Information on Result #1195788
Digital (3, 7, 314)-net over F25, using net defined by OOA based on linear OOA(257, 314, F25, 4, 4) (dual of [(314, 4), 1249, 5]-NRT-code), using
- OA 2-folding and stacking [i] based on linear OA(257, 628, F25, 4) (dual of [628, 621, 5]-code), using
- construction XX applied to C1 = C([623,1]), C2 = C([0,2]), C3 = C1 + C2 = C([0,1]), and C∩ = C1 ∩ C2 = C([623,2]) [i] based on
- linear OA(255, 624, F25, 3) (dual of [624, 619, 4]-code or 624-cap in PG(4,25)), using the primitive BCH-code C(I) with length 624 = 252−1, defining interval I = {−1,0,1}, and designed minimum distance d ≥ |I|+1 = 4 [i]
- linear OA(255, 624, F25, 3) (dual of [624, 619, 4]-code or 624-cap in PG(4,25)), using the primitive expurgated narrow-sense BCH-code C(I) with length 624 = 252−1, defining interval I = [0,2], and designed minimum distance d ≥ |I|+1 = 4 [i]
- linear OA(257, 624, F25, 4) (dual of [624, 617, 5]-code), using the primitive BCH-code C(I) with length 624 = 252−1, defining interval I = {−1,0,1,2}, and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(253, 624, F25, 2) (dual of [624, 621, 3]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 624 = 252−1, defining interval I = [0,1], and designed minimum distance d ≥ |I|+1 = 3 [i]
- linear OA(250, 2, F25, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(250, s, F25, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- linear OA(250, 2, F25, 0) (dual of [2, 2, 1]-code) (see above)
- construction XX applied to C1 = C([623,1]), C2 = C([0,2]), C3 = C1 + C2 = C([0,1]), and C∩ = C1 ∩ C2 = C([623,2]) [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 (35, 43, 2097464)-net over F25 | [i] | (u, u+v)-Construction for Nets | |
| 2 | Digital (23, 32, 4220)-net over F25 | [i] | ||
| 3 | Digital (31, 40, 97971)-net over F25 | [i] | ||
| 4 | Digital (39, 48, 2097464)-net over F25 | [i] | ||
| 5 | Digital (88, 101, 2797142)-net over F25 | [i] | Generalized (u, u+v)-Construction for Nets | |
| 6 | Digital (84, 96, 2797142)-net over F25 | [i] | ||
| 7 | Digital (94, 108, 2397370)-net over F25 | [i] | ||
| 8 | Digital (85, 98, 2796828)-net over F25 | [i] | ||
| 9 | Digital (81, 93, 2796828)-net over F25 | [i] | ||
| 10 | Digital (90, 104, 2397056)-net over F25 | [i] | ||
| 11 | Digital (81, 94, 2796514)-net over F25 | [i] | ||
| 12 | Digital (77, 89, 2796514)-net over F25 | [i] | ||