Information on Result #526583
There is no linear OA(98, 378870, F9, 3) (dual of [378870, 378862, 4]-code or 378870-cap in PG(7,9)), because removing affine subspaces would yield
- linear OA(95, 704, F9, 3) (dual of [704, 699, 4]-code or 704-cap in PG(4,9)), but
- 5376-cap in AG(5,9), but
- 2 times the recursive bound from Bierbrauer and Edel [i] would yield 82-cap in AG(3,9), but
- 42570-cap in AG(6,9), but
- base reduction for affine caps [i] would yield 42570-cap in AG(12,3), but
- 6 times the recursive bound from Bierbrauer and Edel [i] would yield 113-cap in AG(6,3), but
- base reduction for affine caps [i] would yield 42570-cap in AG(12,3), but
- 330223-cap in AG(7,9), but
- base reduction for affine caps [i] would yield 330223-cap in AG(14,3), but
- 8 times the recursive bound from Bierbrauer and Edel [i] would yield 113-cap in AG(6,3) (see above)
- base reduction for affine caps [i] would yield 330223-cap in AG(14,3), but
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(98, 378870, F9, 2, 3) (dual of [(378870, 2), 757732, 4]-NRT-code) | [i] | Depth Reduction | |
| 2 | No linear OOA(98, 378870, F9, 3, 3) (dual of [(378870, 3), 1136602, 4]-NRT-code) | [i] | ||
| 3 | No digital (5, 8, 378870)-net over F9 | [i] | Extracting Embedded Orthogonal Array | |