MinT - Information on Result #599701

Information on Result #599701

There is no digital (2, 12, 17)-net over F₅, because extracting embedded orthogonal array would yield linear OA(5¹², 17, F₅, 10) (dual of [17, 5, 11]-code), but

constructionÂ Y1 [i] would yield
1. OA(5¹¹, 13, S₅, 10), but
  - the (dual) Plotkin bound shows that MÂ â‰¥ 732 421875 / 11 > 5¹¹ [i]
2. linear OA(5⁵, 17, F₅, 4) (dual of [17, 12, 5]-code), but
  - discarding factors / shortening the dual code would yield linear OA(5⁵, 13, F₅, 4) (dual of [13, 8, 5]-code), but
    - â€œBouâ€ bound on codes from Brouwerâ€™s database [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 (2, 13, 17)-net over F₅	[i]		m-Reduction
2	No digital (2, 14, 17)-net over F₅	[i]
3	No digital (2, 15, 17)-net over F₅	[i]
4	No digital (2, 16, 17)-net over F₅	[i]
5	No digital (2, 17, 17)-net over F₅	[i]