Information on Result #1187936
Digital (181, 217, 3641)-net over F4, using net defined by OOA based on linear OOA(4217, 3641, F4, 36, 36) (dual of [(3641, 36), 130859, 37]-NRT-code), using
- OA 18-folding and stacking [i] based on linear OA(4217, 65538, F4, 36) (dual of [65538, 65321, 37]-code), using
- discarding factors / shortening the dual code based on linear OA(4217, 65544, F4, 36) (dual of [65544, 65327, 37]-code), using
- 1 times truncation [i] based on linear OA(4218, 65545, F4, 37) (dual of [65545, 65327, 38]-code), using
- construction X applied to Ce(36) ⊂ Ce(34) [i] based on
- linear OA(4217, 65536, F4, 37) (dual of [65536, 65319, 38]-code), using an extension Ce(36) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,36], and designed minimum distance d ≥ |I|+1 = 37 [i]
- linear OA(4209, 65536, F4, 35) (dual of [65536, 65327, 36]-code), using an extension Ce(34) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,34], and designed minimum distance d ≥ |I|+1 = 35 [i]
- linear OA(41, 9, F4, 1) (dual of [9, 8, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(41, s, F4, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- construction X applied to Ce(36) ⊂ Ce(34) [i] based on
- 1 times truncation [i] based on linear OA(4218, 65545, F4, 37) (dual of [65545, 65327, 38]-code), using
- discarding factors / shortening the dual code based on linear OA(4217, 65544, F4, 36) (dual of [65544, 65327, 37]-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 (204, 240, 3658)-net over F4 | [i] | (u, u+v)-Construction for Nets | |
| 2 | Digital (206, 242, 3662)-net over F4 | [i] | ||