MinT - Information on Result #563286

Information on Result #563286

There is no linear OOA(8⁷⁷, 41, F₈, 2, 73) (dual of [(41, 2), 5, 74]-NRT-code), because 41 step m-reduction would yield linear OA(8³⁶, 41, F₈, 32) (dual of [41, 5, 33]-code), but

constructionÂ Y1 [i] would yield
1. OA(8³⁵, 37, S₈, 32), but
  - the (dual) Plotkin bound shows that MÂ â‰¥ 1622 592768 292133 633915 780102 881280 / 33 > 8³⁵ [i]
2. OA(8⁵, 41, S₈, 4), but
  - discarding factors would yield OA(8⁵, 37, S₈, 4), but
    - the Rao or (dual) Hamming bound shows that MÂ â‰¥ 32894 > 8⁵ [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(8⁷⁸, 42, F₈, 2, 74) (dual of [(42, 2), 6, 75]-NRT-code)	[i]		Truncation for OOAs
2	No linear OOA(8⁷⁹, 42, F₈, 2, 75) (dual of [(42, 2), 5, 76]-NRT-code)	[i]
3	No linear OOA(8⁸⁰, 43, F₈, 2, 76) (dual of [(43, 2), 6, 77]-NRT-code)	[i]
4	No linear OOA(8⁸¹, 43, F₈, 2, 77) (dual of [(43, 2), 5, 78]-NRT-code)	[i]
5	No linear OOA(8⁷⁷, 41, F₈, 3, 73) (dual of [(41, 3), 46, 74]-NRT-code)	[i]		Depth Reduction