MinT - Information on Result #558274

Information on Result #558274

There is no linear OOA(3²²⁹, 175, F₃, 2, 174) (dual of [(175, 2), 121, 175]-NRT-code), because 63 step m-reduction would yield linear OA(3¹⁶⁶, 175, F₃, 111) (dual of [175, 9, 112]-code), but

constructionÂ Y1 [i] would yield
1. linear OA(3¹⁶⁵, 171, F₃, 111) (dual of [171, 6, 112]-code), but
  - residual code [i] would yield linear OA(3⁵⁴, 59, F₃, 37) (dual of [59, 5, 38]-code), but
    - 1 times truncation [i] would yield linear OA(3⁵³, 58, F₃, 36) (dual of [58, 5, 37]-code), but
      - residual code [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, 175, 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(3²²⁹, 175, F₃, 3, 174) (dual of [(175, 3), 296, 175]-NRT-code)	[i]	Depth Reduction
2	No linear OOA(3²²⁹, 175, F₃, 4, 174) (dual of [(175, 4), 471, 175]-NRT-code)	[i]
3	No linear OOA(3²²⁹, 175, F₃, 5, 174) (dual of [(175, 5), 646, 175]-NRT-code)	[i]