Information on Result #1234465
Digital (50, 60, large)-net over F81, using generalized (u, u+v)-construction based on
- digital (0, 0, 106288)-net over F81, using
- s-reduction based on digital (0, 0, s)-net over F81 for arbitrarily large s, using
- digital (0, 0, 106288)-net over F81 (see above)
- digital (0, 0, 106288)-net over F81 (see above)
- digital (0, 0, 106288)-net over F81 (see above)
- digital (0, 0, 106288)-net over F81 (see above)
- digital (0, 0, 106288)-net over F81 (see above)
- digital (0, 0, 106288)-net over F81 (see above)
- digital (0, 0, 106288)-net over F81 (see above)
- digital (0, 0, 106288)-net over F81 (see above)
- digital (0, 0, 106288)-net over F81 (see above)
- digital (0, 0, 106288)-net over F81 (see above)
- digital (0, 0, 106288)-net over F81 (see above)
- digital (0, 0, 106288)-net over F81 (see above)
- digital (0, 0, 106288)-net over F81 (see above)
- digital (0, 0, 106288)-net over F81 (see above)
- digital (0, 0, 106288)-net over F81 (see above)
- digital (0, 0, 106288)-net over F81 (see above)
- digital (0, 0, 106288)-net over F81 (see above)
- digital (0, 0, 106288)-net over F81 (see above)
- digital (0, 0, 106288)-net over F81 (see above)
- digital (0, 0, 106288)-net over F81 (see above)
- digital (0, 0, 106288)-net over F81 (see above)
- digital (0, 0, 106288)-net over F81 (see above)
- digital (0, 0, 106288)-net over F81 (see above)
- digital (0, 0, 106288)-net over F81 (see above)
- digital (0, 0, 106288)-net over F81 (see above)
- digital (0, 0, 106288)-net over F81 (see above)
- digital (0, 0, 106288)-net over F81 (see above)
- digital (0, 0, 106288)-net over F81 (see above)
- digital (0, 0, 106288)-net over F81 (see above)
- digital (0, 0, 106288)-net over F81 (see above)
- digital (0, 0, 106288)-net over F81 (see above)
- digital (0, 0, 106288)-net over F81 (see above)
- digital (0, 0, 106288)-net over F81 (see above)
- digital (0, 0, 106288)-net over F81 (see above)
- digital (0, 0, 106288)-net over F81 (see above)
- digital (0, 0, 106288)-net over F81 (see above)
- digital (0, 0, 106288)-net over F81 (see above)
- digital (0, 0, 106288)-net over F81 (see above)
- digital (0, 0, 106288)-net over F81 (see above)
- digital (0, 0, 106288)-net over F81 (see above)
- digital (0, 0, 106288)-net over F81 (see above)
- digital (0, 0, 106288)-net over F81 (see above)
- digital (0, 0, 106288)-net over F81 (see above)
- digital (0, 0, 106288)-net over F81 (see above)
- digital (0, 0, 106288)-net over F81 (see above)
- digital (0, 0, 106288)-net over F81 (see above)
- digital (0, 0, 106288)-net over F81 (see above)
- digital (0, 0, 106288)-net over F81 (see above)
- digital (0, 0, 106288)-net over F81 (see above)
- digital (0, 0, 106288)-net over F81 (see above)
- digital (0, 0, 106288)-net over F81 (see above)
- digital (0, 0, 106288)-net over F81 (see above)
- digital (0, 0, 106288)-net over F81 (see above)
- digital (0, 0, 106288)-net over F81 (see above)
- digital (0, 0, 106288)-net over F81 (see above)
- digital (0, 0, 106288)-net over F81 (see above)
- digital (0, 0, 106288)-net over F81 (see above)
- digital (0, 0, 106288)-net over F81 (see above)
- digital (0, 0, 106288)-net over F81 (see above)
- digital (0, 0, 106288)-net over F81 (see above)
- digital (0, 0, 106288)-net over F81 (see above)
- digital (0, 0, 106288)-net over F81 (see above)
- digital (0, 0, 106288)-net over F81 (see above)
- digital (0, 0, 106288)-net over F81 (see above)
- digital (0, 0, 106288)-net over F81 (see above)
- digital (0, 0, 106288)-net over F81 (see above)
- digital (0, 0, 106288)-net over F81 (see above)
- digital (0, 0, 106288)-net over F81 (see above)
- digital (0, 0, 106288)-net over F81 (see above)
