100, F27, 13, 13) (dual of [(1398100, 13), 18175239, 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 (92, 105, 2809328)-net over F27 | [i] | (u, u+v)-Construction for Nets | |