Information on Result #1179536
Digital (18, 22, 1048579)-net over F8, using net defined by OOA based on linear OOA(822, 1048579, F8, 4, 4) (dual of [(1048579, 4), 4194294, 5]-NRT-code), using
- appending kth column [i] based on linear OOA(822, 1048579, F8, 3, 4) (dual of [(1048579, 3), 3145715, 5]-NRT-code), using
- OA 2-folding and stacking [i] based on linear OA(822, 2097158, F8, 4) (dual of [2097158, 2097136, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(822, 2097159, F8, 4) (dual of [2097159, 2097137, 5]-code), using
- construction X applied to Ce(3) ⊂ Ce(2) [i] based on
- linear OA(822, 2097152, F8, 4) (dual of [2097152, 2097130, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [i]
- linear OA(815, 2097152, F8, 3) (dual of [2097152, 2097137, 4]-code or 2097152-cap in PG(14,8)), using an extension Ce(2) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,2], and designed minimum distance d ≥ |I|+1 = 3 [i]
- linear OA(80, 7, F8, 0) (dual of [7, 7, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(80, s, F8, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- construction X applied to Ce(3) ⊂ Ce(2) [i] based on
- discarding factors / shortening the dual code based on linear OA(822, 2097159, F8, 4) (dual of [2097159, 2097137, 5]-code), using
- OA 2-folding and stacking [i] based on linear OA(822, 2097158, F8, 4) (dual of [2097158, 2097136, 5]-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 (72, 80, 5242879)-net over F8 | [i] | (u, u+v)-Construction for Nets | |
| 2 | Digital (79, 88, 5242879)-net over F8 | [i] | ||
| 3 | Digital (151, 164, 6640988)-net over F8 | [i] | Generalized (u, u+v)-Construction for Nets | |
| 4 | Digital (152, 165, 6641044)-net over F8 | [i] | ||
| 5 | Digital (144, 156, 6640988)-net over F8 | [i] | ||
| 6 | Digital (145, 157, 6641044)-net over F8 | [i] | ||
| 7 | Digital (148, 161, 6640979)-net over F8 | [i] | ||
| 8 | Digital (141, 153, 6640979)-net over F8 | [i] | ||