MinT - Information on Result #599619

Information on Result #599619

There is no digital (63, 255, 261)-net over F₄, because extracting embedded orthogonal array would yield linear OA(4²⁵⁵, 261, F₄, 192) (dual of [261, 6, 193]-code), but

constructionÂ Y1 [i] would yield
1. linear OA(4²⁵⁴, 258, F₄, 192) (dual of [258, 4, 193]-code), but
  - Griesmer bound [i]
2. linear OA(4⁶, 261, F₄, 3) (dual of [261, 255, 4]-code or 261-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]

Mode: Bound (linear).

Optimality

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

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		Method
1	No digital (63, 256, 261)-net over F₄	[i]	m-Reduction
2	No digital (63, 257, 261)-net over F₄	[i]
3	No digital (63, 258, 261)-net over F₄	[i]
4	No digital (63, 259, 261)-net over F₄	[i]
5	No digital (63, 260, 261)-net over F₄	[i]