MinT - Information on Result #598968

Information on Result #598968

There is no digital (19, 58, 66)-net over F₃, because extracting embedded orthogonal array would yield linear OA(3⁵⁸, 66, F₃, 39) (dual of [66, 8, 40]-code), but

constructionÂ Y1 [i] would yield
1. linear OA(3⁵⁷, 62, F₃, 39) (dual of [62, 5, 40]-code), but
  - residual code [i] would yield linear OA(3¹⁸, 22, F₃, 13) (dual of [22, 4, 14]-code), but
    - 1 times truncation [i] would yield linear OA(3¹⁷, 21, F₃, 12) (dual of [21, 4, 13]-code), but
      - â€œHNâ€ bound on codes from Brouwerâ€™s database [i]
2. OA(3⁸, 66, S₃, 4), but
  - discarding factors would yield OA(3⁸, 58, S₃, 4), but
    - the Rao or (dual) Hamming bound shows that MÂ â‰¥ 6729 > 3⁸ [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 (19, 59, 66)-net over F₃	[i]	m-Reduction
2	No digital (19, 60, 66)-net over F₃	[i]
3	No digital (19, 61, 66)-net over F₃	[i]
4	No digital (19, 62, 66)-net over F₃	[i]
5	No digital (19, 63, 66)-net over F₃	[i]
6	No digital (19, 64, 66)-net over F₃	[i]
7	No digital (19, 65, 66)-net over F₃	[i]
8	No digital (19, 66, 66)-net over F₃	[i]
9	No digital (19, 67, 66)-net over F₃	[i]
10	No digital (19, 68, 66)-net over F₃	[i]
11	No digital (19, 69, 66)-net over F₃	[i]
12	No digital (19, 70, 66)-net over F₃	[i]
13	No digital (19, 71, 66)-net over F₃	[i]
14	No digital (19, 72, 66)-net over F₃	[i]
15	No digital (19, 73, 66)-net over F₃	[i]
16	No digital (19, 74, 66)-net over F₃	[i]
17	No digital (19, 75, 66)-net over F₃	[i]
18	No digital (19, 76, 66)-net over F₃	[i]
19	No digital (19, 77, 66)-net over F₃	[i]
20	No digital (19, 78, 66)-net over F₃	[i]
21	No digital (19, 79, 66)-net over F₃	[i]
22	No digital (19, 80, 66)-net over F₃	[i]
23	No digital (19, 81, 66)-net over F₃	[i]
24	No digital (19, 82, 66)-net over F₃	[i]
25	No digital (19, 83, 66)-net over F₃	[i]
26	No digital (19, 84, 66)-net over F₃	[i]
27	No digital (19, 85, 66)-net over F₃	[i]
28	No digital (19, 86, 66)-net over F₃	[i]
29	No digital (19, 87, 66)-net over F₃	[i]
30	No digital (19, 88, 66)-net over F₃	[i]
31	No digital (19, 89, 66)-net over F₃	[i]
32	No digital (19, 90, 66)-net over F₃	[i]
33	No digital (19, 91, 66)-net over F₃	[i]
34	No digital (19, 92, 66)-net over F₃	[i]
35	No digital (19, 93, 66)-net over F₃	[i]
36	No digital (19, 94, 66)-net over F₃	[i]
37	No digital (19, 95, 66)-net over F₃	[i]
38	No digital (19, 96, 66)-net over F₃	[i]
39	No digital (19, 97, 66)-net over F₃	[i]
40	No digital (19, 98, 66)-net over F₃	[i]
41	No digital (19, 99, 66)-net over F₃	[i]