MinT - Information on Result #599373

Information on Result #599373

There is no digital (12, 48, 57)-net over F₄, because extracting embedded orthogonal array would yield linear OA(4⁴⁸, 57, F₄, 36) (dual of [57, 9, 37]-code), but

constructionÂ Y1 [i] would yield
1. linear OA(4⁴⁷, 51, F₄, 36) (dual of [51, 4, 37]-code), but
  - a result by Landjev, Maruta, and Hill [i]
2. OA(4⁹, 57, S₄, 6), but
  - discarding factors would yield OA(4⁹, 40, S₄, 6), but
    - the Rao or (dual) Hamming bound shows that MÂ â‰¥ 273901 > 4⁹ [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		This result only	Method
1	No digital (12, 49, 57)-net over F₄	[i]		m-Reduction
2	No digital (12, 50, 57)-net over F₄	[i]
3	No digital (12, 51, 57)-net over F₄	[i]