MinT - Information on Result #599905

Information on Result #599905

There is no digital (4, 7, 945412)-net over F₁₆, because extracting embedded orthogonal array would yield linear OA(16⁷, 945412, F₁₆, 3) (dual of [945412, 945405, 4]-code or 945412-cap in PG(6,16)), but

removing affine subspaces [i] would yield
1. linear OA(16⁵, 3934, F₁₆, 3) (dual of [3934, 3929, 4]-code or 3934-cap in PG(4,16)), but
  - bound for caps in PG(4,Â b) [i]
2. 58269-cap in AG(5,16), but
  - 2 times the recursive bound from Bierbrauer and Edel [i] would yield 257-cap in AG(3,16), but
    - affine subcap of ovoid is optimal [i]
3. 883211-cap in AG(6,16), but
  - 3 times the recursive bound from Bierbrauer and Edel [i] would yield 257-cap in AG(3,16) (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.