Information on Result #1234590
Digital (23, 29, large)-net over F128, using generalized (u, u+v)-construction based on
- digital (0, 0, 699051)-net over F128, using
- s-reduction based on digital (0, 0, s)-net over F128 for arbitrarily large s, using
- digital (0, 0, 699051)-net over F128 (see above)
- digital (0, 0, 699051)-net over F128 (see above)
- digital (0, 0, 699051)-net over F128 (see above)
- digital (0, 0, 699051)-net over F128 (see above)
- digital (0, 0, 699051)-net over F128 (see above)
- digital (0, 0, 699051)-net over F128 (see above)
- digital (0, 0, 699051)-net over F128 (see above)
- digital (0, 0, 699051)-net over F128 (see above)
- digital (0, 0, 699051)-net over F128 (see above)
- digital (0, 0, 699051)-net over F128 (see above)
- digital (0, 0, 699051)-net over F128 (see above)
- digital (0, 0, 699051)-net over F128 (see above)
- digital (0, 0, 699051)-net over F128 (see above)
- digital (0, 0, 699051)-net over F128 (see above)
- digital (0, 0, 699051)-net over F128 (see above)
- digital (0, 0, 699051)-net over F128 (see above)
- digital (0, 0, 699051)-net over F128 (see above)
- digital (0, 0, 699051)-net over F128 (see above)
- digital (0, 0, 699051)-net over F128 (see above)
- digital (0, 0, 699051)-net over F128 (see above)
- digital (0, 0, 699051)-net over F128 (see above)
- digital (0, 0, 699051)-net over F128 (see above)
- digital (0, 0, 699051)-net over F128 (see above)
- digital (0, 0, 699051)-net over F128 (see above)
- digital (0, 0, 699051)-net over F128 (see above)
- digital (0, 0, 699051)-net over F128 (see above)
- digital (0, 0, 699051)-net over F128 (see above)
- digital (0, 0, 699051)-net over F128 (see above)
- digital (0, 0, 699051)-net over F128 (see above)
- digital (0, 0, 699051)-net over F128 (see above)
- digital (0, 0, 699051)-net over F128 (see above)
- digital (0, 0, 699051)-net over F128 (see above)
- digital (0, 0, 699051)-net over F128 (see above)
- digital (0, 0, 699051)-net over F128 (see above)
- digital (0, 0, 699051)-net over F128 (see above)
- digital (0, 0, 699051)-net over F128 (see above)
- digital (0, 0, 699051)-net over F128 (see above)
- digital (0, 0, 699051)-net over F128 (see above)
- digital (0, 0, 699051)-net over F128 (see above)
- digital (0, 0, 699051)-net over F128 (see above)
- digital (0, 0, 699051)-net over F128 (see above)
- digital (0, 0, 699051)-net over F128 (see above)
- digital (0, 0, 699051)-net over F128 (see above)
- digital (0, 0, 699051)-net over F128 (see above)
- digital (0, 0, 699051)-net over F128 (see above)
- digital (0, 0, 699051)-net over F128 (see above)
- digital (0, 0, 699051)-net over F128 (see above)
- digital (0, 0, 699051)-net over F128 (see above)
- digital (0, 0, 699051)-net over F128 (see above)
- digital (0, 0, 699051)-net over F128 (see above)
- digital (0, 0, 699051)-net over F128 (see above)
- digital (0, 0, 699051)-net over F128 (see above)
- digital (0, 0, 699051)-net over F128 (see above)
- digital (0, 0, 699051)-net over F128 (see above)
- digital (0, 0, 699051)-net over F128 (see above)
- digital (0, 0, 699051)-net over F128 (see above)
- digital (0, 0, 699051)-net over F128 (see above)
- digital (0, 0, 699051)-net over F128 (see above)
- digital (0, 0, 699051)-net over F128 (see above)
- digital (0, 0, 699051)-net over F128 (see above)
- digital (0, 0, 699051)-net over F128 (see above)
- digital (0, 0, 699051)-net over F128 (see above)
- digital (0, 0, 699051)-net over F128 (see above)
- digital (0, 0, 699051)-net over F128 (see above)
- digital (0, 0, 699051)-net over F128 (see above)
- digital (0, 0, 699051)-net over F128 (see above)
- digital (0, 0, 699051)-net over F128 (see above)
- digital (0, 0, 699051)-net over F128 (see above)
- digital (0, 0, 699051)-net over F128 (see above)
- digital (0, 0, 699051)-net over F128 (see above)
- digital (0, 0, 699051)-net over F128 (see above)
- digital (0, 0, 699051)-net over F128 (see above)
- digital (0, 0, 699051)-net over F128 (see above)
- digital (0, 0, 699051)-net over F128 (see above)
- digital (0, 0, 699051)-net over F128 (see above)
- digital (0, 0, 699051)-net over F128 (see above)
- digital (0, 0, 699051)-net over F128 (see above)
- digital (0, 0, 699051)-net over F128 (see above)
- digital (0, 0, 699051)-net over F128 (see above)
- digital (0, 0, 699051)-net over F128 (see above)
- digital (0, 0, 699051)-net over F128 (see above)
- digital (0, 0, 699051)-net over F128 (see above)
- digital (0, 0, 699051)-net over F128 (see above)
- digital (0, 0, 699051)-net over F128 (see above)
