Information on Result #1203064
Digital (10, 16, 699051)-net over F128, using net defined by OOA 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
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 (13, 19, 699180)-net over F128 | [i] | (u, u+v)-Construction for Nets | |
| 2 | Digital (14, 20, 715436)-net over F128 | [i] | ||
| 3 | Digital (49, 61, 2097151)-net over F128 | [i] | ||
| 4 | Digital (52, 65, 2097151)-net over F128 | [i] | ||
| 5 | (43, 55, 2097151)-net in base 128 | [i] | ||
| 6 | (46, 59, 2097151)-net in base 128 | [i] | ||
| 7 | Digital (22, 28, 6941863)-net over F128 | [i] | Generalized (u, u+v)-Construction for Nets | |
| 8 | Digital (23, 29, large)-net over F128 | [i] | ||
| 9 | Digital (63, 75, 2812587)-net over F128 | [i] | ||
| 10 | Digital (65, 77, 3495253)-net over F128 | [i] | ||
| 11 | (22, 28, 699051)-net in base 16 | [i] | Base Change | |