MinT - Information on Result #547904

Information on Result #547904

There is no linear OA(4¹⁹³, 208, F₄, 144) (dual of [208, 15, 145]-code), because constructionÂ Y1 would yield

linear OA(4¹⁹², 200, F₄, 144) (dual of [200, 8, 145]-code), but
- constructionÂ Y1 [i] would yield
  1. linear OA(4¹⁹¹, 196, F₄, 144) (dual of [196, 5, 145]-code), but
    - residual code [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, 200, 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, 208, 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(4¹⁹⁴, 209, F₄, 145) (dual of [209, 15, 146]-code)	[i]	Truncation
2	No linear OA(4¹⁹⁵, 210, F₄, 146) (dual of [210, 15, 147]-code)	[i]
3	No linear OA(4¹⁹⁶, 211, F₄, 147) (dual of [211, 15, 148]-code)	[i]
4	No linear OOA(4¹⁹⁴, 208, F₄, 2, 145) (dual of [(208, 2), 222, 146]-NRT-code)	[i]	m-Reduction for OOAs
5	No linear OOA(4¹⁹⁵, 208, F₄, 2, 146) (dual of [(208, 2), 221, 147]-NRT-code)	[i]
6	No linear OOA(4¹⁹⁶, 208, F₄, 2, 147) (dual of [(208, 2), 220, 148]-NRT-code)	[i]
7	No linear OOA(4¹⁹³, 208, F₄, 2, 144) (dual of [(208, 2), 223, 145]-NRT-code)	[i]	Depth Reduction
8	No linear OOA(4¹⁹³, 208, F₄, 3, 144) (dual of [(208, 3), 431, 145]-NRT-code)	[i]	Depth Reduction
9	No digital (49, 193, 208)-net over F₄	[i]	Extracting Embedded Orthogonal Array
10	No linear OA(4¹⁹⁴, 226, F₄, 144) (dual of [226, 32, 145]-code)	[i]	ConstructionÂ Y1 (Bound)