MinT - Information on Result #548624

Information on Result #548624

There is no linear OA(4²¹⁹, 231, F₄, 164) (dual of [231, 12, 165]-code), because constructionÂ Y1 would yield

linear OA(4²¹⁸, 225, F₄, 164) (dual of [225, 7, 165]-code), but
- residual code [i] would yield linear OA(4⁵⁴, 60, F₄, 41) (dual of [60, 6, 42]-code), but
  - 1 times truncation [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, 231, 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(4²²⁰, 232, F₄, 165) (dual of [232, 12, 166]-code)	[i]	Truncation
2	No linear OA(4²²¹, 233, F₄, 166) (dual of [233, 12, 167]-code)	[i]
3	No linear OA(4²²², 234, F₄, 167) (dual of [234, 12, 168]-code)	[i]
4	No linear OOA(4²²⁰, 231, F₄, 2, 165) (dual of [(231, 2), 242, 166]-NRT-code)	[i]	m-Reduction for OOAs
5	No linear OOA(4²²¹, 231, F₄, 2, 166) (dual of [(231, 2), 241, 167]-NRT-code)	[i]
6	No linear OOA(4²²², 231, F₄, 2, 167) (dual of [(231, 2), 240, 168]-NRT-code)	[i]
7	No linear OOA(4²¹⁹, 231, F₄, 2, 164) (dual of [(231, 2), 243, 165]-NRT-code)	[i]	Depth Reduction
8	No linear OOA(4²¹⁹, 231, F₄, 3, 164) (dual of [(231, 3), 474, 165]-NRT-code)	[i]	Depth Reduction
9	No digital (55, 219, 231)-net over F₄	[i]	Extracting Embedded Orthogonal Array