Information on Result #1195392
Digital (63, 81, 116509)-net over F16, using net defined by OOA based on linear OOA(1681, 116509, F16, 18, 18) (dual of [(116509, 18), 2097081, 19]-NRT-code), using
- OA 9-folding and stacking [i] based on linear OA(1681, 1048581, F16, 18) (dual of [1048581, 1048500, 19]-code), using
- construction X applied to Ce(17) ⊂ Ce(16) [i] based on
- linear OA(1681, 1048576, F16, 18) (dual of [1048576, 1048495, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 165−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(1676, 1048576, F16, 17) (dual of [1048576, 1048500, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 165−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(160, 5, F16, 0) (dual of [5, 5, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(160, s, F16, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- construction X applied to Ce(17) ⊂ Ce(16) [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 (64, 82, 116509)-net over F16 | [i] | Net Duplication | |
| 2 | Digital (65, 83, 116509)-net over F16 | [i] | ||
| 3 | Digital (72, 90, 116526)-net over F16 | [i] | (u, u+v)-Construction for Nets | |
| 4 | Digital (73, 91, 116533)-net over F16 | [i] | ||
| 5 | Digital (74, 92, 116542)-net over F16 | [i] | ||
| 6 | Digital (75, 93, 116547)-net over F16 | [i] | ||
| 7 | Digital (76, 94, 116554)-net over F16 | [i] | ||
| 8 | Digital (77, 95, 116558)-net over F16 | [i] | ||
| 9 | Digital (78, 96, 116574)-net over F16 | [i] | ||