MinT - Information on Result #548560

Information on Result #548560

There is no linear OA(2¹⁸⁴, 249, F₂, 86) (dual of [249, 65, 87]-code), because constructionÂ Y1 would yield

linear OA(2¹⁸³, 225, F₂, 86) (dual of [225, 42, 87]-code), but
- constructionÂ Y1 [i] would yield
  1. linear OA(2¹⁸², 211, F₂, 86) (dual of [211, 29, 87]-code), but
    - adding a parity check bit [i] would yield linear OA(2¹⁸³, 212, F₂, 87) (dual of [212, 29, 88]-code), but
      - â€œBKâ€ bound on codes from Brouwerâ€™s database [i]
  2. OA(2⁴², 225, S₂, 14), but
    - discarding factors would yield OA(2⁴², 219, S₂, 14), but
      - the Rao or (dual) Hamming bound shows that MÂ â‰¥ 4 498367 189624 > 2⁴² [i]
OA(2⁶⁵, 249, S₂, 24), but
- discarding factors would yield OA(2⁶⁵, 231, S₂, 24), but
  - the Rao or (dual) Hamming bound shows that MÂ â‰¥ 38 110539 835438 477924 > 2⁶⁵ [i]

Mode: Bound (linear).

None.

The following results depend on this result:

	Result		Method
1	No linear OA(2¹⁸⁵, 250, F₂, 87) (dual of [250, 65, 88]-code)	[i]	Truncation
2	No linear OOA(2¹⁸⁵, 249, F₂, 2, 87) (dual of [(249, 2), 313, 88]-NRT-code)	[i]	m-Reduction for OOAs
3	No linear OOA(2¹⁸⁴, 249, F₂, 2, 86) (dual of [(249, 2), 314, 87]-NRT-code)	[i]	Depth Reduction
4	No linear OOA(2¹⁸⁴, 249, F₂, 3, 86) (dual of [(249, 3), 563, 87]-NRT-code)	[i]
5	No linear OOA(2¹⁸⁴, 249, F₂, 4, 86) (dual of [(249, 4), 812, 87]-NRT-code)	[i]
6	No linear OOA(2¹⁸⁴, 249, F₂, 5, 86) (dual of [(249, 5), 1061, 87]-NRT-code)	[i]
7	No linear OOA(2¹⁸⁴, 249, F₂, 6, 86) (dual of [(249, 6), 1310, 87]-NRT-code)	[i]
8	No linear OOA(2¹⁸⁴, 249, F₂, 7, 86) (dual of [(249, 7), 1559, 87]-NRT-code)	[i]
9	No linear OOA(2¹⁸⁴, 249, F₂, 8, 86) (dual of [(249, 8), 1808, 87]-NRT-code)	[i]
10	No digital (98, 184, 249)-net over F₂	[i]	Extracting Embedded Orthogonal Array