MinT - Information on Result #563795

Information on Result #563795

There is no linear OOA(9⁸⁵, 45, F₉, 2, 81) (dual of [(45, 2), 5, 82]-NRT-code), because 45 step m-reduction would yield linear OA(9⁴⁰, 45, F₉, 36) (dual of [45, 5, 37]-code), but

constructionÂ Y1 [i] would yield
1. OA(9³⁹, 41, S₉, 36), but
  - the (dual) Plotkin bound shows that MÂ â‰¥ 739 044147 071729 616580 416051 031916 488005 / 37 > 9³⁹ [i]
2. OA(9⁵, 45, S₉, 4), but
  - discarding factors would yield OA(9⁵, 44, S₉, 4), but
    - the Rao or (dual) Hamming bound shows that MÂ â‰¥ 60897 > 9⁵ [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(9⁸⁶, 46, F₉, 2, 82) (dual of [(46, 2), 6, 83]-NRT-code)	[i]		Truncation for OOAs
2	No linear OOA(9⁸⁷, 46, F₉, 2, 83) (dual of [(46, 2), 5, 84]-NRT-code)	[i]
3	No linear OOA(9⁸⁸, 47, F₉, 2, 84) (dual of [(47, 2), 6, 85]-NRT-code)	[i]
4	No linear OOA(9⁸⁹, 47, F₉, 2, 85) (dual of [(47, 2), 5, 86]-NRT-code)	[i]
5	No linear OOA(9⁹⁰, 48, F₉, 2, 86) (dual of [(48, 2), 6, 87]-NRT-code)	[i]
6	No linear OOA(9⁹¹, 48, F₉, 2, 87) (dual of [(48, 2), 5, 88]-NRT-code)	[i]
7	No linear OOA(9⁹², 49, F₉, 2, 88) (dual of [(49, 2), 6, 89]-NRT-code)	[i]
8	No linear OOA(9⁹³, 49, F₉, 2, 89) (dual of [(49, 2), 5, 90]-NRT-code)	[i]
9	No linear OOA(9⁸⁵, 45, F₉, 3, 81) (dual of [(45, 3), 50, 82]-NRT-code)	[i]		Depth Reduction