MinT - Information on Result #598965

Information on Result #598965

There is no digital (18, 54, 62)-net over F₃, because extracting embedded orthogonal array would yield linear OA(3⁵⁴, 62, F₃, 36) (dual of [62, 8, 37]-code), but

constructionÂ Y1 [i] would yield
1. linear OA(3⁵³, 58, F₃, 36) (dual of [58, 5, 37]-code), but
  - residual code [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, 62, 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 (18, 55, 62)-net over F₃	[i]	m-Reduction
2	No digital (18, 56, 62)-net over F₃	[i]
3	No digital (18, 57, 62)-net over F₃	[i]
4	No digital (18, 58, 62)-net over F₃	[i]
5	No digital (18, 59, 62)-net over F₃	[i]
6	No digital (18, 60, 62)-net over F₃	[i]
7	No digital (18, 61, 62)-net over F₃	[i]
8	No digital (18, 62, 62)-net over F₃	[i]
9	No digital (18, 63, 62)-net over F₃	[i]
10	No digital (18, 64, 62)-net over F₃	[i]
11	No digital (18, 65, 62)-net over F₃	[i]
12	No digital (18, 66, 62)-net over F₃	[i]
13	No digital (18, 67, 62)-net over F₃	[i]
14	No digital (18, 68, 62)-net over F₃	[i]
15	No digital (18, 69, 62)-net over F₃	[i]
16	No digital (18, 70, 62)-net over F₃	[i]
17	No digital (18, 71, 62)-net over F₃	[i]
18	No digital (18, 72, 62)-net over F₃	[i]
19	No digital (18, 73, 62)-net over F₃	[i]
20	No digital (18, 74, 62)-net over F₃	[i]
21	No digital (18, 75, 62)-net over F₃	[i]
22	No digital (18, 76, 62)-net over F₃	[i]
23	No digital (18, 77, 62)-net over F₃	[i]
24	No digital (18, 78, 62)-net over F₃	[i]
25	No digital (18, 79, 62)-net over F₃	[i]
26	No digital (18, 80, 62)-net over F₃	[i]
27	No digital (18, 81, 62)-net over F₃	[i]
28	No digital (18, 82, 62)-net over F₃	[i]
29	No digital (18, 83, 62)-net over F₃	[i]
30	No digital (18, 84, 62)-net over F₃	[i]
31	No digital (18, 85, 62)-net over F₃	[i]
32	No digital (18, 86, 62)-net over F₃	[i]
33	No digital (18, 87, 62)-net over F₃	[i]
34	No digital (18, 88, 62)-net over F₃	[i]
35	No digital (18, 89, 62)-net over F₃	[i]
36	No digital (18, 90, 62)-net over F₃	[i]
37	No digital (18, 91, 62)-net over F₃	[i]
38	No digital (18, 92, 62)-net over F₃	[i]
39	No digital (18, 93, 62)-net over F₃	[i]
40	No digital (18, 94, 62)-net over F₃	[i]
41	No digital (18, 95, 62)-net over F₃	[i]