Information on Result #1190736
Digital (58, 76, 1868)-net over F7, using net defined by OOA based on linear OOA(776, 1868, F7, 18, 18) (dual of [(1868, 18), 33548, 19]-NRT-code), using
- OA 9-folding and stacking [i] based on linear OA(776, 16812, F7, 18) (dual of [16812, 16736, 19]-code), using
- construction X applied to Ce(17) ⊂ Ce(16) [i] based on
- linear OA(776, 16807, F7, 18) (dual of [16807, 16731, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 16806 = 75−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(771, 16807, F7, 17) (dual of [16807, 16736, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 16806 = 75−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(70, 5, F7, 0) (dual of [5, 5, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(70, s, F7, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- construction X applied to Ce(17) ⊂ Ce(16) [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 (59, 77, 1868)-net over F7 | [i] | Net Duplication | |
| 2 | Digital (60, 78, 1868)-net over F7 | [i] | ||
| 3 | Digital (67, 85, 1876)-net over F7 | [i] | (u, u+v)-Construction for Nets | |
| 4 | Digital (68, 86, 1881)-net over F7 | [i] | ||
| 5 | Digital (70, 88, 1882)-net over F7 | [i] | ||
| 6 | Digital (71, 89, 1884)-net over F7 | [i] | ||
| 7 | Digital (72, 90, 1889)-net over F7 | [i] | ||