MinT - Information on Result #547820

Information on Result #547820

There is no linear OA(3²⁴⁴, 259, F₃, 162) (dual of [259, 15, 163]-code), because constructionÂ Y1 would yield

linear OA(3²⁴³, 253, F₃, 162) (dual of [253, 10, 163]-code), but
- constructionÂ Y1 [i] would yield
  1. linear OA(3²⁴², 249, F₃, 162) (dual of [249, 7, 163]-code), but
    - residual code [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]
  2. OA(3¹⁰, 253, 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]
OA(3¹⁵, 259, S₃, 6), but
- discarding factors would yield OA(3¹⁵, 222, S₃, 6), but
  - the Rao or (dual) Hamming bound shows that MÂ â‰¥ 14 490089 > 3¹⁵ [i]

Mode: Bound (linear).

None.

The following results depend on this result:

	Result		Method
1	No linear OA(3²⁴⁵, 260, F₃, 163) (dual of [260, 15, 164]-code)	[i]	Truncation
2	No linear OA(3²⁴⁶, 261, F₃, 164) (dual of [261, 15, 165]-code)	[i]	Truncation
3	No linear OOA(3²⁴⁵, 259, F₃, 2, 163) (dual of [(259, 2), 273, 164]-NRT-code)	[i]	m-Reduction for OOAs
4	No linear OOA(3²⁴⁶, 259, F₃, 2, 164) (dual of [(259, 2), 272, 165]-NRT-code)	[i]	m-Reduction for OOAs
5	No linear OOA(3²⁴⁴, 259, F₃, 2, 162) (dual of [(259, 2), 274, 163]-NRT-code)	[i]	Depth Reduction
6	No linear OOA(3²⁴⁴, 259, F₃, 3, 162) (dual of [(259, 3), 533, 163]-NRT-code)	[i]
7	No linear OOA(3²⁴⁴, 259, F₃, 4, 162) (dual of [(259, 4), 792, 163]-NRT-code)	[i]
8	No linear OOA(3²⁴⁴, 259, F₃, 5, 162) (dual of [(259, 5), 1051, 163]-NRT-code)	[i]
9	No digital (82, 244, 259)-net over F₃	[i]	Extracting Embedded Orthogonal Array