MinT - Information on Result #526588

Information on Result #526588

There is no linear OA(27⁶, 513972, F₂₇, 3) (dual of [513972, 513966, 4]-code or 513972-cap in PG(5,27)), because removing affine subspaces would yield

linear OA(27⁵, 19157, F₂₇, 3) (dual of [19157, 19152, 4]-code or 19157-cap in PG(4,27)), but
- bound for caps in PG(4,Â b) [i]
494816-cap in AG(5,27), but
- 2 times the recursive bound from Bierbrauer and Edel [i] would yield 730-cap in AG(3,27), but
  - affine subcap of ovoid is optimal [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.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		This result only	Method
1	No linear OOA(27⁶, 513972, F₂₇, 2, 3) (dual of [(513972, 2), 1027938, 4]-NRT-code)	[i]		Depth Reduction
2	No digital (3, 6, 513972)-net over F₂₇	[i]		Extracting Embedded Orthogonal Array