MinT - Information on Result #547083

Information on Result #547083

There is no linear OA(3²⁴⁶, 253, F₃, 165) (dual of [253, 7, 166]-code), because residual code would yield linear OA(3⁸¹, 87, F₃, 55) (dual of [87, 6, 56]-code), but

1 times truncation [i] would yield linear OA(3⁸⁰, 86, F₃, 54) (dual of [86, 6, 55]-code), but
- residual code [i] would yield linear OA(3²⁶, 31, F₃, 18) (dual of [31, 5, 19]-code), but
  - residual code [i] would yield linear OA(3⁸, 12, F₃, 6) (dual of [12, 4, 7]-code), but
    - residual code [i] would yield linear OA(3², 5, F₃, 2) (dual of [5, 3, 3]-code or 5-arc in PG(1,3)), but
      - improvement by Maruta on the Griesmer bound [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		This result only	Method
1	No linear OA(3²⁴⁷, 254, F₃, 166) (dual of [254, 7, 167]-code)	[i]		Truncation
2	No linear OA(3²⁴⁸, 255, F₃, 167) (dual of [255, 7, 168]-code)	[i]		Truncation
3	No linear OOA(3²⁴⁶, 253, F₃, 2, 165) (dual of [(253, 2), 260, 166]-NRT-code)	[i]		Depth Reduction
4	No linear OOA(3²⁴⁶, 253, F₃, 3, 165) (dual of [(253, 3), 513, 166]-NRT-code)	[i]
5	No linear OOA(3²⁴⁶, 253, F₃, 4, 165) (dual of [(253, 4), 766, 166]-NRT-code)	[i]
6	No linear OOA(3²⁴⁶, 253, F₃, 5, 165) (dual of [(253, 5), 1019, 166]-NRT-code)	[i]
7	No linear OA(3²⁴⁷, 257, F₃, 165) (dual of [257, 10, 166]-code)	[i]		ConstructionÂ Y1 (Bound)