MinT - Information on Result #599720

Information on Result #599720

There is no digital (8, 11, 952350)-net over F₅, because extracting embedded orthogonal array would yield linear OA(5¹¹, 952350, F₅, 3) (dual of [952350, 952339, 4]-code or 952350-cap in PG(10,5)), but

removing affine subspaces [i] would yield
1. linear OA(5⁶, 435, F₅, 3) (dual of [435, 429, 4]-code or 435-cap in PG(5,5)), but
  - 1 times Hill recurrence [i] would yield linear OA(5⁵, 89, F₅, 3) (dual of [89, 84, 4]-code or 89-cap in PG(4,5)), but
    - a result by Edel, Storme, and Sziklai [i]
2. 1719-cap in AG(6,5), but
  - 2 times the recursive bound from Bierbrauer and Edel [i] would yield 89-cap in AG(4,5), but
    - embedding in projective space [i] would yield linear OA(5⁵, 89, F₅, 3) (dual of [89, 84, 4]-code or 89-cap in PG(4,5)) (see above)
3. 7740-cap in AG(7,5), but
  - 3 times the recursive bound from Bierbrauer and Edel [i] would yield 89-cap in AG(4,5) (see above)
4. 35209-cap in AG(8,5), but
  - 4 times the recursive bound from Bierbrauer and Edel [i] would yield 89-cap in AG(4,5) (see above)
5. 161486-cap in AG(9,5), but
  - 5 times the recursive bound from Bierbrauer and Edel [i] would yield 89-cap in AG(4,5) (see above)
6. 745766-cap in AG(10,5), but
  - 6 times the recursive bound from Bierbrauer and Edel [i] would yield 89-cap in AG(4,5) (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.