MinT - Information on Result #555285

Information on Result #555285

There is no linear OOA(3¹⁵, 30, F₃, 2, 10) (dual of [(30, 2), 45, 11]-NRT-code), because 1 step m-reduction 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, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		Method
1	No linear OOA(3¹⁵, 30, F₃, 3, 10) (dual of [(30, 3), 75, 11]-NRT-code)	[i]	Depth Reduction
2	No linear OOA(3¹⁵, 30, F₃, 4, 10) (dual of [(30, 4), 105, 11]-NRT-code)	[i]
3	No linear OOA(3¹⁵, 30, F₃, 5, 10) (dual of [(30, 5), 135, 11]-NRT-code)	[i]