MinT - Information on Result #599875

Information on Result #599875

There is no digital (5, 8, 378870)-net over F₉, because extracting embedded orthogonal array would yield linear OA(9⁸, 378870, F₉, 3) (dual of [378870, 378862, 4]-code or 378870-cap in PG(7,9)), but

removing affine subspaces [i] would yield
1. 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]
2. 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]
3. 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]
4. 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)

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

None.