Information on Result #599718
There is no digital (7, 32, 66)-net over F5, because extracting embedded orthogonal array would yield linear OA(532, 66, F5, 25) (dual of [66, 34, 26]-code), but
- construction Y1 [i] would yield
- linear OA(531, 39, F5, 25) (dual of [39, 8, 26]-code), but
- construction Y1 [i] would yield
- linear OA(530, 33, F5, 25) (dual of [33, 3, 26]-code), but
- OA(58, 39, S5, 6), but
- discarding factors would yield OA(58, 34, S5, 6), but
- the Rao or (dual) Hamming bound shows that M ≥ 392089 > 58 [i]
- discarding factors would yield OA(58, 34, S5, 6), but
- construction Y1 [i] would yield
- OA(534, 66, S5, 27), but
- discarding factors would yield OA(534, 65, S5, 27), but
- the linear programming bound shows that M ≥ 64 241548 253700 687835 401117 197195 381929 859807 132743 299007 415771 484375 / 105 626721 073484 056311 392841 841080 747283 817551 > 534 [i]
- discarding factors would yield OA(534, 65, S5, 27), but
- linear OA(531, 39, F5, 25) (dual of [39, 8, 26]-code), but
Mode: Bound (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 | No digital (7, 33, 66)-net over F5 | [i] | m-Reduction | |