MinT - Information on Result #598922

Information on Result #598922

There is no digital (5, 14, 30)-net over F₃, because extracting embedded orthogonal array would yield linear OA(3¹⁴, 30, F₃, 9) (dual of [30, 16, 10]-code), but

constructionÂ Y1 [i] would yield
1. linear OA(3¹³, 19, F₃, 9) (dual of [19, 6, 10]-code), but
  - constructionÂ Y1 [i] would yield
    1. linear OA(3¹², 15, F₃, 9) (dual of [15, 3, 10]-code), but
      - Griesmer bound [i]
    2. OA(3⁶, 19, S₃, 4), but
      - the linear programming bound shows that MÂ â‰¥ 51975 / 67 > 3⁶ [i]
2. linear OA(3¹⁶, 30, F₃, 11) (dual of [30, 14, 12]-code), but
  - discarding factors / shortening the dual code would yield linear OA(3¹⁶, 24, F₃, 11) (dual of [24, 8, 12]-code), but
    - â€œBSâ€ bound on codes from Brouwerâ€™s database [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 (5, 15, 30)-net over F₃	[i]		m-Reduction