MinT - Information on Result #547907

Information on Result #547907

There is no linear OA(4¹⁹⁸, 213, F₄, 148) (dual of [213, 15, 149]-code), because constructionÂ Y1 would yield

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]
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).

None.

The following results depend on this result:

	Result		Method
1	No linear OA(4¹⁹⁹, 214, F₄, 149) (dual of [214, 15, 150]-code)	[i]	Truncation
2	No linear OA(4²⁰⁰, 215, F₄, 150) (dual of [215, 15, 151]-code)	[i]
3	No linear OA(4²⁰¹, 216, F₄, 151) (dual of [216, 15, 152]-code)	[i]
4	No linear OOA(4¹⁹⁹, 213, F₄, 2, 149) (dual of [(213, 2), 227, 150]-NRT-code)	[i]	m-Reduction for OOAs
5	No linear OOA(4²⁰⁰, 213, F₄, 2, 150) (dual of [(213, 2), 226, 151]-NRT-code)	[i]
6	No linear OOA(4²⁰¹, 213, F₄, 2, 151) (dual of [(213, 2), 225, 152]-NRT-code)	[i]
7	No linear OOA(4¹⁹⁸, 213, F₄, 2, 148) (dual of [(213, 2), 228, 149]-NRT-code)	[i]	Depth Reduction
8	No linear OOA(4¹⁹⁸, 213, F₄, 3, 148) (dual of [(213, 3), 441, 149]-NRT-code)	[i]	Depth Reduction
9	No digital (50, 198, 213)-net over F₄	[i]	Extracting Embedded Orthogonal Array