Information on Result #526574
There is no linear OA(78, 74325, F7, 3) (dual of [74325, 74317, 4]-code or 74325-cap in PG(7,7)), because removing affine subspaces would yield
- linear OA(76, 1659, F7, 3) (dual of [1659, 1653, 4]-code or 1659-cap in PG(5,7)), but
- 9735-cap in AG(6,7), but
- 2 times the recursive bound from Bierbrauer and Edel [i] would yield 239-cap in AG(4,7), but
- 62933-cap in AG(7,7), but
- 3 times the recursive bound from Bierbrauer and Edel [i] would yield 239-cap in AG(4,7) (see above)
Mode: Bound (linear).
Optimality
Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | No linear OOA(78, 74325, F7, 2, 3) (dual of [(74325, 2), 148642, 4]-NRT-code) | [i] | Depth Reduction | |
| 2 | No linear OOA(78, 74325, F7, 3, 3) (dual of [(74325, 3), 222967, 4]-NRT-code) | [i] | ||
| 3 | No digital (5, 8, 74325)-net over F7 | [i] | Extracting Embedded Orthogonal Array | |