MinT - Information on Result #547894

Information on Result #547894

There is no linear OA(4¹⁷⁷, 199, F₄, 132) (dual of [199, 22, 133]-code), because constructionÂ Y1 would yield

linear OA(4¹⁷⁶, 187, F₄, 132) (dual of [187, 11, 133]-code), but
- constructionÂ Y1 [i] would yield
  1. linear OA(4¹⁷⁵, 181, F₄, 132) (dual of [181, 6, 133]-code), but
    - constructionÂ Y1 [i] would yield
      1. linear OA(4¹⁷⁴, 178, F₄, 132) (dual of [178, 4, 133]-code), but
        Griesmer bound [i]
      2. linear OA(4⁶, 181, F₄, 3) (dual of [181, 175, 4]-code or 181-cap in PG(5,4)), but
        discarding factors / shortening the dual code would yield linear OA(4⁶, 160, F₄, 3) (dual of [160, 154, 4]-code or 160-cap in PG(5,4)), but
        1 times Hill recurrence [i] would yield linear OA(4⁵, 42, F₄, 3) (dual of [42, 37, 4]-code or 42-cap in PG(4,4)), but
        41 is the largest size of a cap in PG(4,Â 4) [i]
  2. OA(4¹¹, 187, S₄, 6), but
    - discarding factors would yield OA(4¹¹, 99, S₄, 6), but
      - the Rao or (dual) Hamming bound shows that MÂ â‰¥ 4 278880 > 4¹¹ [i]
OA(4²², 199, S₄, 12), but
- discarding factors would yield OA(4²², 164, S₄, 12), but
  - the Rao or (dual) Hamming bound shows that MÂ â‰¥ 18 187369 733464 > 4²² [i]

Mode: Bound (linear).

None.

The following results depend on this result:

	Result		Method
1	No linear OA(4¹⁷⁸, 200, F₄, 133) (dual of [200, 22, 134]-code)	[i]	Truncation
2	No linear OA(4¹⁷⁹, 201, F₄, 134) (dual of [201, 22, 135]-code)	[i]
3	No linear OA(4¹⁸⁰, 202, F₄, 135) (dual of [202, 22, 136]-code)	[i]
4	No linear OOA(4¹⁷⁸, 199, F₄, 2, 133) (dual of [(199, 2), 220, 134]-NRT-code)	[i]	m-Reduction for OOAs
5	No linear OOA(4¹⁷⁹, 199, F₄, 2, 134) (dual of [(199, 2), 219, 135]-NRT-code)	[i]
6	No linear OOA(4¹⁸⁰, 199, F₄, 2, 135) (dual of [(199, 2), 218, 136]-NRT-code)	[i]
7	No linear OOA(4¹⁷⁷, 199, F₄, 2, 132) (dual of [(199, 2), 221, 133]-NRT-code)	[i]	Depth Reduction
8	No linear OOA(4¹⁷⁷, 199, F₄, 3, 132) (dual of [(199, 3), 420, 133]-NRT-code)	[i]	Depth Reduction
9	No digital (45, 177, 199)-net over F₄	[i]	Extracting Embedded Orthogonal Array