MinT - Information on Result #599433

Information on Result #599433

There is no digital (40, 160, 172)-net over F₄, because extracting embedded orthogonal array would yield linear OA(4¹⁶⁰, 172, F₄, 120) (dual of [172, 12, 121]-code), but

constructionÂ Y1 [i] would yield
1. linear OA(4¹⁵⁹, 166, F₄, 120) (dual of [166, 7, 121]-code), but
  - residual code [i] would yield linear OA(4³⁹, 45, F₄, 30) (dual of [45, 6, 31]-code), but
    - â€œDaâ€ bound on codes from Brouwerâ€™s database [i]
2. OA(4¹², 172, 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 (40, 161, 172)-net over F₄	[i]	m-Reduction
2	No digital (40, 162, 172)-net over F₄	[i]
3	No digital (40, 163, 172)-net over F₄	[i]