MinT - Information on Result #599850

Information on Result #599850

There is no digital (22, 158, 266)-net over F₈, because extracting embedded orthogonal array would yield linear OA(8¹⁵⁸, 266, F₈, 136) (dual of [266, 108, 137]-code), but

residual code [i] would yield OA(8²², 129, S₈, 17), but
- 1 times truncation [i] would yield OA(8²¹, 128, S₈, 16), but
  - the linear programming bound shows that MÂ â‰¥ 1 008968 613742 170487 095115 575000 563712 / 108734 057573 457133 > 8²¹ [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 (22, 159, 266)-net over F₈	[i]	m-Reduction
2	No digital (22, 160, 266)-net over F₈	[i]
3	No digital (22, 161, 266)-net over F₈	[i]
4	No digital (22, 162, 266)-net over F₈	[i]
5	No digital (22, 163, 266)-net over F₈	[i]
6	No digital (22, 164, 266)-net over F₈	[i]
7	No digital (22, 165, 266)-net over F₈	[i]