Information on Result #1234179
Digital (59, 69, large)-net over F64, using generalized (u, u+v)-construction based on
- digital (0, 0, 131073)-net over F64, using
- s-reduction based on digital (0, 0, s)-net over F64 for arbitrarily large s, using
- digital (0, 0, 131073)-net over F64 (see above)
- digital (0, 0, 131073)-net over F64 (see above)
- digital (0, 0, 131073)-net over F64 (see above)
- digital (0, 0, 131073)-net over F64 (see above)
- digital (0, 0, 131073)-net over F64 (see above)
- digital (0, 0, 131073)-net over F64 (see above)
- digital (0, 0, 131073)-net over F64 (see above)
- digital (0, 0, 131073)-net over F64 (see above)
- digital (0, 0, 131073)-net over F64 (see above)
- digital (0, 0, 131073)-net over F64 (see above)
- digital (0, 0, 131073)-net over F64 (see above)
- digital (0, 0, 131073)-net over F64 (see above)
- digital (0, 0, 131073)-net over F64 (see above)
- digital (0, 0, 131073)-net over F64 (see above)
- digital (0, 0, 131073)-net over F64 (see above)
- digital (0, 0, 131073)-net over F64 (see above)
- digital (0, 0, 131073)-net over F64 (see above)
- digital (0, 0, 131073)-net over F64 (see above)
- digital (0, 0, 131073)-net over F64 (see above)
- digital (0, 0, 131073)-net over F64 (see above)
- digital (0, 0, 131073)-net over F64 (see above)
- digital (0, 0, 131073)-net over F64 (see above)
- digital (0, 0, 131073)-net over F64 (see above)
- digital (0, 0, 131073)-net over F64 (see above)
- digital (0, 0, 131073)-net over F64 (see above)
- digital (0, 0, 131073)-net over F64 (see above)
- digital (0, 0, 131073)-net over F64 (see above)
- digital (0, 0, 131073)-net over F64 (see above)
- digital (0, 0, 131073)-net over F64 (see above)
- digital (0, 0, 131073)-net over F64 (see above)
- digital (0, 0, 131073)-net over F64 (see above)
- digital (0, 0, 131073)-net over F64 (see above)
- digital (0, 0, 131073)-net over F64 (see above)
- digital (0, 0, 131073)-net over F64 (see above)
- digital (0, 0, 131073)-net over F64 (see above)
- digital (0, 0, 131073)-net over F64 (see above)
- digital (0, 0, 131073)-net over F64 (see above)
- digital (0, 0, 131073)-net over F64 (see above)
- digital (0, 0, 131073)-net over F64 (see above)
- digital (0, 0, 131073)-net over F64 (see above)
- digital (0, 0, 131073)-net over F64 (see above)
- digital (0, 0, 131073)-net over F64 (see above)
- digital (0, 0, 131073)-net over F64 (see above)
- digital (0, 0, 131073)-net over F64 (see above)
- digital (0, 0, 131073)-net over F64 (see above)
- digital (0, 0, 131073)-net over F64 (see above)
- digital (0, 0, 131073)-net over F64 (see above)
- digital (0, 0, 131073)-net over F64 (see above)
- digital (0, 0, 131073)-net over F64 (see above)
- digital (0, 0, 131073)-net over F64 (see above)
- digital (0, 0, 131073)-net over F64 (see above)
- digital (0, 0, 131073)-net over F64 (see above)
- digital (0, 0, 131073)-net over F64 (see above)
- digital (0, 1, 131073)-net over F64, using
- s-reduction based on digital (0, 1, s)-net over F64 for arbitrarily large s, using
- digital (0, 1, 131073)-net over F64 (see above)
- digital (0, 1, 131073)-net over F64 (see above)
- digital (0, 1, 131073)-net over F64 (see above)
- digital (0, 1, 131073)-net over F64 (see above)
- digital (2, 4, 131073)-net over F64, using
- s-reduction based on digital (2, 4, 266305)-net over F64, using
- digital (2, 4, 131073)-net over F64 (see above)
- digital (3, 6, 131073)-net over F64, using
- s-reduction based on digital (3, 6, 270402)-net over F64, using
- net defined by OOA [i] based on linear OOA(646, 270402, F64, 3, 3) (dual of [(270402, 3), 811200, 4]-NRT-code), using
- appending kth column [i] based on linear OOA(646, 270402, F64, 2, 3) (dual of [(270402, 2), 540798, 4]-NRT-code), using
- net defined by OOA [i] based on linear OOA(646, 270402, F64, 3, 3) (dual of [(270402, 3), 811200, 4]-NRT-code), using
- s-reduction based on digital (3, 6, 270402)-net over F64, using
- digital (8, 13, 131073)-net over F64, using
- net defined by OOA [i] based on linear OOA(6413, 131073, F64, 5, 5) (dual of [(131073, 5), 655352, 6]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OA(6413, 262147, F64, 5) (dual of [262147, 262134, 6]-code), using
- construction X applied to Ce(4) ⊂ Ce(3) [i] based on
- linear OA(6413, 262144, F64, 5) (dual of [262144, 262131, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(6410, 262144, F64, 4) (dual of [262144, 262134, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [i]
- linear OA(640, 3, F64, 0) (dual of [3, 3, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(640, s, F64, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- construction X applied to Ce(4) ⊂ Ce(3) [i] based on
- OOA 2-folding and stacking with additional row [i] based on linear OA(6413, 262147, F64, 5) (dual of [262147, 262134, 6]-code), using
- net defined by OOA [i] based on linear OOA(6413, 131073, F64, 5, 5) (dual of [(131073, 5), 655352, 6]-NRT-code), using
- digital (27, 37, 1677720)-net over F64, using
- net defined by OOA [i] based on linear OOA(6437, 1677720, F64, 10, 10) (dual of [(1677720, 10), 16777163, 11]-NRT-code), using
- OA 5-folding and stacking [i] based on linear OA(6437, 8388600, F64, 10) (dual of [8388600, 8388563, 11]-code), using
- discarding factors / shortening the dual code based on linear OA(6437, large, F64, 10) (dual of [large, large−37, 11]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 644−1, defining interval I = [0,9], and designed minimum distance d ≥ |I|+1 = 11 [i]
- discarding factors / shortening the dual code based on linear OA(6437, large, F64, 10) (dual of [large, large−37, 11]-code), using
- OA 5-folding and stacking [i] based on linear OA(6437, 8388600, F64, 10) (dual of [8388600, 8388563, 11]-code), using
- net defined by OOA [i] based on linear OOA(6437, 1677720, F64, 10, 10) (dual of [(1677720, 10), 16777163, 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 (60, 69, large)-net over F64 | [i] | t-Expansion | |
| 2 | Digital (61, 69, large)-net over F64 | [i] | ||
| 3 | Digital (62, 69, large)-net over F64 | [i] | ||
| 4 | Digital (60, 70, large)-net over F64 | [i] | Net Duplication | |
| 5 | Digital (61, 71, large)-net over F64 | [i] | ||
| 6 | Digital (62, 72, large)-net over F64 | [i] | ||
| 7 | Digital (59, 68, large)-net over F64 | [i] | m-Reduction | |
| 8 | Digital (59, 67, large)-net over F64 | [i] | ||
| 9 | Digital (59, 66, large)-net over F64 | [i] | ||
| 10 | Digital (59, 65, large)-net over F64 | [i] | ||
| 11 | Digital (59, 64, large)-net over F64 | [i] | ||
| 12 | Digital (59, 63, large)-net over F64 | [i] | ||
| 13 | Digital (59, 62, large)-net over F64 | [i] | ||