MinT - Information on Result #599846

Information on Result #599846

There is no digital (21, 157, 238)-net over F₈, because extracting embedded orthogonal array would yield linear OA(8¹⁵⁷, 238, F₈, 136) (dual of [238, 81, 137]-code), but

residual code [i] would yield OA(8²¹, 101, S₈, 17), but
- 1 times truncation [i] would yield OA(8²⁰, 100, S₈, 16), but
  - the linear programming bound shows that MÂ â‰¥ 766 916854 670851 025894 998613 688320 / 621 810617 698353 > 8²⁰ [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 (21, 158, 238)-net over F₈	[i]	m-Reduction
2	No digital (21, 159, 238)-net over F₈	[i]
3	No digital (21, 160, 238)-net over F₈	[i]
4	No digital (21, 161, 238)-net over F₈	[i]
5	No digital (21, 162, 238)-net over F₈	[i]
6	No digital (21, 163, 238)-net over F₈	[i]
7	No digital (21, 164, 238)-net over F₈	[i]