MinT - Information on Result #599587

Information on Result #599587

There is no digital (60, 240, 252)-net over F₄, because extracting embedded orthogonal array would yield linear OA(4²⁴⁰, 252, F₄, 180) (dual of [252, 12, 181]-code), but

constructionÂ Y1 [i] would yield
1. linear OA(4²³⁹, 246, F₄, 180) (dual of [246, 7, 181]-code), but
  - residual code [i] would yield linear OA(4⁵⁹, 65, F₄, 45) (dual of [65, 6, 46]-code), but
    - 1 times truncation [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, 252, 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 (60, 241, 252)-net over F₄	[i]	m-Reduction
2	No digital (60, 242, 252)-net over F₄	[i]
3	No digital (60, 243, 252)-net over F₄	[i]