Information on Result #1234177
Digital (63, 74, 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, 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 (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 (30, 41, 1677720)-net over F64, using
- net defined by OOA [i] based on linear OOA(6441, 1677720, F64, 11, 11) (dual of [(1677720, 11), 18454879, 12]-NRT-code), using
- OOA 5-folding and stacking with additional row [i] based on linear OA(6441, 8388601, F64, 11) (dual of [8388601, 8388560, 12]-code), using
- discarding factors / shortening the dual code based on linear OA(6441, large, F64, 11) (dual of [large, large−41, 12]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 16777217 | 648−1, defining interval I = [0,5], and minimum distance d ≥ |{−5,−4,…,5}|+1 = 12 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(6441, large, F64, 11) (dual of [large, large−41, 12]-code), using
- OOA 5-folding and stacking with additional row [i] based on linear OA(6441, 8388601, F64, 11) (dual of [8388601, 8388560, 12]-code), using
- net defined by OOA [i] based on linear OOA(6441, 1677720, F64, 11, 11) (dual of [(1677720, 11), 18454879, 12]-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 (64, 74, large)-net over F64 | [i] | t-Expansion | |
| 2 | Digital (65, 74, large)-net over F64 | [i] | ||
| 3 | Digital (66, 74, large)-net over F64 | [i] | ||
| 4 | Digital (67, 74, large)-net over F64 | [i] | ||
| 5 | Digital (68, 74, large)-net over F64 | [i] | ||
| 6 | Digital (69, 74, large)-net over F64 | [i] | ||
| 7 | Digital (70, 74, large)-net over F64 | [i] | ||
| 8 | Digital (71, 74, large)-net over F64 | [i] | ||
| 9 | Digital (64, 75, large)-net over F64 | [i] | Net Duplication | |
| 10 | Digital (65, 76, large)-net over F64 | [i] | ||
| 11 | Digital (66, 77, large)-net over F64 | [i] | ||
| 12 | Digital (67, 78, large)-net over F64 | [i] | ||
| 13 | Digital (68, 79, large)-net over F64 | [i] | ||
| 14 | Digital (69, 80, large)-net over F64 | [i] | ||
| 15 | Digital (70, 81, large)-net over F64 | [i] | ||
| 16 | Digital (71, 82, large)-net over F64 | [i] | ||
| 17 | Digital (72, 83, large)-net over F64 | [i] | ||
| 18 | Digital (73, 84, large)-net over F64 | [i] | ||
| 19 | Digital (74, 85, large)-net over F64 | [i] | ||
| 20 | Digital (75, 86, large)-net over F64 | [i] | ||
| 21 | Digital (63, 73, large)-net over F64 | [i] | m-Reduction | |
| 22 | Digital (63, 72, large)-net over F64 | [i] | ||
| 23 | Digital (63, 71, large)-net over F64 | [i] | ||
| 24 | Digital (63, 70, large)-net over F64 | [i] | ||
| 25 | Digital (63, 69, large)-net over F64 | [i] | ||
| 26 | Digital (63, 68, large)-net over F64 | [i] | ||
| 27 | Digital (63, 67, large)-net over F64 | [i] | ||
| 28 | Digital (63, 66, large)-net over F64 | [i] | ||