MinT - Information on Result #548601

Information on Result #548601

There is no linear OA(3¹⁷⁰, 179, F₃, 114) (dual of [179, 9, 115]-code), because constructionÂ Y1 would yield

linear OA(3¹⁶⁹, 175, F₃, 114) (dual of [175, 6, 115]-code), but
- residual code [i] would yield linear OA(3⁵⁵, 60, F₃, 38) (dual of [60, 5, 39]-code), but
  - 2 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]
OA(3⁹, 179, 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).

None.

The following results depend on this result:

	Result		Method
1	No linear OA(3¹⁷¹, 180, F₃, 115) (dual of [180, 9, 116]-code)	[i]	Truncation
2	No linear OA(3¹⁷², 181, F₃, 116) (dual of [181, 9, 117]-code)	[i]	Truncation
3	No linear OOA(3¹⁷¹, 179, F₃, 2, 115) (dual of [(179, 2), 187, 116]-NRT-code)	[i]	m-Reduction for OOAs
4	No linear OOA(3¹⁷², 179, F₃, 2, 116) (dual of [(179, 2), 186, 117]-NRT-code)	[i]	m-Reduction for OOAs
5	No linear OOA(3¹⁷⁰, 179, F₃, 2, 114) (dual of [(179, 2), 188, 115]-NRT-code)	[i]	Depth Reduction
6	No linear OOA(3¹⁷⁰, 179, F₃, 3, 114) (dual of [(179, 3), 367, 115]-NRT-code)	[i]
7	No linear OOA(3¹⁷⁰, 179, F₃, 4, 114) (dual of [(179, 4), 546, 115]-NRT-code)	[i]
8	No linear OOA(3¹⁷⁰, 179, F₃, 5, 114) (dual of [(179, 5), 725, 115]-NRT-code)	[i]
9	No digital (56, 170, 179)-net over F₃	[i]	Extracting Embedded Orthogonal Array