Information on Result #598902
There is no digital (132, 238, 335)-net over F2, because extracting embedded orthogonal array would yield linear OA(2238, 335, F2, 106) (dual of [335, 97, 107]-code), but
- construction Y1 [i] would yield
- OA(2237, 299, S2, 106), but
- the linear programming bound shows that M ≥ 2 372623 864838 720824 144751 616230 912568 605364 469958 081012 522169 374458 839809 772727 298051 538944 / 10 001354 293176 388857 > 2237 [i]
- OA(297, 335, S2, 36), but
- discarding factors would yield OA(297, 324, S2, 36), but
- the Rao or (dual) Hamming bound shows that M ≥ 158757 007614 184387 760434 595956 > 297 [i]
- discarding factors would yield OA(297, 324, S2, 36), but
- OA(2237, 299, S2, 106), 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 (132, 239, 335)-net over F2 | [i] | m-Reduction | |