MinT - Information on Result #526586

Information on Result #526586

There is no linear OA(16⁷, 945412, F₁₆, 3) (dual of [945412, 945405, 4]-code or 945412-cap in PG(6,16)), because removing affine subspaces would yield

linear OA(16⁵, 3934, F₁₆, 3) (dual of [3934, 3929, 4]-code or 3934-cap in PG(4,16)), but
- bound for caps in PG(4,Â b) [i]
58269-cap in AG(5,16), but
- 2 times the recursive bound from Bierbrauer and Edel [i] would yield 257-cap in AG(3,16), but
  - affine subcap of ovoid is optimal [i]
883211-cap in AG(6,16), but
- 3 times the recursive bound from Bierbrauer and Edel [i] would yield 257-cap in AG(3,16) (see above)

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(16⁷, 945412, F₁₆, 2, 3) (dual of [(945412, 2), 1890817, 4]-NRT-code)	[i]		Depth Reduction
2	No digital (4, 7, 945412)-net over F₁₆	[i]		Extracting Embedded Orthogonal Array