Information on Result #1234073
Digital (33, 40, large)-net over F49, using generalized (u, u+v)-construction based on
- digital (0, 0, 120100)-net over F49, using
- s-reduction based on digital (0, 0, s)-net over F49 for arbitrarily large s, using
- digital (0, 0, 120100)-net over F49 (see above)
- digital (0, 0, 120100)-net over F49 (see above)
- digital (0, 0, 120100)-net over F49 (see above)
- digital (0, 0, 120100)-net over F49 (see above)
- digital (0, 0, 120100)-net over F49 (see above)
- digital (0, 0, 120100)-net over F49 (see above)
- digital (0, 0, 120100)-net over F49 (see above)
- digital (0, 0, 120100)-net over F49 (see above)
- digital (0, 0, 120100)-net over F49 (see above)
- digital (0, 0, 120100)-net over F49 (see above)
- digital (0, 0, 120100)-net over F49 (see above)
- digital (0, 0, 120100)-net over F49 (see above)
- digital (0, 0, 120100)-net over F49 (see above)
- digital (0, 0, 120100)-net over F49 (see above)
- digital (0, 0, 120100)-net over F49 (see above)
- digital (0, 0, 120100)-net over F49 (see above)
- digital (0, 0, 120100)-net over F49 (see above)
- digital (0, 0, 120100)-net over F49 (see above)
- digital (0, 0, 120100)-net over F49 (see above)
- digital (0, 0, 120100)-net over F49 (see above)
- digital (0, 0, 120100)-net over F49 (see above)
- digital (0, 0, 120100)-net over F49 (see above)
- digital (0, 0, 120100)-net over F49 (see above)
- digital (0, 0, 120100)-net over F49 (see above)
- digital (0, 0, 120100)-net over F49 (see above)
- digital (0, 0, 120100)-net over F49 (see above)
- digital (0, 0, 120100)-net over F49 (see above)
- digital (0, 0, 120100)-net over F49 (see above)
- digital (0, 0, 120100)-net over F49 (see above)
- digital (0, 0, 120100)-net over F49 (see above)
- digital (0, 0, 120100)-net over F49 (see above)
- digital (0, 0, 120100)-net over F49 (see above)
- digital (0, 0, 120100)-net over F49 (see above)
- digital (0, 0, 120100)-net over F49 (see above)
- digital (0, 0, 120100)-net over F49 (see above)
- digital (0, 0, 120100)-net over F49 (see above)
- digital (0, 0, 120100)-net over F49 (see above)
- digital (0, 0, 120100)-net over F49 (see above)
- digital (0, 0, 120100)-net over F49 (see above)
- digital (0, 0, 120100)-net over F49 (see above)
- digital (0, 0, 120100)-net over F49 (see above)
- digital (0, 1, 120100)-net over F49, using
- s-reduction based on digital (0, 1, s)-net over F49 for arbitrarily large s, using
- digital (0, 1, 120100)-net over F49 (see above)
- digital (0, 1, 120100)-net over F49 (see above)
- digital (0, 1, 120100)-net over F49 (see above)
- digital (2, 4, 120100)-net over F49, using
- digital (4, 7, 1921601)-net over F49, using
- s-reduction based on digital (4, 7, 5769603)-net over F49, using
- net defined by OOA [i] based on linear OOA(497, 5769603, F49, 3, 3) (dual of [(5769603, 3), 17308802, 4]-NRT-code), using
- appending kth column [i] based on linear OOA(497, 5769603, F49, 2, 3) (dual of [(5769603, 2), 11539199, 4]-NRT-code), using
- net defined by OOA [i] based on linear OOA(497, 5769603, F49, 3, 3) (dual of [(5769603, 3), 17308802, 4]-NRT-code), using
- s-reduction based on digital (4, 7, 5769603)-net over F49, using
- digital (18, 25, 1921601)-net over F49, using
- net defined by OOA [i] based on linear OOA(4925, 1921601, F49, 7, 7) (dual of [(1921601, 7), 13451182, 8]-NRT-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OA(4925, 5764804, F49, 7) (dual of [5764804, 5764779, 8]-code), using
- discarding factors / shortening the dual code based on linear OA(4925, 5764805, F49, 7) (dual of [5764805, 5764780, 8]-code), using
- construction X applied to Ce(6) ⊂ Ce(5) [i] based on
- linear OA(4925, 5764801, F49, 7) (dual of [5764801, 5764776, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 5764800 = 494−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(4921, 5764801, F49, 6) (dual of [5764801, 5764780, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 5764800 = 494−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(490, 4, F49, 0) (dual of [4, 4, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(490, s, F49, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- construction X applied to Ce(6) ⊂ Ce(5) [i] based on
- discarding factors / shortening the dual code based on linear OA(4925, 5764805, F49, 7) (dual of [5764805, 5764780, 8]-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OA(4925, 5764804, F49, 7) (dual of [5764804, 5764779, 8]-code), using
- net defined by OOA [i] based on linear OOA(4925, 1921601, F49, 7, 7) (dual of [(1921601, 7), 13451182, 8]-NRT-code), using
Mode: Constructive and linear.
Optimality
Show details for fixed k and m, k and t, m and t.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Digital (34, 41, large)-net over F49 | [i] | Net Duplication | |
| 2 | Digital (33, 39, large)-net over F49 | [i] | m-Reduction | |
| 3 | Digital (33, 38, large)-net over F49 | [i] | ||
| 4 | Digital (33, 37, large)-net over F49 | [i] | ||
| 5 | Digital (33, 36, large)-net over F49 | [i] | ||