MinT - Information on Result #599856

Information on Result #599856

There is no digital (25, 161, 415)-net over F₈, because extracting embedded orthogonal array would yield linear OA(8¹⁶¹, 415, F₈, 136) (dual of [415, 254, 137]-code), but

residual code [i] would yield OA(8²⁵, 278, S₈, 17), but
- 1 times truncation [i] would yield OA(8²⁴, 277, S₈, 16), but
  - the linear programming bound shows that MÂ â‰¥ 78638 403871 838919 782431 803777 157693 440000 / 16 504446 602386 301789 > 8²⁴ [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 (25, 162, 415)-net over F₈	[i]	m-Reduction
2	No digital (25, 163, 415)-net over F₈	[i]
3	No digital (25, 164, 415)-net over F₈	[i]
4	No digital (25, 165, 415)-net over F₈	[i]
5	No digital (25, 166, 415)-net over F₈	[i]
6	No digital (25, 167, 415)-net over F₈	[i]
7	No digital (25, 168, 415)-net over F₈	[i]