Information on Result #599410
There is no digital (37, 136, 167)-net over F4, because extracting embedded orthogonal array would yield linear OA(4136, 167, F4, 99) (dual of [167, 31, 100]-code), but
- construction Y1 [i] would yield
- OA(4135, 149, S4, 99), but
- the linear programming bound shows that M ≥ 2 040610 487096 181427 758937 498317 933435 839690 422249 792187 355243 784188 300883 648114 289820 041216 / 970 822125 > 4135 [i]
- OA(431, 167, S4, 18), but
- the linear programming bound shows that M ≥ 10 709160 698850 412098 268143 898591 232000 / 2 251884 149854 892341 > 431 [i]
- OA(4135, 149, S4, 99), 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 (37, 137, 167)-net over F4 | [i] | m-Reduction | |
| 2 | No digital (37, 138, 167)-net over F4 | [i] | ||