MinT - Information on Result #548541

Information on Result #548541

There is no linear OA(2¹³², 185, F₂, 62) (dual of [185, 53, 63]-code), because constructionÂ Y1 would yield

linear OA(2¹³¹, 165, F₂, 62) (dual of [165, 34, 63]-code), but
- constructionÂ Y1 [i] would yield
  1. 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]
  2. OA(2³⁴, 165, S₂, 12), but
    - discarding factors would yield OA(2³⁴, 154, S₂, 12), but
      - the Rao or (dual) Hamming bound shows that MÂ â‰¥ 17486 314616 > 2³⁴ [i]
OA(2⁵³, 185, S₂, 20), but
- discarding factors would yield OA(2⁵³, 182, S₂, 20), but
  - the Rao or (dual) Hamming bound shows that MÂ â‰¥ 9064 436853 738748 > 2⁵³ [i]

Mode: Bound (linear).

None.

The following results depend on this result:

	Result		Method
1	No linear OA(2¹³³, 186, F₂, 63) (dual of [186, 53, 64]-code)	[i]	Truncation
2	No linear OOA(2¹³³, 185, F₂, 2, 63) (dual of [(185, 2), 237, 64]-NRT-code)	[i]	m-Reduction for OOAs
3	No linear OOA(2¹³², 185, F₂, 2, 62) (dual of [(185, 2), 238, 63]-NRT-code)	[i]	Depth Reduction
4	No linear OOA(2¹³², 185, F₂, 3, 62) (dual of [(185, 3), 423, 63]-NRT-code)	[i]
5	No linear OOA(2¹³², 185, F₂, 4, 62) (dual of [(185, 4), 608, 63]-NRT-code)	[i]
6	No linear OOA(2¹³², 185, F₂, 5, 62) (dual of [(185, 5), 793, 63]-NRT-code)	[i]
7	No linear OOA(2¹³², 185, F₂, 6, 62) (dual of [(185, 6), 978, 63]-NRT-code)	[i]
8	No linear OOA(2¹³², 185, F₂, 7, 62) (dual of [(185, 7), 1163, 63]-NRT-code)	[i]
9	No linear OOA(2¹³², 185, F₂, 8, 62) (dual of [(185, 8), 1348, 63]-NRT-code)	[i]
10	No digital (70, 132, 185)-net over F₂	[i]	Extracting Embedded Orthogonal Array