MinT - Information on Result #599808

Information on Result #599808

There is no digital (4, 7, 27650)-net over F₈, because extracting embedded orthogonal array would yield linear OA(8⁷, 27650, F₈, 3) (dual of [27650, 27643, 4]-code or 27650-cap in PG(6,8)), but

removing affine subspaces [i] would yield
1. linear OA(8⁵, 494, F₈, 3) (dual of [494, 489, 4]-code or 494-cap in PG(4,8)), but
  - bound for caps in PG(4,Â b) [i]
2. 3284-cap in AG(5,8), but
  - 2 times the recursive bound from Bierbrauer and Edel [i] would yield 65-cap in AG(3,8), but
    - affine subcap of ovoid is optimal [i]
3. 23874-cap in AG(6,8), but
  - 3 times the recursive bound from Bierbrauer and Edel [i] would yield 65-cap in AG(3,8) (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.