MinT - Information on Result #548553

Information on Result #548553

There is no linear OA(2¹⁷¹, 235, F₂, 80) (dual of [235, 64, 81]-code), because constructionÂ Y1 would yield

linear OA(2¹⁷⁰, 211, F₂, 80) (dual of [211, 41, 81]-code), but
- constructionÂ Y1 [i] would yield
  1. linear OA(2¹⁶⁹, 197, F₂, 80) (dual of [197, 28, 81]-code), but
    - adding a parity check bit [i] would yield linear OA(2¹⁷⁰, 198, F₂, 81) (dual of [198, 28, 82]-code), but
      - â€œBKâ€ bound on codes from Brouwerâ€™s database [i]
  2. OA(2⁴¹, 211, S₂, 14), but
    - discarding factors would yield OA(2⁴¹, 198, S₂, 14), but
      - the Rao or (dual) Hamming bound shows that MÂ â‰¥ 2 206433 399776 > 2⁴¹ [i]
OA(2⁶⁴, 235, S₂, 24), but
- discarding factors would yield OA(2⁶⁴, 218, S₂, 24), but
  - the Rao or (dual) Hamming bound shows that MÂ â‰¥ 18 753208 478511 637348 > 2⁶⁴ [i]

Mode: Bound (linear).

None.

The following results depend on this result:

	Result		Method
1	No linear OA(2¹⁷², 236, F₂, 81) (dual of [236, 64, 82]-code)	[i]	Truncation
2	No linear OOA(2¹⁷², 235, F₂, 2, 81) (dual of [(235, 2), 298, 82]-NRT-code)	[i]	m-Reduction for OOAs
3	No linear OOA(2¹⁷¹, 235, F₂, 2, 80) (dual of [(235, 2), 299, 81]-NRT-code)	[i]	Depth Reduction
4	No linear OOA(2¹⁷¹, 235, F₂, 3, 80) (dual of [(235, 3), 534, 81]-NRT-code)	[i]
5	No linear OOA(2¹⁷¹, 235, F₂, 4, 80) (dual of [(235, 4), 769, 81]-NRT-code)	[i]
6	No linear OOA(2¹⁷¹, 235, F₂, 5, 80) (dual of [(235, 5), 1004, 81]-NRT-code)	[i]
7	No linear OOA(2¹⁷¹, 235, F₂, 6, 80) (dual of [(235, 6), 1239, 81]-NRT-code)	[i]
8	No linear OOA(2¹⁷¹, 235, F₂, 7, 80) (dual of [(235, 7), 1474, 81]-NRT-code)	[i]
9	No linear OOA(2¹⁷¹, 235, F₂, 8, 80) (dual of [(235, 8), 1709, 81]-NRT-code)	[i]
10	No digital (91, 171, 235)-net over F₂	[i]	Extracting Embedded Orthogonal Array
11	Linear OA(2⁸³, 175, F₂, 22) (dual of [175, 92, 23]-code)	[i]	ConstructionÂ Y1