Information on Result #1185870
Digital (53, 60, 1398121)-net over F4, using net defined by OOA based on linear OOA(460, 1398121, F4, 9, 7) (dual of [(1398121, 9), 12583029, 8]-NRT-code), using
- OOA stacking with additional row [i] based on linear OOA(460, 1398122, F4, 3, 7) (dual of [(1398122, 3), 4194306, 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(456, 1398105, F4, 3, 7) (dual of [(1398105, 3), 4194259, 8]-NRT-code), using
- OOA 3-folding [i] based on linear OA(456, 4194315, F4, 7) (dual of [4194315, 4194259, 8]-code), using
- construction X applied to Ce(6) ⊂ Ce(5) [i] based on
- linear OA(456, 4194304, F4, 7) (dual of [4194304, 4194248, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 4194303 = 411−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(445, 4194304, F4, 6) (dual of [4194304, 4194259, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 4194303 = 411−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(40, 11, F4, 0) (dual of [11, 11, 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(456, 4194315, F4, 7) (dual of [4194315, 4194259, 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 (205, 219, 4993234)-net over F4 | [i] | (u, u+v)-Construction for Nets | |
| 2 | Digital (216, 231, 4993234)-net over F4 | [i] | ||