MinT - Information on Result #555875

Information on Result #555875

There is no linear OOA(3⁹⁷, 66, F₃, 2, 78) (dual of [(66, 2), 35, 79]-NRT-code), because 39 step m-reduction would yield linear OA(3⁵⁸, 66, F₃, 39) (dual of [66, 8, 40]-code), but

constructionÂ Y1 [i] would yield
1. linear OA(3⁵⁷, 62, F₃, 39) (dual of [62, 5, 40]-code), but
  - residual code [i] would yield linear OA(3¹⁸, 22, F₃, 13) (dual of [22, 4, 14]-code), but
    - 1 times truncation [i] would yield linear OA(3¹⁷, 21, F₃, 12) (dual of [21, 4, 13]-code), but
      - â€œHNâ€ bound on codes from Brouwerâ€™s database [i]
2. OA(3⁸, 66, S₃, 4), but
  - discarding factors would yield OA(3⁸, 58, S₃, 4), but
    - the Rao or (dual) Hamming bound shows that MÂ â‰¥ 6729 > 3⁸ [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(3⁹⁷, 66, F₃, 3, 78) (dual of [(66, 3), 101, 79]-NRT-code)	[i]	Depth Reduction
2	No linear OOA(3⁹⁷, 66, F₃, 4, 78) (dual of [(66, 4), 167, 79]-NRT-code)	[i]
3	No linear OOA(3⁹⁷, 66, F₃, 5, 78) (dual of [(66, 5), 233, 79]-NRT-code)	[i]