MinT - Information on Result #548619

Information on Result #548619

There is no linear OA(4¹⁶¹, 186, F₄, 120) (dual of [186, 25, 121]-code), because constructionÂ Y1 would yield

linear OA(4¹⁶⁰, 172, F₄, 120) (dual of [172, 12, 121]-code), but
- constructionÂ Y1 [i] would yield
  1. linear OA(4¹⁵⁹, 166, F₄, 120) (dual of [166, 7, 121]-code), but
    - residual code [i] would yield linear OA(4³⁹, 45, F₄, 30) (dual of [45, 6, 31]-code), but
      - â€œDaâ€ bound on codes from Brouwerâ€™s database [i]
  2. OA(4¹², 172, 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]
OA(4²⁵, 186, S₄, 14), but
- discarding factors would yield OA(4²⁵, 162, S₄, 14), but
  - the Rao or (dual) Hamming bound shows that MÂ â‰¥ 1131 065428 484512 > 4²⁵ [i]

Mode: Bound (linear).

None.

The following results depend on this result:

	Result		Method
1	No linear OA(4¹⁶², 187, F₄, 121) (dual of [187, 25, 122]-code)	[i]	Truncation
2	No linear OA(4¹⁶³, 188, F₄, 122) (dual of [188, 25, 123]-code)	[i]
3	No linear OA(4¹⁶⁴, 189, F₄, 123) (dual of [189, 25, 124]-code)	[i]
4	No linear OOA(4¹⁶², 186, F₄, 2, 121) (dual of [(186, 2), 210, 122]-NRT-code)	[i]	m-Reduction for OOAs
5	No linear OOA(4¹⁶³, 186, F₄, 2, 122) (dual of [(186, 2), 209, 123]-NRT-code)	[i]
6	No linear OOA(4¹⁶⁴, 186, F₄, 2, 123) (dual of [(186, 2), 208, 124]-NRT-code)	[i]
7	No linear OOA(4¹⁶¹, 186, F₄, 2, 120) (dual of [(186, 2), 211, 121]-NRT-code)	[i]	Depth Reduction
8	No linear OOA(4¹⁶¹, 186, F₄, 3, 120) (dual of [(186, 3), 397, 121]-NRT-code)	[i]	Depth Reduction
9	No digital (41, 161, 186)-net over F₄	[i]	Extracting Embedded Orthogonal Array