- digital (0, 0, 699051)-net over F128 (see above)
- digital (0, 0, 699051)-net over F128 (see above)
- digital (0, 0, 699051)-net over F128 (see above)
- digital (0, 0, 699051)-net over F128 (see above)
- digital (0, 0, 699051)-net over F128 (see above)
- digital (0, 0, 699051)-net over F128 (see above)
- digital (0, 0, 699051)-net over F128 (see above)
- digital (0, 0, 699051)-net over F128 (see above)
- digital (0, 0, 699051)-net over F128 (see above)
- digital (0, 0, 699051)-net over F128 (see above)
- digital (0, 0, 699051)-net over F128 (see above)
- digital (0, 0, 699051)-net over F128 (see above)
- digital (0, 0, 699051)-net over F128 (see above)
- digital (0, 0, 699051)-net over F128 (see above)
- digital (0, 0, 699051)-net over F128 (see above)
- digital (0, 0, 699051)-net over F128 (see above)
- digital (0, 0, 699051)-net over F128 (see above)
- digital (0, 0, 699051)-net over F128 (see above)
- digital (0, 0, 699051)-net over F128 (see above)
- digital (0, 0, 699051)-net over F128 (see above)
- digital (0, 0, 699051)-net over F128 (see above)
- digital (0, 0, 699051)-net over F128 (see above)
- digital (0, 0, 699051)-net over F128 (see above)
- digital (0, 0, 699051)-net over F128 (see above)
- digital (0, 0, 699051)-net over F128 (see above)
- digital (0, 0, 699051)-net over F128 (see above)
- digital (0, 0, 699051)-net over F128 (see above)
- digital (0, 0, 699051)-net over F128 (see above)
- digital (0, 0, 699051)-net over F128 (see above)
- digital (0, 0, 699051)-net over F128 (see above)
- digital (0, 0, 699051)-net over F128 (see above)
- digital (0, 0, 699051)-net over F128 (see above)
- digital (0, 0, 699051)-net over F128 (see above)
- digital (0, 0, 699051)-net over F128 (see above)
- digital (0, 0, 699051)-net over F128 (see above)
- digital (0, 0, 699051)-net over F128 (see above)
- digital (0, 0, 699051)-net over F128 (see above)
- digital (0, 1, 699051)-net over F128, using
- s-reduction based on digital (0, 1, s)-net over F128 for arbitrarily large s, using
- digital (0, 1, 699051)-net over F128 (see above)
- digital (0, 1, 699051)-net over F128 (see above)
- digital (2, 4, 699051)-net over F128, using
- s-reduction based on digital (2, 4, 2113665)-net over F128, using
- digital (3, 6, 699051)-net over F128, using
- s-reduction based on digital (3, 6, 2130050)-net over F128, using
- net defined by OOA [i] based on linear OOA(1286, 2130050, F128, 3, 3) (dual of [(2130050, 3), 6390144, 4]-NRT-code), using
- appending kth column [i] based on linear OOA(1286, 2130050, F128, 2, 3) (dual of [(2130050, 2), 4260094, 4]-NRT-code), using
- net defined by OOA [i] based on linear OOA(1286, 2130050, F128, 3, 3) (dual of [(2130050, 3), 6390144, 4]-NRT-code), using
- s-reduction based on digital (3, 6, 2130050)-net over F128, using
- digital (10, 16, 699051)-net over F128, using
- net defined by OOA [i] based on linear OOA(12816, 699051, F128, 6, 6) (dual of [(699051, 6), 4194290, 7]-NRT-code), using
- OA 3-folding and stacking [i] based on linear OA(12816, 2097153, F128, 6) (dual of [2097153, 2097137, 7]-code), using
- discarding factors / shortening the dual code based on linear OA(12816, 2097155, F128, 6) (dual of [2097155, 2097139, 7]-code), using
- construction X applied to Ce(5) ⊂ Ce(4) [i] based on
- linear OA(12816, 2097152, F128, 6) (dual of [2097152, 2097136, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(12813, 2097152, F128, 5) (dual of [2097152, 2097139, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(1280, 3, F128, 0) (dual of [3, 3, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(1280, s, F128, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- construction X applied to Ce(5) ⊂ Ce(4) [i] based on
- discarding factors / shortening the dual code based on linear OA(12816, 2097155, F128, 6) (dual of [2097155, 2097139, 7]-code), using
- OA 3-folding and stacking [i] based on linear OA(12816, 2097153, F128, 6) (dual of [2097153, 2097137, 7]-code), using
- net defined by OOA [i] based on linear OOA(12816, 699051, F128, 6, 6) (dual of [(699051, 6), 4194290, 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 F128 | [i] | t-Expansion | |
| 2 | Digital (25, 29, large)-net over F128 | [i] | ||
| 3 | Digital (24, 30, large)-net over F128 | [i] | Net Duplication | |
| 4 | Digital (25, 31, large)-net over F128 | [i] | ||
| 5 | Digital (23, 28, large)-net over F128 | [i] | m-Reduction | |
| 6 | Digital (23, 27, large)-net over F128 | [i] | ||
| 7 | Digital (23, 26, large)-net over F128 | [i] | ||