Information on Result #1203138
Digital (8, 16, 4097)-net over F128, using net defined by OOA based on linear OOA(12816, 4097, F128, 8, 8) (dual of [(4097, 8), 32760, 9]-NRT-code), using
- OA 4-folding and stacking [i] based on linear OA(12816, 16388, F128, 8) (dual of [16388, 16372, 9]-code), using
- discarding factors / shortening the dual code based on linear OA(12816, 16389, F128, 8) (dual of [16389, 16373, 9]-code), using
- construction X applied to Ce(7) ⊂ Ce(5) [i] based on
- linear OA(12815, 16384, F128, 8) (dual of [16384, 16369, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(12811, 16384, F128, 6) (dual of [16384, 16373, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(1281, 5, F128, 1) (dual of [5, 4, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(1281, s, F128, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- construction X applied to Ce(7) ⊂ Ce(5) [i] based on
- discarding factors / shortening the dual code based on linear OA(12816, 16389, F128, 8) (dual of [16389, 16373, 9]-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 (61, 77, 1052672)-net over F128 | [i] | (u, u+v)-Construction for Nets | |
| 2 | (53, 69, 1052672)-net in base 128 | [i] | ||
| 3 | (55, 72, 1052672)-net in base 128 | [i] | ||
| 4 | (20, 28, 4097)-net in base 16 | [i] | Base Change | |