Information on Result #599297
There is no digital (84, 231, 373)-net over F3, because extracting embedded orthogonal array would yield linear OA(3231, 373, F3, 147) (dual of [373, 142, 148]-code), but
- residual code [i] would yield linear OA(384, 225, F3, 49) (dual of [225, 141, 50]-code), but
- 1 times truncation [i] would yield linear OA(383, 224, F3, 48) (dual of [224, 141, 49]-code), but
- the Johnson bound shows that N ≤ 18 650275 231410 181575 562142 123676 906294 083572 717553 183697 141026 684466 < 3141 [i]
- 1 times truncation [i] would yield linear OA(383, 224, F3, 48) (dual of [224, 141, 49]-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 (84, 232, 373)-net over F3 | [i] | m-Reduction | |
| 2 | No digital (84, 233, 373)-net over F3 | [i] | ||