MinT - Information on Result #599866

Information on Result #599866

There is no digital (2, 18, 38)-net over F₉, because extracting embedded orthogonal array would yield linear OA(9¹⁸, 38, F₉, 16) (dual of [38, 20, 17]-code), but

constructionÂ Y1 [i] would yield
1. linear OA(9¹⁷, 20, F₉, 16) (dual of [20, 3, 17]-code), but
  - bound for almost-MDS-codes with dimension nÂ =Â 3 [i]
2. linear OA(9²⁰, 38, F₉, 18) (dual of [38, 18, 19]-code), but
  - discarding factors / shortening the dual code would yield linear OA(9²⁰, 30, F₉, 18) (dual of [30, 10, 19]-code), but
    - residual code [i] would yield OA(9², 11, S₉, 2), but
      - bound for OAs with strength kÂ =Â 2 [i]
      - the Rao or (dual) Hamming bound shows that MÂ â‰¥ 89 > 9² [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 (2, 19, 38)-net over F₉	[i]		m-Reduction