Information on Result #599913
There is no digital (7, 103, 162)-net over F16, because extracting embedded orthogonal array would yield linear OA(16103, 162, F16, 96) (dual of [162, 59, 97]-code), but
- construction Y1 [i] would yield
- linear OA(16102, 107, F16, 96) (dual of [107, 5, 97]-code), but
- construction Y1 [i] would yield
- OA(16101, 103, S16, 96), but
- the (dual) Plotkin bound shows that M ≥ 4627 391781 531740 192663 407156 229397 278798 832780 749968 534992 541566 920840 538654 179420 776324 473078 006993 933138 484175 163508 129792 / 97 > 16101 [i]
- OA(165, 107, S16, 4), but
- discarding factors would yield OA(165, 97, S16, 4), but
- the Rao or (dual) Hamming bound shows that M ≥ 1 049056 > 165 [i]
- discarding factors would yield OA(165, 97, S16, 4), but
- OA(16101, 103, S16, 96), but
- construction Y1 [i] would yield
- OA(1659, 162, S16, 55), but
- discarding factors would yield OA(1659, 158, S16, 55), but
- the linear programming bound shows that M ≥ 1 751872 128079 872472 547941 838539 530895 802398 111785 402312 961189 355293 686055 441948 303058 733784 687094 938824 867840 / 15 835355 243697 262421 313219 417467 218513 > 1659 [i]
- discarding factors would yield OA(1659, 158, S16, 55), but
- linear OA(16102, 107, F16, 96) (dual of [107, 5, 97]-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, 104, 162)-net over F16 | [i] | m-Reduction | |