MinT - Information on Result #578414

Information on Result #578414

There is no linear OOA(9¹³⁰, 45, F₉, 3, 126) (dual of [(45, 3), 5, 127]-NRT-code), because 90 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		Method
1	No linear OOA(9¹³¹, 46, F₉, 3, 127) (dual of [(46, 3), 7, 128]-NRT-code)	[i]	Truncation for OOAs
2	No linear OOA(9¹³², 46, F₉, 3, 128) (dual of [(46, 3), 6, 129]-NRT-code)	[i]
3	No linear OOA(9¹³³, 46, F₉, 3, 129) (dual of [(46, 3), 5, 130]-NRT-code)	[i]
4	No linear OOA(9¹³⁴, 47, F₉, 3, 130) (dual of [(47, 3), 7, 131]-NRT-code)	[i]
5	No linear OOA(9¹³⁵, 47, F₉, 3, 131) (dual of [(47, 3), 6, 132]-NRT-code)	[i]
6	No linear OOA(9¹³⁶, 47, F₉, 3, 132) (dual of [(47, 3), 5, 133]-NRT-code)	[i]
7	No linear OOA(9¹³⁷, 48, F₉, 3, 133) (dual of [(48, 3), 7, 134]-NRT-code)	[i]
8	No linear OOA(9¹³⁸, 48, F₉, 3, 134) (dual of [(48, 3), 6, 135]-NRT-code)	[i]
9	No linear OOA(9¹³⁹, 48, F₉, 3, 135) (dual of [(48, 3), 5, 136]-NRT-code)	[i]