Information on Result #3264004
Digital (48, 66, 7282)-net over F16, using 161 times duplication based on digital (47, 65, 7282)-net over F16, using
- net defined by OOA [i] based on linear OOA(1665, 7282, F16, 18, 18) (dual of [(7282, 18), 131011, 19]-NRT-code), using
- OA 9-folding and stacking [i] based on linear OA(1665, 65538, F16, 18) (dual of [65538, 65473, 19]-code), using
- discarding factors / shortening the dual code based on linear OA(1665, 65540, F16, 18) (dual of [65540, 65475, 19]-code), using
- construction X applied to Ce(17) ⊂ Ce(16) [i] based on
- linear OA(1665, 65536, F16, 18) (dual of [65536, 65471, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 65535 = 164−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(1661, 65536, F16, 17) (dual of [65536, 65475, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 65535 = 164−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(160, 4, F16, 0) (dual of [4, 4, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(160, s, F16, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- construction X applied to Ce(17) ⊂ Ce(16) [i] based on
- discarding factors / shortening the dual code based on linear OA(1665, 65540, F16, 18) (dual of [65540, 65475, 19]-code), using
- OA 9-folding and stacking [i] based on linear OA(1665, 65538, F16, 18) (dual of [65538, 65473, 19]-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 | (70, 88, 7282)-net in base 8 | [i] | Base Change | |