MinT - Information on Result #548059

Information on Result #548059

There is no linear OA(4⁷, 608, F₄, 3) (dual of [608, 601, 4]-code or 608-cap in PG(6,4)), because 1 times Hill recurrence would yield linear OA(4⁶, 154, F₄, 3) (dual of [154, 148, 4]-code or 154-cap in PG(5,4)), but

constructionÂ Y1 [i] would yield
1. 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. linear OA(4¹⁴⁸, 154, F₄, 112) (dual of [154, 6, 113]-code), but
  - discarding factors / shortening the dual code would yield linear OA(4¹⁴⁸, 153, F₄, 112) (dual of [153, 5, 113]-code), but
    - residual code [i] would yield linear OA(4³⁶, 40, F₄, 28) (dual of [40, 4, 29]-code), but
      - residual code [i] would yield linear OA(4⁸, 11, F₄, 7) (dual of [11, 3, 8]-code), but
        improvement by Maruta on the Griesmer bound [i]

Mode: Bound (linear).

Optimality

Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		Method
1	No linear OOA(4⁷, 608, F₄, 2, 3) (dual of [(608, 2), 1209, 4]-NRT-code)	[i]	Depth Reduction
2	No linear OOA(4⁷, 608, F₄, 3, 3) (dual of [(608, 3), 1817, 4]-NRT-code)	[i]	Depth Reduction
3	No digital (4, 7, 608)-net over F₄	[i]	Extracting Embedded Orthogonal Array
4	No linear OA(4⁸, 2359, F₄, 3) (dual of [2359, 2351, 4]-code or 2359-cap in PG(7,4))	[i]	Removing Affine Subspaces
5	No linear OA(4⁹, 8687, F₄, 3) (dual of [8687, 8678, 4]-code or 8687-cap in PG(8,4))	[i]
6	No linear OA(4¹⁰, 31771, F₄, 3) (dual of [31771, 31761, 4]-code or 31771-cap in PG(9,4))	[i]
7	No linear OA(4¹¹, 116635, F₄, 3) (dual of [116635, 116624, 4]-code or 116635-cap in PG(10,4))	[i]
8	No linear OA(4¹², 430675, F₄, 3) (dual of [430675, 430663, 4]-code or 430675-cap in PG(11,4))	[i]
9	No linear OA(4¹³, 1599334, F₄, 3) (dual of [1599334, 1599321, 4]-code or 1599334-cap in PG(12,4))	[i]
10	No linear OA(4¹⁴, 5969552, F₄, 3) (dual of [5969552, 5969538, 4]-code or 5969552-cap in PG(13,4))	[i]