MinT - Information on Result #556400

Information on Result #556400

There is no linear OOA(3¹³⁸, 161, F₃, 2, 90) (dual of [(161, 2), 184, 91]-NRT-code), because 1 step m-reduction would yield linear OA(3¹³⁷, 161, F₃, 89) (dual of [161, 24, 90]-code), but

constructionÂ Y1 [i] would yield
1. OA(3¹³⁶, 149, S₃, 89), but
  - the linear programming bound shows that MÂ â‰¥ 6 385896 362423 839893 456186 755923 270794 744764 572661 578917 513381 685836 804369 / 75 686875 > 3¹³⁶ [i]
2. OA(3²⁴, 161, S₃, 12), but
  - discarding factors would yield OA(3²⁴, 124, S₃, 12), but
    - the Rao or (dual) Hamming bound shows that MÂ â‰¥ 293147 842993 > 3²⁴ [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(3¹³⁸, 161, F₃, 3, 90) (dual of [(161, 3), 345, 91]-NRT-code)	[i]	Depth Reduction
2	No linear OOA(3¹³⁸, 161, F₃, 4, 90) (dual of [(161, 4), 506, 91]-NRT-code)	[i]
3	No linear OOA(3¹³⁸, 161, F₃, 5, 90) (dual of [(161, 5), 667, 91]-NRT-code)	[i]