MinT - Information on Result #599576

Information on Result #599576

There is no digital (59, 235, 247)-net over F₄, because extracting embedded orthogonal array would yield linear OA(4²³⁵, 247, F₄, 176) (dual of [247, 12, 177]-code), but

constructionÂ Y1 [i] would yield
1. linear OA(4²³⁴, 241, F₄, 176) (dual of [241, 7, 177]-code), but
  - residual code [i] would yield linear OA(4⁵⁸, 64, F₄, 44) (dual of [64, 6, 45]-code), but
    - residual code [i] would yield linear OA(4¹⁴, 19, F₄, 11) (dual of [19, 5, 12]-code), but
      - 1 times truncation [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]
2. OA(4¹², 247, 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).

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 (59, 236, 247)-net over F₄	[i]	m-Reduction
2	No digital (59, 237, 247)-net over F₄	[i]
3	No digital (59, 238, 247)-net over F₄	[i]