MinT - Information on Result #3150124

Information on Result #3150124

There is no digital (8, 42, 52)-net over F₅, because 1 times m-reduction would yield digital (8, 41, 52)-net over F₅, but

extracting embedded orthogonal array [i] would yield linear OA(5⁴¹, 52, F₅, 33) (dual of [52, 11, 34]-code), but
- constructionÂ Y1 [i] would yield
  1. linear OA(5⁴⁰, 44, F₅, 33) (dual of [44, 4, 34]-code), but
    - a result by Boukliev, Kapralov, Maruta, and Fukui [i]
  2. OA(5¹¹, 52, S₅, 8), but
    - discarding factors would yield OA(5¹¹, 48, S₅, 8), but
      - the Rao or (dual) Hamming bound shows that MÂ â‰¥ 50 937665 > 5¹¹ [i]

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.