MinT - Information on Result #599358

Information on Result #599358

There is no digital (8, 32, 41)-net over F₄, because extracting embedded orthogonal array would yield linear OA(4³², 41, F₄, 24) (dual of [41, 9, 25]-code), but

constructionÂ Y1 [i] would yield
1. linear OA(4³¹, 35, F₄, 24) (dual of [35, 4, 25]-code), but
  - residual code [i] would yield linear OA(4⁷, 10, F₄, 6) (dual of [10, 3, 7]-code), but
    - bound for almost-MDS-codes with dimension nÂ =Â 3 [i]
2. OA(4⁹, 41, S₄, 6), but
  - discarding factors would yield OA(4⁹, 40, S₄, 6), but
    - the Rao or (dual) Hamming bound shows that MÂ â‰¥ 273901 > 4⁹ [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, 33, 41)-net over F₄	[i]		m-Reduction
2	No digital (8, 34, 41)-net over F₄	[i]
3	No digital (8, 35, 41)-net over F₄	[i]