MinT - Information on Result #599508

Information on Result #599508

There is no digital (51, 200, 230)-net over F₄, because extracting embedded orthogonal array would yield linear OA(4²⁰⁰, 230, F₄, 149) (dual of [230, 30, 150]-code), but

constructionÂ Y1 [i] would yield
1. linear OA(4¹⁹⁹, 214, F₄, 149) (dual of [214, 15, 150]-code), but
  - 1 times truncation [i] 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
        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]
        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]
2. OA(4³⁰, 230, S₄, 16), but
  - the linear programming bound shows that MÂ â‰¥ 57 643098 217881 685156 997061 672960 / 49 293754 184261 > 4³⁰ [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 (51, 201, 230)-net over F₄	[i]		m-Reduction
2	No digital (51, 202, 230)-net over F₄	[i]		m-Reduction