Information on Result #1185848
Digital (38, 45, 21864)-net over F4, using net defined by OOA based on linear OOA(445, 21864, F4, 9, 7) (dual of [(21864, 9), 196731, 8]-NRT-code), using
- OOA stacking with additional row [i] based on linear OOA(445, 21865, F4, 3, 7) (dual of [(21865, 3), 65550, 8]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(44, 17, F4, 3, 3) (dual of [(17, 3), 47, 4]-NRT-code), using
- linear OOA(441, 21848, F4, 3, 7) (dual of [(21848, 3), 65503, 8]-NRT-code), using
- OOA 3-folding [i] based on linear OA(441, 65544, F4, 7) (dual of [65544, 65503, 8]-code), using
- construction X applied to Ce(6) ⊂ Ce(5) [i] based on
- linear OA(441, 65536, F4, 7) (dual of [65536, 65495, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(433, 65536, F4, 6) (dual of [65536, 65503, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(40, 8, F4, 0) (dual of [8, 8, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(40, s, F4, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- construction X applied to Ce(6) ⊂ Ce(5) [i] based on
- OOA 3-folding [i] based on linear OA(441, 65544, F4, 7) (dual of [65544, 65503, 8]-code), using
- (u, u+v)-construction [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 (191, 205, 4815348)-net over F4 | [i] | (u, u+v)-Construction for Nets | |
| 2 | Digital (202, 217, 4815348)-net over F4 | [i] | ||