MinT - Information on Result #563841

Information on Result #563841

There is no linear OOA(9¹⁰⁵, 55, F₉, 2, 100) (dual of [(55, 2), 5, 101]-NRT-code), because 55 step m-reduction would yield linear OA(9⁵⁰, 55, F₉, 45) (dual of [55, 5, 46]-code), but

constructionÂ Y1 [i] would yield
1. OA(9⁴⁹, 51, S₉, 45), but
  - the (dual) Plotkin bound shows that MÂ â‰¥ 1 546132 562196 033993 109383 389296 863818 106322 566003 / 23 > 9⁴⁹ [i]
2. OA(9⁵, 55, 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(9¹⁰⁶, 56, F₉, 2, 101) (dual of [(56, 2), 6, 102]-NRT-code)	[i]	Truncation for OOAs
2	No linear OOA(9¹⁰⁷, 56, F₉, 2, 102) (dual of [(56, 2), 5, 103]-NRT-code)	[i]
3	No linear OOA(9¹⁰⁸, 57, F₉, 2, 103) (dual of [(57, 2), 6, 104]-NRT-code)	[i]
4	No linear OOA(9¹⁰⁹, 57, F₉, 2, 104) (dual of [(57, 2), 5, 105]-NRT-code)	[i]
5	No linear OOA(9¹⁰⁵, 55, F₉, 3, 100) (dual of [(55, 3), 60, 101]-NRT-code)	[i]	Depth Reduction