Information on Result #1195874
Digital (12, 18, 5212)-net over F25, using net defined by OOA based on linear OOA(2518, 5212, F25, 6, 6) (dual of [(5212, 6), 31254, 7]-NRT-code), using
- OA 3-folding and stacking [i] based on linear OA(2518, 15636, F25, 6) (dual of [15636, 15618, 7]-code), using
- construction X applied to Ce(5) ⊂ Ce(2) [i] based on
- linear OA(2516, 15625, F25, 6) (dual of [15625, 15609, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 15624 = 253−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(257, 15625, F25, 3) (dual of [15625, 15618, 4]-code or 15625-cap in PG(6,25)), using an extension Ce(2) of the primitive narrow-sense BCH-code C(I) with length 15624 = 253−1, defining interval I = [1,2], and designed minimum distance d ≥ |I|+1 = 3 [i]
- linear OA(252, 11, F25, 2) (dual of [11, 9, 3]-code or 11-arc in PG(1,25)), using
- discarding factors / shortening the dual code based on linear OA(252, 25, F25, 2) (dual of [25, 23, 3]-code or 25-arc in PG(1,25)), using
- Reed–Solomon code RS(23,25) [i]
- discarding factors / shortening the dual code based on linear OA(252, 25, F25, 2) (dual of [25, 23, 3]-code or 25-arc in PG(1,25)), using
- construction X applied to Ce(5) ⊂ Ce(2) [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 (62, 74, 1403312)-net over F25 | [i] | (u, u+v)-Construction for Nets | |
| 2 | Digital (66, 79, 1403312)-net over F25 | [i] | ||