MinT - Information on Result #548545

Information on Result #548545

There is no linear OA(2¹⁵⁶, 190, F₂, 74) (dual of [190, 34, 75]-code), because constructionÂ Y1 would yield

linear OA(2¹⁵⁵, 178, F₂, 74) (dual of [178, 23, 75]-code), but
- adding a parity check bit [i] would yield linear OA(2¹⁵⁶, 179, F₂, 75) (dual of [179, 23, 76]-code), but
  - â€œBKâ€ bound on codes from Brouwerâ€™s database [i]
OA(2³⁴, 190, 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]

Mode: Bound (linear).

Optimality

Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.

Compare with Markus Grassl’s online database of code parameters.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		This result only	Method
1	No linear OA(2¹⁵⁷, 191, F₂, 75) (dual of [191, 34, 76]-code)	[i]		Truncation
2	No linear OOA(2¹⁵⁷, 190, F₂, 2, 75) (dual of [(190, 2), 223, 76]-NRT-code)	[i]		m-Reduction for OOAs
3	No linear OOA(2¹⁵⁸, 190, F₂, 2, 76) (dual of [(190, 2), 222, 77]-NRT-code)	[i]
4	No linear OOA(2¹⁵⁹, 190, F₂, 2, 77) (dual of [(190, 2), 221, 78]-NRT-code)	[i]
5	No linear OOA(2¹⁵⁶, 190, F₂, 2, 74) (dual of [(190, 2), 224, 75]-NRT-code)	[i]		Depth Reduction
6	No linear OOA(2¹⁵⁶, 190, F₂, 3, 74) (dual of [(190, 3), 414, 75]-NRT-code)	[i]
7	No linear OOA(2¹⁵⁶, 190, F₂, 4, 74) (dual of [(190, 4), 604, 75]-NRT-code)	[i]
8	No linear OOA(2¹⁵⁶, 190, F₂, 5, 74) (dual of [(190, 5), 794, 75]-NRT-code)	[i]
9	No linear OOA(2¹⁵⁶, 190, F₂, 6, 74) (dual of [(190, 6), 984, 75]-NRT-code)	[i]
10	No linear OOA(2¹⁵⁶, 190, F₂, 7, 74) (dual of [(190, 7), 1174, 75]-NRT-code)	[i]
11	No linear OOA(2¹⁵⁶, 190, F₂, 8, 74) (dual of [(190, 8), 1364, 75]-NRT-code)	[i]
12	No digital (82, 156, 190)-net over F₂	[i]		Extracting Embedded Orthogonal Array
13	No linear OA(2¹⁵⁷, 210, F₂, 74) (dual of [210, 53, 75]-code)	[i]		ConstructionÂ Y1 (Bound)