MinT - Information on Result #599872

Information on Result #599872

There is no digital (4, 31, 85)-net over F₉, because extracting embedded orthogonal array would yield linear OA(9³¹, 85, F₉, 27) (dual of [85, 54, 28]-code), but

constructionÂ Y1 [i] would yield
1. linear OA(9³⁰, 37, F₉, 27) (dual of [37, 7, 28]-code), but
  - constructionÂ Y1 [i] would yield
    1. OA(9²⁹, 31, S₉, 27), but
      - the (dual) Plotkin bound shows that MÂ â‰¥ 42391 158275 216203 514294 433201 / 7 > 9²⁹ [i]
    2. OA(9⁷, 37, S₉, 6), but
      - the linear programming bound shows that MÂ â‰¥ 8306 954271 / 1613 > 9⁷ [i]
2. OA(9⁵⁴, 85, S₉, 48), but
  - discarding factors would yield OA(9⁵⁴, 83, S₉, 48), but
    - the linear programming bound shows that MÂ â‰¥ 10132 927410 689078 360872 417149 617665 028299 664062 593121 142935 280521 657389 / 2 927120 765949 062837 > 9⁵⁴ [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 (4, 32, 85)-net over F₉	[i]		m-Reduction
2	No digital (4, 33, 85)-net over F₉	[i]
3	No digital (4, 34, 85)-net over F₉	[i]