MinT - Information on Result #599904

Information on Result #599904

There is no digital (3, 51, 68)-net over F₁₆, because extracting embedded orthogonal array would yield linear OA(16⁵¹, 68, F₁₆, 48) (dual of [68, 17, 49]-code), but

residual code [i] would yield OA(16³, 19, S₁₆, 3), but
- 1 times truncation [i] would yield OA(16², 18, S₁₆, 2), but
  - bound for OAs with strength kÂ =Â 2 [i]
  - the Rao or (dual) Hamming bound shows that MÂ â‰¥ 271 > 16² [i]

Mode: Bound (linear).

Optimality

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

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		Method
1	No digital (3, 52, 68)-net over F₁₆	[i]	m-Reduction
2	No digital (3, 53, 68)-net over F₁₆	[i]
3	No digital (3, 54, 68)-net over F₁₆	[i]
4	No digital (3, 55, 68)-net over F₁₆	[i]
5	No digital (3, 56, 68)-net over F₁₆	[i]
6	No digital (3, 57, 68)-net over F₁₆	[i]
7	No digital (3, 58, 68)-net over F₁₆	[i]
8	No digital (3, 59, 68)-net over F₁₆	[i]
9	No digital (3, 60, 68)-net over F₁₆	[i]