MinT - Information on Result #547905

Information on Result #547905

There is no linear OA(4¹⁹⁴, 226, F₄, 144) (dual of [226, 32, 145]-code), because constructionÂ Y1 would yield

linear OA(4¹⁹³, 208, F₄, 144) (dual of [208, 15, 145]-code), but
- constructionÂ Y1 [i] would yield
  1. 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]
  2. 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]
OA(4³², 226, S₄, 18), but
- discarding factors would yield OA(4³², 195, S₄, 18), but
  - the Rao or (dual) Hamming bound shows that MÂ â‰¥ 18 632959 071185 877328 > 4³² [i]

Mode: Bound (linear).

None.

The following results depend on this result:

	Result		Method
1	No linear OA(4¹⁹⁵, 227, F₄, 145) (dual of [227, 32, 146]-code)	[i]	Truncation
2	No linear OA(4¹⁹⁶, 228, F₄, 146) (dual of [228, 32, 147]-code)	[i]
3	No linear OA(4¹⁹⁷, 229, F₄, 147) (dual of [229, 32, 148]-code)	[i]
4	No linear OOA(4¹⁹⁵, 226, F₄, 2, 145) (dual of [(226, 2), 257, 146]-NRT-code)	[i]	m-Reduction for OOAs
5	No linear OOA(4¹⁹⁶, 226, F₄, 2, 146) (dual of [(226, 2), 256, 147]-NRT-code)	[i]
6	No linear OOA(4¹⁹⁷, 226, F₄, 2, 147) (dual of [(226, 2), 255, 148]-NRT-code)	[i]
7	No linear OOA(4¹⁹⁴, 226, F₄, 2, 144) (dual of [(226, 2), 258, 145]-NRT-code)	[i]	Depth Reduction
8	No linear OOA(4¹⁹⁴, 226, F₄, 3, 144) (dual of [(226, 3), 484, 145]-NRT-code)	[i]	Depth Reduction
9	No digital (50, 194, 226)-net over F₄	[i]	Extracting Embedded Orthogonal Array