MinT - Information on Result #599707

Information on Result #599707

There is no digital (4, 7, 2153)-net over F₅, because extracting embedded orthogonal array would yield linear OA(5⁷, 2153, F₅, 3) (dual of [2153, 2146, 4]-code or 2153-cap in PG(6,5)), 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)

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.