Information on Result #1234581
Digital (36, 44, large)-net over F128, using generalized (u, u+v)-construction based on
- digital (0, 0, 524288)-net over F128, using
- s-reduction based on digital (0, 0, s)-net over F128 for arbitrarily large s, using
- digital (0, 0, 524288)-net over F128 (see above)
- digital (0, 0, 524288)-net over F128 (see above)
- digital (0, 0, 524288)-net over F128 (see above)
- digital (0, 0, 524288)-net over F128 (see above)
- digital (0, 0, 524288)-net over F128 (see above)
- digital (0, 0, 524288)-net over F128 (see above)
- digital (0, 0, 524288)-net over F128 (see above)
- digital (0, 0, 524288)-net over F128 (see above)
- digital (0, 0, 524288)-net over F128 (see above)
- digital (0, 0, 524288)-net over F128 (see above)
- digital (0, 0, 524288)-net over F128 (see above)
- digital (0, 0, 524288)-net over F128 (see above)
- digital (0, 0, 524288)-net over F128 (see above)
- digital (0, 0, 524288)-net over F128 (see above)
- digital (0, 0, 524288)-net over F128 (see above)
- digital (0, 0, 524288)-net over F128 (see above)
- digital (0, 0, 524288)-net over F128 (see above)
- digital (0, 0, 524288)-net over F128 (see above)
- digital (0, 0, 524288)-net over F128 (see above)
- digital (0, 0, 524288)-net over F128 (see above)
- digital (0, 0, 524288)-net over F128 (see above)
- digital (0, 0, 524288)-net over F128 (see above)
- digital (0, 0, 524288)-net over F128 (see above)
- digital (0, 0, 524288)-net over F128 (see above)
- digital (0, 0, 524288)-net over F128 (see above)
- digital (0, 0, 524288)-net over F128 (see above)
- digital (0, 0, 524288)-net over F128 (see above)
- digital (0, 0, 524288)-net over F128 (see above)
- digital (0, 0, 524288)-net over F128 (see above)
- digital (0, 0, 524288)-net over F128 (see above)
- digital (0, 0, 524288)-net over F128 (see above)
- digital (0, 0, 524288)-net over F128 (see above)
- digital (0, 0, 524288)-net over F128 (see above)
- digital (0, 0, 524288)-net over F128 (see above)
- digital (0, 0, 524288)-net over F128 (see above)
- digital (0, 0, 524288)-net over F128 (see above)
- digital (0, 0, 524288)-net over F128 (see above)
- digital (0, 0, 524288)-net over F128 (see above)
- digital (0, 0, 524288)-net over F128 (see above)
- digital (0, 0, 524288)-net over F128 (see above)
- digital (0, 0, 524288)-net over F128 (see above)
- digital (0, 0, 524288)-net over F128 (see above)
- digital (0, 0, 524288)-net over F128 (see above)
- digital (0, 0, 524288)-net over F128 (see above)
- digital (0, 0, 524288)-net over F128 (see above)
- digital (0, 0, 524288)-net over F128 (see above)
- digital (0, 0, 524288)-net over F128 (see above)
- digital (0, 0, 524288)-net over F128 (see above)
- digital (0, 0, 524288)-net over F128 (see above)
- digital (0, 0, 524288)-net over F128 (see above)
- digital (0, 0, 524288)-net over F128 (see above)
- digital (0, 0, 524288)-net over F128 (see above)
- digital (0, 0, 524288)-net over F128 (see above)
- digital (0, 0, 524288)-net over F128 (see above)
- digital (0, 0, 524288)-net over F128 (see above)
- digital (0, 0, 524288)-net over F128 (see above)
- digital (0, 0, 524288)-net over F128 (see above)
- digital (0, 0, 524288)-net over F128 (see above)
- digital (0, 0, 524288)-net over F128 (see above)
- digital (0, 0, 524288)-net over F128 (see above)
- digital (0, 0, 524288)-net over F128 (see above)
- digital (0, 0, 524288)-net over F128 (see above)
- digital (0, 0, 524288)-net over F128 (see above)
- digital (0, 0, 524288)-net over F128 (see above)
- digital (0, 0, 524288)-net over F128 (see above)
- digital (0, 0, 524288)-net over F128 (see above)
- digital (0, 0, 524288)-net over F128 (see above)
- digital (0, 0, 524288)-net over F128 (see above)
- digital (0, 0, 524288)-net over F128 (see above)
- digital (0, 0, 524288)-net over F128 (see above)
- digital (0, 0, 524288)-net over F128 (see above)
- digital (0, 0, 524288)-net over F128 (see above)
- digital (0, 0, 524288)-net over F128 (see above)
- digital (0, 0, 524288)-net over F128 (see above)
- digital (0, 0, 524288)-net over F128 (see above)
- digital (0, 0, 524288)-net over F128 (see above)
- digital (0, 0, 524288)-net over F128 (see above)
- digital (0, 0, 524288)-net over F128 (see above)
- digital (0, 0, 524288)-net over F128 (see above)
- digital (0, 0, 524288)-net over F128 (see above)
- digital (0, 0, 524288)-net over F128 (see above)
- digital (0, 0, 524288)-net over F128 (see above)
- digital (0, 0, 524288)-net over F128 (see above)
- digital (0, 0, 524288)-net over F128 (see above)
- digital (0, 0, 524288)-net over F128 (see above)
- digital (0, 0, 524288)-net over F128 (see above)
- digital (0, 0, 524288)-net over F128 (see above)
- digital (0, 0, 524288)-net over F128 (see above)
