Information on Result #1195426
Digital (68, 87, 116509)-net over F16, using net defined by OOA based on linear OOA(1687, 116509, F16, 19, 19) (dual of [(116509, 19), 2213584, 20]-NRT-code), using
- OOA 9-folding and stacking with additional row [i] based on linear OA(1687, 1048582, F16, 19) (dual of [1048582, 1048495, 20]-code), using
- discarding factors / shortening the dual code based on linear OA(1687, 1048587, F16, 19) (dual of [1048587, 1048500, 20]-code), using
- construction X applied to Ce(18) ⊂ Ce(16) [i] based on
- linear OA(1686, 1048576, F16, 19) (dual of [1048576, 1048490, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 165−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [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(161, 11, F16, 1) (dual of [11, 10, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(161, s, F16, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- construction X applied to Ce(18) ⊂ Ce(16) [i] based on
- discarding factors / shortening the dual code based on linear OA(1687, 1048587, F16, 19) (dual of [1048587, 1048500, 20]-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 (69, 88, 116509)-net over F16 | [i] | Net Duplication | |
| 2 | Digital (83, 102, 116574)-net over F16 | [i] | (u, u+v)-Construction for Nets | |