MinT - Information on Result #548603

Information on Result #548603

There is no linear OA(3¹⁷⁶, 190, F₃, 117) (dual of [190, 14, 118]-code), because constructionÂ Y1 would yield

linear OA(3¹⁷⁵, 184, F₃, 117) (dual of [184, 9, 118]-code), but
- constructionÂ Y1 [i] would yield
  1. linear OA(3¹⁷⁴, 180, F₃, 117) (dual of [180, 6, 118]-code), but
    - residual code [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, 184, 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]
OA(3¹⁴, 190, S₃, 6), but
- discarding factors would yield OA(3¹⁴, 154, S₃, 6), but
  - the Rao or (dual) Hamming bound shows that MÂ â‰¥ 4 822665 > 3¹⁴ [i]

Mode: Bound (linear).

None.

The following results depend on this result:

	Result		Method
1	No linear OA(3¹⁷⁷, 191, F₃, 118) (dual of [191, 14, 119]-code)	[i]	Truncation
2	No linear OA(3¹⁷⁸, 192, F₃, 119) (dual of [192, 14, 120]-code)	[i]	Truncation
3	No linear OOA(3¹⁷⁷, 190, F₃, 2, 118) (dual of [(190, 2), 203, 119]-NRT-code)	[i]	m-Reduction for OOAs
4	No linear OOA(3¹⁷⁸, 190, F₃, 2, 119) (dual of [(190, 2), 202, 120]-NRT-code)	[i]	m-Reduction for OOAs
5	No linear OOA(3¹⁷⁶, 190, F₃, 2, 117) (dual of [(190, 2), 204, 118]-NRT-code)	[i]	Depth Reduction
6	No linear OOA(3¹⁷⁶, 190, F₃, 3, 117) (dual of [(190, 3), 394, 118]-NRT-code)	[i]
7	No linear OOA(3¹⁷⁶, 190, F₃, 4, 117) (dual of [(190, 4), 584, 118]-NRT-code)	[i]
8	No linear OOA(3¹⁷⁶, 190, F₃, 5, 117) (dual of [(190, 5), 774, 118]-NRT-code)	[i]
9	No digital (59, 176, 190)-net over F₃	[i]	Extracting Embedded Orthogonal Array