MinT - Information on Result #526589

Information on Result #526589

There is no linear OA(32⁶, 1018859, F₃₂, 3) (dual of [1018859, 1018853, 4]-code or 1018859-cap in PG(5,32)), because removing affine subspaces would yield

linear OA(32⁵, 31934, F₃₂, 3) (dual of [31934, 31929, 4]-code or 31934-cap in PG(4,32)), but
- bound for caps in PG(4,Â b) [i]
986926-cap in AG(5,32), but
- 2 times the recursive bound from Bierbrauer and Edel [i] would yield 1025-cap in AG(3,32), 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(32⁶, 1018859, F₃₂, 2, 3) (dual of [(1018859, 2), 2037712, 4]-NRT-code)	[i]		Depth Reduction
2	No digital (3, 6, 1018859)-net over F₃₂	[i]		Extracting Embedded Orthogonal Array