Information on Result #599281
There is no digital (82, 229, 355)-net over F3, because extracting embedded orthogonal array would yield linear OA(3229, 355, F3, 147) (dual of [355, 126, 148]-code), but
- residual code [i] would yield linear OA(382, 207, F3, 49) (dual of [207, 125, 50]-code), but
- 1 times truncation [i] would yield linear OA(381, 206, F3, 48) (dual of [206, 125, 49]-code), but
- the Johnson bound shows that N ≤ 390067 621362 525166 675859 888729 736992 372634 079787 564789 713745 < 3125 [i]
- 1 times truncation [i] would yield linear OA(381, 206, F3, 48) (dual of [206, 125, 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 (82, 230, 355)-net over F3 | [i] | m-Reduction | |
| 2 | No digital (82, 231, 355)-net over F3 | [i] | ||