Information on Result #1203268
Digital (18, 28, 419431)-net over F128, using net defined by OOA based on linear OOA(12828, 419431, F128, 10, 10) (dual of [(419431, 10), 4194282, 11]-NRT-code), using
- OA 5-folding and stacking [i] based on linear OA(12828, 2097155, F128, 10) (dual of [2097155, 2097127, 11]-code), using
- construction X applied to Ce(9) ⊂ Ce(8) [i] based on
- linear OA(12828, 2097152, F128, 10) (dual of [2097152, 2097124, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(12825, 2097152, F128, 9) (dual of [2097152, 2097127, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [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(9) ⊂ Ce(8) [i] based on
Mode: Constructive and linear.
Optimality
Show details for fixed k and m, k and s, k and t, m and s, m and t, t and s.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Digital (19, 29, 419431)-net over F128 | [i] | Net Duplication | |
| 2 | Digital (23, 33, 419560)-net over F128 | [i] | (u, u+v)-Construction for Nets | |
| 3 | Digital (24, 34, 419581)-net over F128 | [i] | ||
| 4 | Digital (25, 35, 427559)-net over F128 | [i] | ||
| 5 | Digital (47, 57, 3516326)-net over F128 | [i] | Generalized (u, u+v)-Construction for Nets | |
| 6 | Digital (48, 58, 4548582)-net over F128 | [i] | ||
| 7 | Digital (49, 59, 7032518)-net over F128 | [i] | ||
| 8 | Digital (50, 60, large)-net over F128 | [i] | ||
| 9 | (39, 49, 419431)-net in base 16 | [i] | Base Change | |