MinT - Information on Result #548566

Information on Result #548566

There is no linear OA(2²⁵⁵, 288, F₂, 124) (dual of [288, 33, 125]-code), because constructionÂ Y1 would yield

linear OA(2²⁵⁴, 278, F₂, 124) (dual of [278, 24, 125]-code), but
- residual code [i] would yield linear OA(2¹³⁰, 153, F₂, 62) (dual of [153, 23, 63]-code), but
  - adding a parity check bit [i] would yield linear OA(2¹³¹, 154, F₂, 63) (dual of [154, 23, 64]-code), but
    - â€œBKâ€ bound on codes from Brouwerâ€™s database [i]
OA(2³³, 288, S₂, 10), but
- discarding factors would yield OA(2³³, 254, S₂, 10), but
  - the Rao or (dual) Hamming bound shows that MÂ â‰¥ 8640 218941 > 2³³ [i]

Mode: Bound (linear).

None.

The following results depend on this result:

	Result		Method
1	No linear OA(2²⁵⁶, 289, F₂, 125) (dual of [289, 33, 126]-code)	[i]	Truncation
2	No linear OOA(2²⁵⁶, 288, F₂, 2, 125) (dual of [(288, 2), 320, 126]-NRT-code)	[i]	m-Reduction for OOAs
3	No linear OOA(2²⁵⁵, 288, F₂, 2, 124) (dual of [(288, 2), 321, 125]-NRT-code)	[i]	Depth Reduction
4	No linear OOA(2²⁵⁵, 288, F₂, 3, 124) (dual of [(288, 3), 609, 125]-NRT-code)	[i]
5	No linear OOA(2²⁵⁵, 288, F₂, 4, 124) (dual of [(288, 4), 897, 125]-NRT-code)	[i]
6	No linear OOA(2²⁵⁵, 288, F₂, 5, 124) (dual of [(288, 5), 1185, 125]-NRT-code)	[i]
7	No linear OOA(2²⁵⁵, 288, F₂, 6, 124) (dual of [(288, 6), 1473, 125]-NRT-code)	[i]
8	No linear OOA(2²⁵⁵, 288, F₂, 7, 124) (dual of [(288, 7), 1761, 125]-NRT-code)	[i]
9	No linear OOA(2²⁵⁵, 288, F₂, 8, 124) (dual of [(288, 8), 2049, 125]-NRT-code)	[i]
10	No digital (131, 255, 288)-net over F₂	[i]	Extracting Embedded Orthogonal Array
11	No linear OA(2²⁵⁶, 304, F₂, 124) (dual of [304, 48, 125]-code)	[i]	ConstructionÂ Y1 (Bound)