MinT - Information on Result #599873

Information on Result #599873

There is no digital (4, 36, 50)-net over F₉, because extracting embedded orthogonal array would yield linear OA(9³⁶, 50, F₉, 32) (dual of [50, 14, 33]-code), but

constructionÂ Y1 [i] would yield
1. linear OA(9³⁵, 38, F₉, 32) (dual of [38, 3, 33]-code), but
  - â€œMasâ€ bound on codes from Brouwerâ€™s database [i]
2. linear OA(9¹⁴, 50, F₉, 12) (dual of [50, 36, 13]-code), but
  - discarding factors / shortening the dual code would yield linear OA(9¹⁴, 44, F₉, 12) (dual of [44, 30, 13]-code), but
    - constructionÂ Y1 [i] would yield
      1. linear OA(9¹³, 17, F₉, 12) (dual of [17, 4, 13]-code), but
        â€œMPaâ€ bound on codes from Brouwerâ€™s database [i]
      2. linear OA(9³⁰, 44, F₉, 27) (dual of [44, 14, 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 (4, 37, 50)-net over F₉	[i]		m-Reduction
2	No digital (4, 38, 50)-net over F₉	[i]
3	No digital (4, 39, 50)-net over F₉	[i]