MinT - Information on Result #599869

Information on Result #599869

There is no digital (3, 28, 58)-net over F₉, because extracting embedded orthogonal array would yield linear OA(9²⁸, 58, F₉, 25) (dual of [58, 30, 26]-code), but

constructionÂ Y1 [i] would yield
1. OA(9²⁷, 31, S₉, 25), but
  - the linear programming bound shows that MÂ â‰¥ 25644 034018 340666 323462 064529 / 377 > 9²⁷ [i]
2. linear OA(9³⁰, 58, F₉, 27) (dual of [58, 28, 28]-code), but
  - discarding factors / shortening the dual code would yield linear OA(9³⁰, 39, F₉, 27) (dual of [39, 9, 28]-code), but
    - residual code [i] would yield OA(9³, 11, S₉, 3), but
      - bound for OAs with index unity [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 (3, 29, 58)-net over F₉	[i]		m-Reduction