Information on Result #599376
There is no digital (14, 54, 67)-net over F4, because extracting embedded orthogonal array would yield linear OA(454, 67, F4, 40) (dual of [67, 13, 41]-code), but
- construction Y1 [i] would yield
- linear OA(453, 59, F4, 40) (dual of [59, 6, 41]-code), but
- residual code [i] would yield linear OA(413, 18, F4, 10) (dual of [18, 5, 11]-code), but
- “Liz†bound on codes from Brouwer’s database [i]
- residual code [i] would yield linear OA(413, 18, F4, 10) (dual of [18, 5, 11]-code), but
- OA(413, 67, S4, 8), but
- the linear programming bound shows that M ≥ 921996 181504 / 13559 > 413 [i]
- linear OA(453, 59, F4, 40) (dual of [59, 6, 41]-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 (14, 55, 67)-net over F4 | [i] | m-Reduction | |
| 2 | No digital (14, 56, 67)-net over F4 | [i] | ||