MinT - Information on Result #548555

Information on Result #548555

There is no linear OA(2¹⁷⁴, 228, F₂, 82) (dual of [228, 54, 83]-code), because constructionÂ Y1 would yield

linear OA(2¹⁷³, 208, F₂, 82) (dual of [208, 35, 83]-code), but
- constructionÂ Y1 [i] would yield
  1. linear OA(2¹⁷², 196, F₂, 82) (dual of [196, 24, 83]-code), but
    - adding a parity check bit [i] would yield linear OA(2¹⁷³, 197, F₂, 83) (dual of [197, 24, 84]-code), but
      - â€œBKâ€ bound on codes from Brouwerâ€™s database [i]
  2. OA(2³⁵, 208, S₂, 12), but
    - discarding factors would yield OA(2³⁵, 173, S₂, 12), but
      - the Rao or (dual) Hamming bound shows that MÂ â‰¥ 35365 229344 > 2³⁵ [i]
OA(2⁵⁴, 228, S₂, 20), but
- discarding factors would yield OA(2⁵⁴, 195, S₂, 20), but
  - the Rao or (dual) Hamming bound shows that MÂ â‰¥ 18304 094847 646336 > 2⁵⁴ [i]

Mode: Bound (linear).

None.

The following results depend on this result:

	Result		Method
1	No linear OA(2¹⁷⁵, 229, F₂, 83) (dual of [229, 54, 84]-code)	[i]	Truncation
2	No linear OOA(2¹⁷⁵, 228, F₂, 2, 83) (dual of [(228, 2), 281, 84]-NRT-code)	[i]	m-Reduction for OOAs
3	No linear OOA(2¹⁷⁴, 228, F₂, 2, 82) (dual of [(228, 2), 282, 83]-NRT-code)	[i]	Depth Reduction
4	No linear OOA(2¹⁷⁴, 228, F₂, 3, 82) (dual of [(228, 3), 510, 83]-NRT-code)	[i]
5	No linear OOA(2¹⁷⁴, 228, F₂, 4, 82) (dual of [(228, 4), 738, 83]-NRT-code)	[i]
6	No linear OOA(2¹⁷⁴, 228, F₂, 5, 82) (dual of [(228, 5), 966, 83]-NRT-code)	[i]
7	No linear OOA(2¹⁷⁴, 228, F₂, 6, 82) (dual of [(228, 6), 1194, 83]-NRT-code)	[i]
8	No linear OOA(2¹⁷⁴, 228, F₂, 7, 82) (dual of [(228, 7), 1422, 83]-NRT-code)	[i]
9	No linear OOA(2¹⁷⁴, 228, F₂, 8, 82) (dual of [(228, 8), 1650, 83]-NRT-code)	[i]
10	No digital (92, 174, 228)-net over F₂	[i]	Extracting Embedded Orthogonal Array
11	No linear OA(2¹⁷⁵, 260, F₂, 82) (dual of [260, 85, 83]-code)	[i]	ConstructionÂ Y1 (Bound)