Information on Result #1858738
There is no digital (4, m, 77)-net over F16 for arbitrarily large m, because m-reduction would yield digital (4, 68, 77)-net over F16, but
- extracting embedded orthogonal array [i] would yield linear OA(1668, 77, F16, 64) (dual of [77, 9, 65]-code), but
- construction Y1 [i] would yield
- OA(1667, 69, S16, 64), but
- the (dual) Plotkin bound shows that M ≥ 7588 550360 256754 183279 148073 529370 729071 901715 047420 004889 892225 542594 864082 845696 / 13 > 1667 [i]
- OA(169, 77, S16, 8), but
- the Rao or (dual) Hamming bound shows that M ≥ 68757 087631 > 169 [i]
- OA(1667, 69, S16, 64), 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 (4, 76)-sequence over F16 | [i] | Net from Sequence | |
| 2 | No digital (4, 4+k, 77)-net over F16 for arbitrarily large k | [i] | Logical Equivalence (for Nets with Unbounded m) | |
| 3 | No digital (4, m, 77)-net over F16 with unbounded m | [i] | ||