MinT - Information on Result #3143200

Information on Result #3143200

There is no digital (8, 24, 37)-net over F₃, because 1 times m-reduction would yield digital (8, 23, 37)-net over F₃, but

extracting embedded orthogonal array [i] would yield linear OA(3²³, 37, F₃, 15) (dual of [37, 14, 16]-code), but
- constructionÂ Y1 [i] would yield
  1. linear OA(3²², 28, F₃, 15) (dual of [28, 6, 16]-code), but
    - â€œHHMâ€ bound on codes from Brouwerâ€™s database [i]
  2. linear OA(3¹⁴, 37, F₃, 9) (dual of [37, 23, 10]-code), but
    - discarding factors / shortening the dual code would yield linear OA(3¹⁴, 31, F₃, 9) (dual of [31, 17, 10]-code), but
      - residual code [i] would yield linear OA(3⁵, 21, F₃, 3) (dual of [21, 16, 4]-code or 21-cap in PG(4,3)), but
        20 is the largest size of a cap in PG(4,Â 3) [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.