MinT - Information on Result #556477

Information on Result #556477

There is no linear OOA(3¹⁴⁴, 168, F₃, 2, 95) (dual of [(168, 2), 192, 96]-NRT-code), because 1 step m-reduction would yield linear OA(3¹⁴³, 168, F₃, 94) (dual of [168, 25, 95]-code), but

constructionÂ Y1 [i] would yield
1. linear OA(3¹⁴², 156, F₃, 94) (dual of [156, 14, 95]-code), but
  - constructionÂ Y1 [i] would yield
    1. OA(3¹⁴¹, 150, S₃, 94), but
      - the linear programming bound shows that MÂ â‰¥ 2 507699 731904 749483 156305 303283 721699 486095 458197 011266 969583 191489 627021 / 107749 > 3¹⁴¹ [i]
    2. OA(3¹⁴, 156, S₃, 6), but
      - discarding factors would yield OA(3¹⁴, 154, S₃, 6), but
        the Rao or (dual) Hamming bound shows that MÂ â‰¥ 4 822665 > 3¹⁴ [i]
2. OA(3²⁵, 168, S₃, 12), but
  - discarding factors would yield OA(3²⁵, 148, S₃, 12), but
    - the Rao or (dual) Hamming bound shows that MÂ â‰¥ 861032 991633 > 3²⁵ [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(3¹⁴⁴, 168, F₃, 3, 95) (dual of [(168, 3), 360, 96]-NRT-code)	[i]	Depth Reduction
2	No linear OOA(3¹⁴⁴, 168, F₃, 4, 95) (dual of [(168, 4), 528, 96]-NRT-code)	[i]
3	No linear OOA(3¹⁴⁴, 168, F₃, 5, 95) (dual of [(168, 5), 696, 96]-NRT-code)	[i]