MinT - Information on Result #548597

Information on Result #548597

There is no linear OA(3¹⁶³, 177, F₃, 108) (dual of [177, 14, 109]-code), because constructionÂ Y1 would yield

linear OA(3¹⁶², 171, F₃, 108) (dual of [171, 9, 109]-code), but
- constructionÂ Y1 [i] would yield
  1. linear OA(3¹⁶¹, 167, F₃, 108) (dual of [167, 6, 109]-code), but
    - residual code [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, 171, 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, 177, 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(3¹⁶⁴, 178, F₃, 109) (dual of [178, 14, 110]-code)	[i]	Truncation
2	No linear OA(3¹⁶⁵, 179, F₃, 110) (dual of [179, 14, 111]-code)	[i]	Truncation
3	No linear OOA(3¹⁶⁴, 177, F₃, 2, 109) (dual of [(177, 2), 190, 110]-NRT-code)	[i]	m-Reduction for OOAs
4	No linear OOA(3¹⁶⁵, 177, F₃, 2, 110) (dual of [(177, 2), 189, 111]-NRT-code)	[i]	m-Reduction for OOAs
5	No linear OOA(3¹⁶³, 177, F₃, 2, 108) (dual of [(177, 2), 191, 109]-NRT-code)	[i]	Depth Reduction
6	No linear OOA(3¹⁶³, 177, F₃, 3, 108) (dual of [(177, 3), 368, 109]-NRT-code)	[i]
7	No linear OOA(3¹⁶³, 177, F₃, 4, 108) (dual of [(177, 4), 545, 109]-NRT-code)	[i]
8	No linear OOA(3¹⁶³, 177, F₃, 5, 108) (dual of [(177, 5), 722, 109]-NRT-code)	[i]
9	No digital (55, 163, 177)-net over F₃	[i]	Extracting Embedded Orthogonal Array
10	No linear OA(3¹⁶⁴, 189, F₃, 108) (dual of [189, 25, 109]-code)	[i]	ConstructionÂ Y1 (Bound)