MinT - Information on Result #547821

Information on Result #547821

There is no linear OA(3²⁴⁷, 257, F₃, 165) (dual of [257, 10, 166]-code), because constructionÂ Y1 would yield

linear OA(3²⁴⁶, 253, F₃, 165) (dual of [253, 7, 166]-code), but
- residual code [i] would yield linear OA(3⁸¹, 87, F₃, 55) (dual of [87, 6, 56]-code), but
  - 1 times truncation [i] would yield linear OA(3⁸⁰, 86, F₃, 54) (dual of [86, 6, 55]-code), but
    - residual code [i] would yield linear OA(3²⁶, 31, F₃, 18) (dual of [31, 5, 19]-code), but
      - residual code [i] would yield linear OA(3⁸, 12, F₃, 6) (dual of [12, 4, 7]-code), but
        residual code [i] would yield linear OA(3², 5, F₃, 2) (dual of [5, 3, 3]-code or 5-arc in PG(1,3)), but
        improvement by Maruta on the Griesmer bound [i]
OA(3¹⁰, 257, S₃, 4), but
- discarding factors would yield OA(3¹⁰, 172, S₃, 4), but
  - the Rao or (dual) Hamming bound shows that MÂ â‰¥ 59169 > 3¹⁰ [i]

Mode: Bound (linear).

None.

The following results depend on this result:

	Result		Method
1	No linear OA(3²⁴⁸, 258, F₃, 166) (dual of [258, 10, 167]-code)	[i]	Truncation
2	No linear OA(3²⁴⁹, 259, F₃, 167) (dual of [259, 10, 168]-code)	[i]	Truncation
3	No linear OOA(3²⁴⁸, 257, F₃, 2, 166) (dual of [(257, 2), 266, 167]-NRT-code)	[i]	m-Reduction for OOAs
4	No linear OOA(3²⁴⁹, 257, F₃, 2, 167) (dual of [(257, 2), 265, 168]-NRT-code)	[i]	m-Reduction for OOAs
5	No linear OOA(3²⁴⁷, 257, F₃, 2, 165) (dual of [(257, 2), 267, 166]-NRT-code)	[i]	Depth Reduction
6	No linear OOA(3²⁴⁷, 257, F₃, 3, 165) (dual of [(257, 3), 524, 166]-NRT-code)	[i]
7	No linear OOA(3²⁴⁷, 257, F₃, 4, 165) (dual of [(257, 4), 781, 166]-NRT-code)	[i]
8	No linear OOA(3²⁴⁷, 257, F₃, 5, 165) (dual of [(257, 5), 1038, 166]-NRT-code)	[i]
9	No digital (82, 247, 257)-net over F₃	[i]	Extracting Embedded Orthogonal Array