MinT - Information on Result #599528

Information on Result #599528

There is no digital (54, 214, 226)-net over F₄, because extracting embedded orthogonal array would yield linear OA(4²¹⁴, 226, F₄, 160) (dual of [226, 12, 161]-code), but

constructionÂ Y1 [i] would yield
1. linear OA(4²¹³, 220, F₄, 160) (dual of [220, 7, 161]-code), but
  - residual code [i] would yield linear OA(4⁵³, 59, F₄, 40) (dual of [59, 6, 41]-code), but
    - residual code [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, 226, 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 (54, 215, 226)-net over F₄	[i]	m-Reduction
2	No digital (54, 216, 226)-net over F₄	[i]
3	No digital (54, 217, 226)-net over F₄	[i]