MinT - Information on Result #599705

Information on Result #599705

There is no digital (3, 15, 25)-net over F₅, because extracting embedded orthogonal array would yield linear OA(5¹⁵, 25, F₅, 12) (dual of [25, 10, 13]-code), but

constructionÂ Y1 [i] would yield
1. linear OA(5¹⁴, 17, F₅, 12) (dual of [17, 3, 13]-code), but
  - a result by Hill [i]
2. linear OA(5¹⁰, 25, F₅, 8) (dual of [25, 15, 9]-code), but
  - discarding factors / shortening the dual code would yield linear OA(5¹⁰, 22, F₅, 8) (dual of [22, 12, 9]-code), but
    - constructionÂ Y1 [i] would yield
      1. linear OA(5⁹, 12, F₅, 8) (dual of [12, 3, 9]-code), but
        bound for almost-MDS-codes with dimension nÂ =Â 3 [i]
      2. linear OA(5¹², 22, F₅, 10) (dual of [22, 10, 11]-code), but
        discarding factors / shortening the dual code would yield linear OA(5¹², 18, F₅, 10) (dual of [18, 6, 11]-code), but
        residual code [i] would yield OA(5², 7, S₅, 2), but
        bound for OAs with strength kÂ =Â 2 [i]
        the Rao or (dual) Hamming bound shows that MÂ â‰¥ 29 > 5² [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 (3, 16, 25)-net over F₅	[i]		m-Reduction
2	No digital (3, 17, 25)-net over F₅	[i]		m-Reduction