MinT - Information on Result #557053

Information on Result #557053

There is no linear OOA(3¹⁸¹, 188, F₃, 2, 122) (dual of [(188, 2), 195, 123]-NRT-code), because 2 step m-reduction would yield linear OA(3¹⁷⁹, 188, F₃, 120) (dual of [188, 9, 121]-code), but

constructionÂ Y1 [i] would yield
1. linear OA(3¹⁷⁸, 184, F₃, 120) (dual of [184, 6, 121]-code), but
  - residual code [i] would yield linear OA(3⁵⁸, 63, F₃, 40) (dual of [63, 5, 41]-code), but
    - 1 times truncation [i] would yield 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(3⁹, 188, S₃, 4), but
  - discarding factors would yield OA(3⁹, 100, S₃, 4), but
    - the Rao or (dual) Hamming bound shows that MÂ â‰¥ 20001 > 3⁹ [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(3¹⁸¹, 188, F₃, 3, 122) (dual of [(188, 3), 383, 123]-NRT-code)	[i]	Depth Reduction
2	No linear OOA(3¹⁸¹, 188, F₃, 4, 122) (dual of [(188, 4), 571, 123]-NRT-code)	[i]
3	No linear OOA(3¹⁸¹, 188, F₃, 5, 122) (dual of [(188, 5), 759, 123]-NRT-code)	[i]