MinT - Information on Result #557665

Information on Result #557665

There is no linear OOA(3²⁰⁹, 154, F₃, 2, 161) (dual of [(154, 2), 99, 162]-NRT-code), because 62 step m-reduction would yield linear OA(3¹⁴⁷, 154, F₃, 99) (dual of [154, 7, 100]-code), but

constructionÂ Y1 [i] would yield
1. linear OA(3¹⁴⁶, 151, F₃, 99) (dual of [151, 5, 100]-code), but
  - Griesmer bound [i]
2. linear OA(3⁷, 154, F₃, 3) (dual of [154, 147, 4]-code or 154-cap in PG(6,3)), but
  - discarding factors / shortening the dual code would yield linear OA(3⁷, 137, F₃, 3) (dual of [137, 130, 4]-code or 137-cap in PG(6,3)), but
    - a result by BarÃ¡t, Edel, Hill, and Storme [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(3²⁰⁹, 154, F₃, 3, 161) (dual of [(154, 3), 253, 162]-NRT-code)	[i]	Depth Reduction
2	No linear OOA(3²⁰⁹, 154, F₃, 4, 161) (dual of [(154, 4), 407, 162]-NRT-code)	[i]
3	No linear OOA(3²⁰⁹, 154, F₃, 5, 161) (dual of [(154, 5), 561, 162]-NRT-code)	[i]