MinT - Information on Result #547976

Information on Result #547976

There is no linear OA(7⁴⁹, 66, F₇, 42) (dual of [66, 17, 43]-code), because constructionÂ Y1 would yield

linear OA(7⁴⁸, 52, F₇, 42) (dual of [52, 4, 43]-code), but
- residual code [i] would yield linear OA(7⁶, 9, F₇, 6) (dual of [9, 3, 7]-code or 9-arc in PG(5,7)), but
  - bound for MDS codes [i]
OA(7¹⁷, 66, S₇, 14), but
- discarding factors would yield OA(7¹⁷, 65, S₇, 14), but
  - the linear programming bound shows that MÂ â‰¥ 64 199960 422464 012484 678956 / 260754 952177 > 7¹⁷ [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 OOA(7⁴⁹, 66, F₇, 2, 42) (dual of [(66, 2), 83, 43]-NRT-code)	[i]		Depth Reduction
2	No linear OOA(7⁴⁹, 66, F₇, 3, 42) (dual of [(66, 3), 149, 43]-NRT-code)	[i]		Depth Reduction
3	No digital (7, 49, 66)-net over F₇	[i]		Extracting Embedded Orthogonal Array