MinT - Information on Result #547880

Information on Result #547880

There is no linear OA(4¹⁵⁰, 165, F₄, 112) (dual of [165, 15, 113]-code), because constructionÂ Y1 would yield

linear OA(4¹⁴⁹, 157, F₄, 112) (dual of [157, 8, 113]-code), but
- constructionÂ Y1 [i] would yield
  1. linear OA(4¹⁴⁸, 153, F₄, 112) (dual of [153, 5, 113]-code), but
    - residual code [i] would yield linear OA(4³⁶, 40, F₄, 28) (dual of [40, 4, 29]-code), but
      - residual code [i] would yield linear OA(4⁸, 11, F₄, 7) (dual of [11, 3, 8]-code), but
        improvement by Maruta on the Griesmer bound [i]
  2. OA(4⁸, 157, 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, 165, 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(4¹⁵¹, 166, F₄, 113) (dual of [166, 15, 114]-code)	[i]	Truncation
2	No linear OA(4¹⁵², 167, F₄, 114) (dual of [167, 15, 115]-code)	[i]
3	No linear OA(4¹⁵³, 168, F₄, 115) (dual of [168, 15, 116]-code)	[i]
4	No linear OOA(4¹⁵¹, 165, F₄, 2, 113) (dual of [(165, 2), 179, 114]-NRT-code)	[i]	m-Reduction for OOAs
5	No linear OOA(4¹⁵², 165, F₄, 2, 114) (dual of [(165, 2), 178, 115]-NRT-code)	[i]
6	No linear OOA(4¹⁵³, 165, F₄, 2, 115) (dual of [(165, 2), 177, 116]-NRT-code)	[i]
7	No linear OOA(4¹⁵⁰, 165, F₄, 2, 112) (dual of [(165, 2), 180, 113]-NRT-code)	[i]	Depth Reduction
8	No linear OOA(4¹⁵⁰, 165, F₄, 3, 112) (dual of [(165, 3), 345, 113]-NRT-code)	[i]	Depth Reduction
9	No digital (38, 150, 165)-net over F₄	[i]	Extracting Embedded Orthogonal Array
10	No linear OA(4¹⁵¹, 185, F₄, 112) (dual of [185, 34, 113]-code)	[i]	ConstructionÂ Y1 (Bound)