MinT - Information on Result #556374

Information on Result #556374

There is no linear OOA(3¹³⁶, 164, F₃, 2, 88) (dual of [(164, 2), 192, 89]-NRT-code), because 1 step m-reduction would yield linear OA(3¹³⁵, 164, F₃, 87) (dual of [164, 29, 88]-code), but

constructionÂ Y1 [i] would yield
1. OA(3¹³⁴, 150, S₃, 87), but
  - the linear programming bound shows that MÂ â‰¥ 1998 191076 053927 805178 143382 564872 985089 052204 487349 698881 740338 723055 870219 / 227413 116931 > 3¹³⁴ [i]
2. OA(3²⁹, 164, S₃, 14), but
  - discarding factors would yield OA(3²⁹, 163, S₃, 14), but
    - the Rao or (dual) Hamming bound shows that MÂ â‰¥ 69 685080 318363 > 3²⁹ [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(3¹³⁶, 164, F₃, 3, 88) (dual of [(164, 3), 356, 89]-NRT-code)	[i]	Depth Reduction
2	No linear OOA(3¹³⁶, 164, F₃, 4, 88) (dual of [(164, 4), 520, 89]-NRT-code)	[i]
3	No linear OOA(3¹³⁶, 164, F₃, 5, 88) (dual of [(164, 5), 684, 89]-NRT-code)	[i]