MinT - Information on Result #548622

Information on Result #548622

There is no linear OA(4²¹⁴, 226, F₄, 160) (dual of [226, 12, 161]-code), because constructionÂ Y1 would yield

linear OA(4²¹³, 220, F₄, 160) (dual of [220, 7, 161]-code), but
- residual code [i] would yield linear OA(4⁵³, 59, F₄, 40) (dual of [59, 6, 41]-code), but
  - residual code [i] would yield linear OA(4¹³, 18, F₄, 10) (dual of [18, 5, 11]-code), but
    - â€œLizâ€ bound on codes from Brouwerâ€™s database [i]
OA(4¹², 226, S₄, 6), but
- discarding factors would yield OA(4¹², 156, S₄, 6), but
  - the Rao or (dual) Hamming bound shows that MÂ â‰¥ 16 866019 > 4¹² [i]

Mode: Bound (linear).

None.

The following results depend on this result:

	Result		Method
1	No linear OA(4²¹⁵, 227, F₄, 161) (dual of [227, 12, 162]-code)	[i]	Truncation
2	No linear OA(4²¹⁶, 228, F₄, 162) (dual of [228, 12, 163]-code)	[i]
3	No linear OA(4²¹⁷, 229, F₄, 163) (dual of [229, 12, 164]-code)	[i]
4	No linear OOA(4²¹⁵, 226, F₄, 2, 161) (dual of [(226, 2), 237, 162]-NRT-code)	[i]	m-Reduction for OOAs
5	No linear OOA(4²¹⁶, 226, F₄, 2, 162) (dual of [(226, 2), 236, 163]-NRT-code)	[i]
6	No linear OOA(4²¹⁷, 226, F₄, 2, 163) (dual of [(226, 2), 235, 164]-NRT-code)	[i]
7	No linear OOA(4²¹⁴, 226, F₄, 2, 160) (dual of [(226, 2), 238, 161]-NRT-code)	[i]	Depth Reduction
8	No linear OOA(4²¹⁴, 226, F₄, 3, 160) (dual of [(226, 3), 464, 161]-NRT-code)	[i]	Depth Reduction
9	No digital (54, 214, 226)-net over F₄	[i]	Extracting Embedded Orthogonal Array
10	No linear OA(4²¹⁵, 238, F₄, 160) (dual of [238, 23, 161]-code)	[i]	ConstructionÂ Y1 (Bound)