Information on Result #1234182
Digital (49, 58, 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, 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 (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 (6, 10, 131073)-net over F64, using
- net defined by OOA [i] based on linear OOA(6410, 131073, F64, 4, 4) (dual of [(131073, 4), 524282, 5]-NRT-code), using
- appending kth column [i] based on linear OOA(6410, 131073, F64, 3, 4) (dual of [(131073, 3), 393209, 5]-NRT-code), using
- OA 2-folding and stacking [i] based on linear OA(6410, 262146, F64, 4) (dual of [262146, 262136, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(6410, 262147, F64, 4) (dual of [262147, 262137, 5]-code), using
- construction X applied to Ce(3) ⊂ Ce(2) [i] based on
- 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(647, 262144, F64, 3) (dual of [262144, 262137, 4]-code or 262144-cap in PG(6,64)), using an extension Ce(2) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,2], and designed minimum distance d ≥ |I|+1 = 3 [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(3) ⊂ Ce(2) [i] based on
- discarding factors / shortening the dual code based on linear OA(6410, 262147, F64, 4) (dual of [262147, 262137, 5]-code), using
- OA 2-folding and stacking [i] based on linear OA(6410, 262146, F64, 4) (dual of [262146, 262136, 5]-code), using
- appending kth column [i] based on linear OOA(6410, 131073, F64, 3, 4) (dual of [(131073, 3), 393209, 5]-NRT-code), using
- net defined by OOA [i] based on linear OOA(6410, 131073, F64, 4, 4) (dual of [(131073, 4), 524282, 5]-NRT-code), using
- digital (24, 33, 2097150)-net over F64, using
- net defined by OOA [i] based on linear OOA(6433, 2097150, F64, 9, 9) (dual of [(2097150, 9), 18874317, 10]-NRT-code), using
- OOA 4-folding and stacking with additional row [i] based on linear OA(6433, 8388601, F64, 9) (dual of [8388601, 8388568, 10]-code), using
- discarding factors / shortening the dual code based on linear OA(6433, large, F64, 9) (dual of [large, large−33, 10]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 16777217 | 648−1, defining interval I = [0,4], and minimum distance d ≥ |{−4,−3,…,4}|+1 = 10 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(6433, large, F64, 9) (dual of [large, large−33, 10]-code), using
- OOA 4-folding and stacking with additional row [i] based on linear OA(6433, 8388601, F64, 9) (dual of [8388601, 8388568, 10]-code), using
- net defined by OOA [i] based on linear OOA(6433, 2097150, F64, 9, 9) (dual of [(2097150, 9), 18874317, 10]-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 (50, 58, large)-net over F64 | [i] | t-Expansion | |
| 2 | Digital (50, 59, large)-net over F64 | [i] | Net Duplication | |
| 3 | Digital (51, 60, large)-net over F64 | [i] | ||
| 4 | Digital (52, 61, large)-net over F64 | [i] | ||
| 5 | Digital (53, 62, large)-net over F64 | [i] | ||
| 6 | Digital (49, 57, large)-net over F64 | [i] | m-Reduction | |
| 7 | Digital (49, 56, large)-net over F64 | [i] | ||
| 8 | Digital (49, 55, large)-net over F64 | [i] | ||
| 9 | Digital (49, 54, large)-net over F64 | [i] | ||
| 10 | Digital (49, 53, large)-net over F64 | [i] | ||
| 11 | Digital (49, 52, large)-net over F64 | [i] | ||