MinT - Information on Result #599722

Information on Result #599722

There is no digital (8, 41, 52)-net over F₅, because extracting embedded orthogonal array 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

The following results depend on this result:

	Result		This result only	Method
1	No digital (8, 42, 52)-net over F₅	[i]		m-Reduction