MinT - Information on Result #547088

Information on Result #547088

There is no linear OA(3²⁵⁰, 257, F₃, 168) (dual of [257, 7, 169]-code), because residual code would yield linear OA(3⁸², 88, F₃, 56) (dual of [88, 6, 57]-code), but

2 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 OOA(3²⁵⁰, 257, F₃, 2, 168) (dual of [(257, 2), 264, 169]-NRT-code)	[i]		Depth Reduction
2	No linear OOA(3²⁵⁰, 257, F₃, 3, 168) (dual of [(257, 3), 521, 169]-NRT-code)	[i]
3	No linear OOA(3²⁵⁰, 257, F₃, 4, 168) (dual of [(257, 4), 778, 169]-NRT-code)	[i]
4	No linear OOA(3²⁵⁰, 257, F₃, 5, 168) (dual of [(257, 5), 1035, 169]-NRT-code)	[i]