MinT - Information on Result #548543

Information on Result #548543

There is no linear OA(2¹⁵¹, 222, F₂, 70) (dual of [222, 71, 71]-code), because constructionÂ Y1 would yield

linear OA(2¹⁵⁰, 194, F₂, 70) (dual of [194, 44, 71]-code), but
- constructionÂ Y1 [i] would yield
  1. linear OA(2¹⁴⁹, 178, F₂, 70) (dual of [178, 29, 71]-code), but
    - adding a parity check bit [i] would yield linear OA(2¹⁵⁰, 179, F₂, 71) (dual of [179, 29, 72]-code), but
      - â€œBKâ€ bound on codes from Brouwerâ€™s database [i]
  2. OA(2⁴⁴, 194, S₂, 16), but
    - discarding factors would yield OA(2⁴⁴, 173, S₂, 16), but
      - the Rao or (dual) Hamming bound shows that MÂ â‰¥ 17 734855 699135 > 2⁴⁴ [i]
OA(2⁷¹, 222, S₂, 28), but
- discarding factors would yield OA(2⁷¹, 209, S₂, 28), but
  - the Rao or (dual) Hamming bound shows that MÂ â‰¥ 2400 648072 841355 873622 > 2⁷¹ [i]

Mode: Bound (linear).

None.

The following results depend on this result:

	Result		Method
1	No linear OA(2¹⁵², 223, F₂, 71) (dual of [223, 71, 72]-code)	[i]	Truncation
2	No linear OOA(2¹⁵², 222, F₂, 2, 71) (dual of [(222, 2), 292, 72]-NRT-code)	[i]	m-Reduction for OOAs
3	No linear OOA(2¹⁵¹, 222, F₂, 2, 70) (dual of [(222, 2), 293, 71]-NRT-code)	[i]	Depth Reduction
4	No linear OOA(2¹⁵¹, 222, F₂, 3, 70) (dual of [(222, 3), 515, 71]-NRT-code)	[i]
5	No linear OOA(2¹⁵¹, 222, F₂, 4, 70) (dual of [(222, 4), 737, 71]-NRT-code)	[i]
6	No linear OOA(2¹⁵¹, 222, F₂, 5, 70) (dual of [(222, 5), 959, 71]-NRT-code)	[i]
7	No linear OOA(2¹⁵¹, 222, F₂, 6, 70) (dual of [(222, 6), 1181, 71]-NRT-code)	[i]
8	No linear OOA(2¹⁵¹, 222, F₂, 7, 70) (dual of [(222, 7), 1403, 71]-NRT-code)	[i]
9	No linear OOA(2¹⁵¹, 222, F₂, 8, 70) (dual of [(222, 8), 1625, 71]-NRT-code)	[i]
10	No digital (81, 151, 222)-net over F₂	[i]	Extracting Embedded Orthogonal Array