MinT - Information on Result #547835

Information on Result #547835

There is no linear OA(4⁴³, 55, F₄, 32) (dual of [55, 12, 33]-code), because constructionÂ Y1 would yield

linear OA(4⁴², 47, F₄, 32) (dual of [47, 5, 33]-code), but
- constructionÂ Y1 [i] would yield
  1. linear OA(4⁴¹, 44, F₄, 32) (dual of [44, 3, 33]-code), but
    - Griesmer bound [i]
  2. linear OA(4⁵, 47, F₄, 3) (dual of [47, 42, 4]-code or 47-cap in PG(4,4)), but
    - discarding factors / shortening the dual code 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]
OA(4¹², 55, S₄, 8), but
- discarding factors would yield OA(4¹², 49, S₄, 8), but
  - the Rao or (dual) Hamming bound shows that MÂ â‰¥ 17 670136 > 4¹² [i]

Mode: Bound (linear).

None.

The following results depend on this result:

	Result		Method
1	No linear OA(4⁴⁴, 56, F₄, 33) (dual of [56, 12, 34]-code)	[i]	Truncation
2	No linear OOA(4⁴⁴, 55, F₄, 2, 33) (dual of [(55, 2), 66, 34]-NRT-code)	[i]	m-Reduction for OOAs
3	No linear OOA(4⁴³, 55, F₄, 2, 32) (dual of [(55, 2), 67, 33]-NRT-code)	[i]	Depth Reduction
4	No linear OOA(4⁴³, 55, F₄, 3, 32) (dual of [(55, 3), 122, 33]-NRT-code)	[i]	Depth Reduction
5	No digital (11, 43, 55)-net over F₄	[i]	Extracting Embedded Orthogonal Array