Information on Result #1858739
There is no digital (5, m, 92)-net over F16 for arbitrarily large m, because m-reduction would yield digital (5, 85, 92)-net over F16, but
- extracting embedded orthogonal array [i] would yield linear OA(1685, 92, F16, 80) (dual of [92, 7, 81]-code), but
- construction Y1 [i] would yield
- OA(1684, 86, S16, 80), but
- the (dual) Plotkin bound shows that M ≥ 4 479489 484355 608421 114884 561136 888556 243290 994469 299069 799978 201927 583742 360321 890761 754986 543214 231552 / 27 > 1684 [i]
- OA(167, 92, S16, 6), but
- discarding factors would yield OA(167, 80, S16, 6), but
- the Rao or (dual) Hamming bound shows that M ≥ 278 002201 > 167 [i]
- discarding factors would yield OA(167, 80, S16, 6), but
- OA(1684, 86, S16, 80), but
- construction Y1 [i] would yield
Mode: Bound (linear).
Optimality
Show details for fixed 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 (5, 91)-sequence over F16 | [i] | Net from Sequence | |
| 2 | No digital (5, 5+k, 92)-net over F16 for arbitrarily large k | [i] | Logical Equivalence (for Nets with Unbounded m) | |
| 3 | No digital (5, m, 92)-net over F16 with unbounded m | [i] | ||