MinT - Information on Result #599502

Information on Result #599502

There is no digital (50, 198, 213)-net over F₄, because extracting embedded orthogonal array would yield linear OA(4¹⁹⁸, 213, F₄, 148) (dual of [213, 15, 149]-code), but

constructionÂ Y1 [i] would yield
1. linear OA(4¹⁹⁷, 205, F₄, 148) (dual of [205, 8, 149]-code), but
  - constructionÂ Y1 [i] would yield
    1. linear OA(4¹⁹⁶, 201, F₄, 148) (dual of [201, 5, 149]-code), but
      - residual code [i] would yield linear OA(4⁴⁸, 52, F₄, 37) (dual of [52, 4, 38]-code), but
        1 times truncation [i] would yield linear OA(4⁴⁷, 51, F₄, 36) (dual of [51, 4, 37]-code), but
        a result by Landjev, Maruta, and Hill [i]
    2. OA(4⁸, 205, S₄, 4), but
      - discarding factors would yield OA(4⁸, 121, S₄, 4), but
        the Rao or (dual) Hamming bound shows that MÂ â‰¥ 65704 > 4⁸ [i]
2. OA(4¹⁵, 213, S₄, 8), but
  - discarding factors would yield OA(4¹⁵, 135, S₄, 8), but
    - the Rao or (dual) Hamming bound shows that MÂ â‰¥ 1082 768311 > 4¹⁵ [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		Method
1	No digital (50, 199, 213)-net over F₄	[i]	m-Reduction
2	No digital (50, 200, 213)-net over F₄	[i]
3	No digital (50, 201, 213)-net over F₄	[i]