- digital (0, 0, 106288)-net over F81 (see above)
- digital (0, 1, 106288)-net over F81, using
- s-reduction based on digital (0, 1, s)-net over F81 for arbitrarily large s, using
- digital (0, 1, 106288)-net over F81 (see above)
- digital (0, 1, 106288)-net over F81 (see above)
- digital (0, 1, 106288)-net over F81 (see above)
- digital (0, 1, 106288)-net over F81 (see above)
- digital (2, 4, 106288)-net over F81, using
- s-reduction based on digital (2, 4, 538084)-net over F81, using
- digital (2, 4, 106288)-net over F81 (see above)
- digital (3, 6, 106288)-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 (8, 13, 106288)-net over F81, using
- s-reduction based on digital (8, 13, 265721)-net over F81, using
- net defined by OOA [i] based on linear OOA(8113, 265721, F81, 5, 5) (dual of [(265721, 5), 1328592, 6]-NRT-code), using
- appending kth column [i] based on linear OOA(8113, 265721, F81, 4, 5) (dual of [(265721, 4), 1062871, 6]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OA(8113, 531443, F81, 5) (dual of [531443, 531430, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(8113, 531444, F81, 5) (dual of [531444, 531431, 6]-code), using
- construction X applied to Ce(4) ⊂ Ce(3) [i] based on
- 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(8110, 531441, F81, 4) (dual of [531441, 531431, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 531440 = 813−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [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(4) ⊂ Ce(3) [i] based on
- discarding factors / shortening the dual code based on linear OA(8113, 531444, F81, 5) (dual of [531444, 531431, 6]-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OA(8113, 531443, F81, 5) (dual of [531443, 531430, 6]-code), using
- appending kth column [i] based on linear OOA(8113, 265721, F81, 4, 5) (dual of [(265721, 4), 1062871, 6]-NRT-code), using
- net defined by OOA [i] based on linear OOA(8113, 265721, F81, 5, 5) (dual of [(265721, 5), 1328592, 6]-NRT-code), using
- s-reduction based on digital (8, 13, 265721)-net over F81, using
- digital (18, 28, 106288)-net over F81, using
- net defined by OOA [i] based on linear OOA(8128, 106288, F81, 10, 10) (dual of [(106288, 10), 1062852, 11]-NRT-code), using
- OA 5-folding and stacking [i] based on linear OA(8128, 531440, F81, 10) (dual of [531440, 531412, 11]-code), using
- discarding factors / shortening the dual code based on linear OA(8128, 531441, F81, 10) (dual of [531441, 531413, 11]-code), using
- an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 531440 = 813−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- discarding factors / shortening the dual code based on linear OA(8128, 531441, F81, 10) (dual of [531441, 531413, 11]-code), using
- OA 5-folding and stacking [i] based on linear OA(8128, 531440, F81, 10) (dual of [531440, 531412, 11]-code), using
- net defined by OOA [i] based on linear OOA(8128, 106288, F81, 10, 10) (dual of [(106288, 10), 1062852, 11]-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 (51, 60, large)-net over F81 | [i] | t-Expansion | |
| 2 | Digital (52, 60, large)-net over F81 | [i] | ||
| 3 | Digital (51, 61, large)-net over F81 | [i] | Net Duplication | |
| 4 | Digital (52, 62, large)-net over F81 | [i] | ||
| 5 | Digital (50, 59, large)-net over F81 | [i] | m-Reduction | |
| 6 | Digital (50, 58, large)-net over F81 | [i] | ||
| 7 | Digital (50, 57, large)-net over F81 | [i] | ||
| 8 | Digital (50, 56, large)-net over F81 | [i] | ||
| 9 | Digital (50, 55, large)-net over F81 | [i] | ||
| 10 | Digital (50, 54, large)-net over F81 | [i] | ||
| 11 | Digital (50, 53, large)-net over F81 | [i] | ||
| 12 | (70, 80, large)-net in base 27 | [i] | Base Change | |