Information on Result #1234478
Digital (23, 29, large)-net over F81, using generalized (u, u+v)-construction based on
- digital (0, 0, 177148)-net over F81, using
- s-reduction based on digital (0, 0, s)-net over F81 for arbitrarily large s, using
- digital (0, 0, 177148)-net over F81 (see above)
- digital (0, 0, 177148)-net over F81 (see above)
- digital (0, 0, 177148)-net over F81 (see above)
- digital (0, 0, 177148)-net over F81 (see above)
- digital (0, 0, 177148)-net over F81 (see above)
- digital (0, 0, 177148)-net over F81 (see above)
- digital (0, 0, 177148)-net over F81 (see above)
- digital (0, 0, 177148)-net over F81 (see above)
- digital (0, 0, 177148)-net over F81 (see above)
- digital (0, 0, 177148)-net over F81 (see above)
- digital (0, 0, 177148)-net over F81 (see above)
- digital (0, 0, 177148)-net over F81 (see above)
- digital (0, 0, 177148)-net over F81 (see above)
- digital (0, 0, 177148)-net over F81 (see above)
- digital (0, 0, 177148)-net over F81 (see above)
- digital (0, 0, 177148)-net over F81 (see above)
- digital (0, 0, 177148)-net over F81 (see above)
- digital (0, 0, 177148)-net over F81 (see above)
- digital (0, 0, 177148)-net over F81 (see above)
- digital (0, 0, 177148)-net over F81 (see above)
- digital (0, 0, 177148)-net over F81 (see above)
- digital (0, 0, 177148)-net over F81 (see above)
- digital (0, 0, 177148)-net over F81 (see above)
- digital (0, 0, 177148)-net over F81 (see above)
- digital (0, 0, 177148)-net over F81 (see above)
- digital (0, 0, 177148)-net over F81 (see above)
- digital (0, 0, 177148)-net over F81 (see above)
- digital (0, 0, 177148)-net over F81 (see above)
- digital (0, 0, 177148)-net over F81 (see above)
- digital (0, 0, 177148)-net over F81 (see above)
- digital (0, 0, 177148)-net over F81 (see above)
- digital (0, 0, 177148)-net over F81 (see above)
- digital (0, 0, 177148)-net over F81 (see above)
- digital (0, 0, 177148)-net over F81 (see above)
- digital (0, 0, 177148)-net over F81 (see above)
- digital (0, 0, 177148)-net over F81 (see above)
- digital (0, 0, 177148)-net over F81 (see above)
- digital (0, 0, 177148)-net over F81 (see above)
- digital (0, 0, 177148)-net over F81 (see above)
- digital (0, 0, 177148)-net over F81 (see above)
- digital (0, 0, 177148)-net over F81 (see above)
- digital (0, 0, 177148)-net over F81 (see above)
- digital (0, 0, 177148)-net over F81 (see above)
- digital (0, 0, 177148)-net over F81 (see above)
- digital (0, 0, 177148)-net over F81 (see above)
- digital (0, 0, 177148)-net over F81 (see above)
- digital (0, 0, 177148)-net over F81 (see above)
- digital (0, 0, 177148)-net over F81 (see above)
- digital (0, 0, 177148)-net over F81 (see above)
- digital (0, 0, 177148)-net over F81 (see above)
- digital (0, 0, 177148)-net over F81 (see above)
- digital (0, 0, 177148)-net over F81 (see above)
- digital (0, 0, 177148)-net over F81 (see above)
- digital (0, 0, 177148)-net over F81 (see above)
- digital (0, 0, 177148)-net over F81 (see above)
- digital (0, 0, 177148)-net over F81 (see above)
- digital (0, 0, 177148)-net over F81 (see above)
- digital (0, 0, 177148)-net over F81 (see above)
- digital (0, 0, 177148)-net over F81 (see above)
- digital (0, 0, 177148)-net over F81 (see above)
- digital (0, 0, 177148)-net over F81 (see above)
- digital (0, 0, 177148)-net over F81 (see above)
- digital (0, 0, 177148)-net over F81 (see above)
- digital (0, 0, 177148)-net over F81 (see above)
- digital (0, 0, 177148)-net over F81 (see above)
- digital (0, 0, 177148)-net over F81 (see above)
- digital (0, 0, 177148)-net over F81 (see above)
- digital (0, 0, 177148)-net over F81 (see above)
- digital (0, 0, 177148)-net over F81 (see above)
- digital (0, 0, 177148)-net over F81 (see above)
- digital (0, 0, 177148)-net over F81 (see above)
- digital (0, 0, 177148)-net over F81 (see above)
- digital (0, 0, 177148)-net over F81 (see above)
- digital (0, 0, 177148)-net over F81 (see above)
- digital (0, 1, 177148)-net over F81, using
- s-reduction based on digital (0, 1, s)-net over F81 for arbitrarily large s, using
- digital (0, 1, 177148)-net over F81 (see above)
- digital (0, 1, 177148)-net over F81 (see above)
- digital (2, 4, 177148)-net over F81, using
- s-reduction based on digital (2, 4, 538084)-net over F81, using
- digital (3, 6, 177148)-net over F81, using
- s-reduction based on digital (3, 6, 538248)-net over F81, using
- net defined by OOA [i] based on linear OOA(816, 538248, F81, 3, 3) (dual of [(538248, 3), 1614738, 4]-NRT-code), using
- appending kth column [i] based on linear OOA(816, 538248, F81, 2, 3) (dual of [(538248, 2), 1076490, 4]-NRT-code), using
- net defined by OOA [i] based on linear OOA(816, 538248, F81, 3, 3) (dual of [(538248, 3), 1614738, 4]-NRT-code), using
- s-reduction based on digital (3, 6, 538248)-net over F81, using
- digital (10, 16, 177148)-net over F81, using
- net defined by OOA [i] based on linear OOA(8116, 177148, F81, 6, 6) (dual of [(177148, 6), 1062872, 7]-NRT-code), using
- OA 3-folding and stacking [i] based on linear OA(8116, 531444, F81, 6) (dual of [531444, 531428, 7]-code), using
- construction X applied to Ce(5) ⊂ Ce(4) [i] based on
- linear OA(8116, 531441, F81, 6) (dual of [531441, 531425, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 531440 = 813−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(8113, 531441, F81, 5) (dual of [531441, 531428, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 531440 = 813−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(810, 3, F81, 0) (dual of [3, 3, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(810, s, F81, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- construction X applied to Ce(5) ⊂ Ce(4) [i] based on
- OA 3-folding and stacking [i] based on linear OA(8116, 531444, F81, 6) (dual of [531444, 531428, 7]-code), using
- net defined by OOA [i] based on linear OOA(8116, 177148, F81, 6, 6) (dual of [(177148, 6), 1062872, 7]-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 (24, 29, large)-net over F81 | [i] | t-Expansion | |
| 2 | Digital (25, 29, large)-net over F81 | [i] | ||
| 3 | Digital (24, 30, large)-net over F81 | [i] | Net Duplication | |
| 4 | Digital (25, 31, large)-net over F81 | [i] | ||
| 5 | Digital (23, 28, large)-net over F81 | [i] | m-Reduction | |
| 6 | Digital (23, 27, large)-net over F81 | [i] | ||
| 7 | Digital (23, 26, large)-net over F81 | [i] | ||