MinT - Information on Result #526584

Information on Result #526584

There is no linear OA(9⁹, 2990280, F₉, 3) (dual of [2990280, 2990271, 4]-code or 2990280-cap in PG(8,9)), 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
- a result by Gronchi and Heim [i]
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
  - affine subcap of ovoid is optimal [i]
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
    - bound on the size of affine caps [i]
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)
2611411-cap in AG(8,9), but
- base reduction for affine caps [i] would yield 2611411-cap in AG(16,3), but
  - 10 times the recursive bound from Bierbrauer and Edel [i] would yield 113-cap in AG(6,3) (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		Method
1	No linear OOA(9⁹, 2990280, F₉, 2, 3) (dual of [(2990280, 2), 5980551, 4]-NRT-code)	[i]	Depth Reduction
2	No linear OOA(9⁹, 2990280, F₉, 3, 3) (dual of [(2990280, 3), 8970831, 4]-NRT-code)	[i]	Depth Reduction
3	No digital (6, 9, 2990280)-net over F₉	[i]	Extracting Embedded Orthogonal Array