MinT - Information on Result #3145672

Information on Result #3145672

There is no digital (59, 199, 188)-net over F₃, because 20 times m-reduction would yield digital (59, 179, 188)-net over F₃, but

extracting embedded orthogonal array [i] would yield linear OA(3¹⁷⁹, 188, F₃, 120) (dual of [188, 9, 121]-code), but
- constructionÂ Y1 [i] would yield
  1. linear OA(3¹⁷⁸, 184, F₃, 120) (dual of [184, 6, 121]-code), but
    - residual code [i] would yield linear OA(3⁵⁸, 63, F₃, 40) (dual of [63, 5, 41]-code), but
      - 1 times truncation [i] would yield linear OA(3⁵⁷, 62, F₃, 39) (dual of [62, 5, 40]-code), but
        residual code [i] would yield linear OA(3¹⁸, 22, F₃, 13) (dual of [22, 4, 14]-code), but
        1 times truncation [i] would yield linear OA(3¹⁷, 21, F₃, 12) (dual of [21, 4, 13]-code), but
        â€œHNâ€ bound on codes from Brouwerâ€™s database [i]
  2. OA(3⁹, 188, S₃, 4), but
    - discarding factors would yield OA(3⁹, 100, S₃, 4), but
      - the Rao or (dual) Hamming bound shows that MÂ â‰¥ 20001 > 3⁹ [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

None.