MinT - Information on Result #599840

Information on Result #599840

There is no digital (19, 155, 161)-net over F₈, because extracting embedded orthogonal array would yield linear OA(8¹⁵⁵, 161, F₈, 136) (dual of [161, 6, 137]-code), but

constructionÂ Y1 [i] would yield
1. linear OA(8¹⁵⁴, 157, F₈, 136) (dual of [157, 3, 137]-code), but
  - Griesmer bound [i]
2. OA(8⁶, 161, S₈, 4), but
  - discarding factors would yield OA(8⁶, 104, S₈, 4), but
    - the Rao or (dual) Hamming bound shows that MÂ â‰¥ 263173 > 8⁶ [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		This result only	Method
1	No digital (19, 156, 161)-net over F₈	[i]		m-Reduction
2	No digital (19, 157, 161)-net over F₈	[i]
3	No digital (19, 158, 161)-net over F₈	[i]
4	No digital (19, 159, 161)-net over F₈	[i]
5	No digital (19, 160, 161)-net over F₈	[i]
6	No digital (19, 161, 161)-net over F₈	[i]
7	No digital (19, 162, 161)-net over F₈	[i]
8	No digital (19, 163, 161)-net over F₈	[i]
9	No digital (19, 164, 161)-net over F₈	[i]
10	No digital (19, 165, 161)-net over F₈	[i]
11	No digital (19, 166, 161)-net over F₈	[i]
12	No digital (19, 167, 161)-net over F₈	[i]
13	No digital (19, 168, 161)-net over F₈	[i]
14	No digital (19, 169, 161)-net over F₈	[i]
15	No digital (19, 170, 161)-net over F₈	[i]
16	No digital (19, 171, 161)-net over F₈	[i]
17	No digital (19, 172, 161)-net over F₈	[i]
18	No digital (19, 173, 161)-net over F₈	[i]