MinT - Information on Result #599854

Information on Result #599854

There is no digital (24, 160, 353)-net over F₈, because extracting embedded orthogonal array would yield linear OA(8¹⁶⁰, 353, F₈, 136) (dual of [353, 193, 137]-code), but

residual code [i] would yield OA(8²⁴, 216, S₈, 17), but
- 1 times truncation [i] would yield OA(8²³, 215, S₈, 16), but
  - the linear programming bound shows that MÂ â‰¥ 9069 643604 547071 244335 560849 505648 640000 / 15 008917 595182 591313 > 8²³ [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 (24, 161, 353)-net over F₈	[i]	m-Reduction
2	No digital (24, 162, 353)-net over F₈	[i]
3	No digital (24, 163, 353)-net over F₈	[i]
4	No digital (24, 164, 353)-net over F₈	[i]
5	No digital (24, 165, 353)-net over F₈	[i]
6	No digital (24, 166, 353)-net over F₈	[i]
7	No digital (24, 167, 353)-net over F₈	[i]