- digital (0, 0, 524288)-net over F128 (see above)
- digital (0, 0, 524288)-net over F128 (see above)
- digital (0, 0, 524288)-net over F128 (see above)
- digital (0, 0, 524288)-net over F128 (see above)
- digital (0, 0, 524288)-net over F128 (see above)
- digital (0, 0, 524288)-net over F128 (see above)
- digital (0, 0, 524288)-net over F128 (see above)
- digital (0, 0, 524288)-net over F128 (see above)
- digital (0, 0, 524288)-net over F128 (see above)
- digital (0, 0, 524288)-net over F128 (see above)
- digital (0, 0, 524288)-net over F128 (see above)
- digital (0, 0, 524288)-net over F128 (see above)
- digital (0, 0, 524288)-net over F128 (see above)
- digital (0, 0, 524288)-net over F128 (see above)
- digital (0, 0, 524288)-net over F128 (see above)
- digital (0, 0, 524288)-net over F128 (see above)
- digital (0, 0, 524288)-net over F128 (see above)
- digital (0, 0, 524288)-net over F128 (see above)
- digital (0, 0, 524288)-net over F128 (see above)
- digital (0, 0, 524288)-net over F128 (see above)
- digital (0, 0, 524288)-net over F128 (see above)
- digital (0, 0, 524288)-net over F128 (see above)
- digital (0, 0, 524288)-net over F128 (see above)
- digital (0, 0, 524288)-net over F128 (see above)
- digital (0, 0, 524288)-net over F128 (see above)
- digital (0, 0, 524288)-net over F128 (see above)
- digital (0, 0, 524288)-net over F128 (see above)
- digital (0, 0, 524288)-net over F128 (see above)
- digital (0, 0, 524288)-net over F128 (see above)
- digital (0, 0, 524288)-net over F128 (see above)
- digital (0, 0, 524288)-net over F128 (see above)
- digital (0, 1, 524288)-net over F128, using
- s-reduction based on digital (0, 1, s)-net over F128 for arbitrarily large s, using
- digital (0, 1, 524288)-net over F128 (see above)
- digital (0, 1, 524288)-net over F128 (see above)
- digital (0, 1, 524288)-net over F128 (see above)
- digital (2, 4, 524288)-net over F128, using
- s-reduction based on digital (2, 4, 2113665)-net over F128, using
- digital (2, 4, 524288)-net over F128 (see above)
- digital (6, 10, 524288)-net over F128, using
- s-reduction based on digital (6, 10, 1048577)-net over F128, using
- net defined by OOA [i] based on linear OOA(12810, 1048577, F128, 4, 4) (dual of [(1048577, 4), 4194298, 5]-NRT-code), using
- OA 2-folding and stacking [i] based on linear OA(12810, 2097154, F128, 4) (dual of [2097154, 2097144, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(12810, 2097155, F128, 4) (dual of [2097155, 2097145, 5]-code), using
- construction X applied to Ce(3) ⊂ Ce(2) [i] based on
- linear OA(12810, 2097152, F128, 4) (dual of [2097152, 2097142, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [i]
- linear OA(1287, 2097152, F128, 3) (dual of [2097152, 2097145, 4]-code or 2097152-cap in PG(6,128)), using an extension Ce(2) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,2], and designed minimum distance d ≥ |I|+1 = 3 [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(3) ⊂ Ce(2) [i] based on
- discarding factors / shortening the dual code based on linear OA(12810, 2097155, F128, 4) (dual of [2097155, 2097145, 5]-code), using
- OA 2-folding and stacking [i] based on linear OA(12810, 2097154, F128, 4) (dual of [2097154, 2097144, 5]-code), using
- net defined by OOA [i] based on linear OOA(12810, 1048577, F128, 4, 4) (dual of [(1048577, 4), 4194298, 5]-NRT-code), using
- s-reduction based on digital (6, 10, 1048577)-net over F128, using
- digital (14, 22, 524288)-net over F128, using
- net defined by OOA [i] based on linear OOA(12822, 524288, F128, 8, 8) (dual of [(524288, 8), 4194282, 9]-NRT-code), using
- OA 4-folding and stacking [i] based on linear OA(12822, 2097152, F128, 8) (dual of [2097152, 2097130, 9]-code), using
- an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- OA 4-folding and stacking [i] based on linear OA(12822, 2097152, F128, 8) (dual of [2097152, 2097130, 9]-code), using
- net defined by OOA [i] based on linear OOA(12822, 524288, F128, 8, 8) (dual of [(524288, 8), 4194282, 9]-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 (37, 44, large)-net over F128 | [i] | t-Expansion | |
| 2 | Digital (38, 44, large)-net over F128 | [i] | ||
| 3 | Digital (39, 44, large)-net over F128 | [i] | ||
| 4 | Digital (37, 45, large)-net over F128 | [i] | Net Duplication | |
| 5 | Digital (38, 46, large)-net over F128 | [i] | ||
| 6 | Digital (39, 47, large)-net over F128 | [i] | ||
| 7 | Digital (36, 43, large)-net over F128 | [i] | m-Reduction | |
| 8 | Digital (36, 42, large)-net over F128 | [i] | ||
| 9 | Digital (36, 41, large)-net over F128 | [i] | ||
| 10 | Digital (36, 40, large)-net over F128 | [i] | ||
| 11 | Digital (36, 39, large)-net over F128 | [i] | ||