MinT - Information on Result #599781

Information on Result #599781

There is no digital (4, 32, 37)-net over F₇, because extracting embedded orthogonal array would yield linear OA(7³², 37, F₇, 28) (dual of [37, 5, 29]-code), but

constructionÂ Y1 [i] would yield
1. OA(7³¹, 33, S₇, 28), but
  - the (dual) Plotkin bound shows that MÂ â‰¥ 5522 138371 219603 231526 496005 / 29 > 7³¹ [i]
2. OA(7⁵, 37, S₇, 4), but
  - discarding factors would yield OA(7⁵, 31, S₇, 4), but
    - the Rao or (dual) Hamming bound shows that MÂ â‰¥ 16927 > 7⁵ [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 (4, 33, 37)-net over F₇	[i]	m-Reduction
2	No digital (4, 34, 37)-net over F₇	[i]
3	No digital (4, 35, 37)-net over F₇	[i]
4	No digital (4, 36, 37)-net over F₇	[i]
5	No digital (4, 37, 37)-net over F₇	[i]
6	No digital (4, 38, 37)-net over F₇	[i]
7	No digital (4, 39, 37)-net over F₇	[i]
8	No digital (4, 40, 37)-net over F₇	[i]
9	No digital (4, 41, 37)-net over F₇	[i]
10	No digital (4, 42, 37)-net over F₇	[i]
11	No digital (4, 43, 37)-net over F₇	[i]
12	No digital (4, 44, 37)-net over F₇	[i]
13	No digital (4, 45, 37)-net over F₇	[i]
14	No digital (4, 46, 37)-net over F₇	[i]
15	No digital (4, 47, 37)-net over F₇	[i]
16	No digital (4, 48, 37)-net over F₇	[i]
17	No digital (4, 49, 37)-net over F₇	[i]
18	No digital (4, 50, 37)-net over F₇	[i]
19	No digital (4, 51, 37)-net over F₇	[i]
20	No digital (4, 52, 37)-net over F₇	[i]
21	No digital (4, 53, 37)-net over F₇	[i]
22	No digital (4, 54, 37)-net over F₇	[i]
23	No digital (4, 55, 37)-net over F₇	[i]
24	No digital (4, 56, 37)-net over F₇	[i]
25	No digital (4, 57, 37)-net over F₇	[i]
26	No digital (4, 58, 37)-net over F₇	[i]
27	No digital (4, 59, 37)-net over F₇	[i]
28	No digital (4, 60, 37)-net over F₇	[i]
29	No digital (4, 61, 37)-net over F₇	[i]
30	No digital (4, 62, 37)-net over F₇	[i]
31	No digital (4, 63, 37)-net over F₇	[i]
32	No digital (4, 64, 37)-net over F₇	[i]
33	No digital (4, 65, 37)-net over F₇	[i]
34	No digital (4, 66, 37)-net over F₇	[i]
35	No digital (4, 67, 37)-net over F₇	[i]
36	No digital (4, 68, 37)-net over F₇	[i]
37	No digital (4, 69, 37)-net over F₇	[i]
38	No digital (4, 70, 37)-net over F₇	[i]
39	No digital (4, 71, 37)-net over F₇	[i]
40	No digital (4, 72, 37)-net over F₇	[i]
41	No digital (4, 73, 37)-net over F₇	[i]
42	No digital (4, 74, 37)-net over F₇	[i]
43	No digital (4, 75, 37)-net over F₇	[i]
44	No digital (4, 76, 37)-net over F₇	[i]
45	No digital (4, 77, 37)-net over F₇	[i]
46	No digital (4, 78, 37)-net over F₇	[i]
47	No digital (4, 79, 37)-net over F₇	[i]
48	No digital (4, 80, 37)-net over F₇	[i]
49	No digital (4, 81, 37)-net over F₇	[i]
50	No digital (4, 82, 37)-net over F₇	[i]
51	No digital (4, 83, 37)-net over F₇	[i]
52	No digital (4, 84, 37)-net over F₇	[i]
53	No digital (4, 85, 37)-net over F₇	[i]
54	No digital (4, 86, 37)-net over F₇	[i]
55	No digital (4, 87, 37)-net over F₇	[i]
56	No digital (4, 88, 37)-net over F₇	[i]
57	No digital (4, 89, 37)-net over F₇	[i]
58	No digital (4, 90, 37)-net over F₇	[i]
59	No digital (4, 91, 37)-net over F₇	[i]
60	No digital (4, 92, 37)-net over F₇	[i]
61	No digital (4, 93, 37)-net over F₇	[i]
62	No digital (4, 94, 37)-net over F₇	[i]
63	No digital (4, 95, 37)-net over F₇	[i]
64	No digital (4, 96, 37)-net over F₇	[i]
65	No digital (4, 97, 37)-net over F₇	[i]
66	No digital (4, 98, 37)-net over F₇	[i]
67	No digital (4, 99, 37)-net over F₇	[i]
68	No digital (4, 100, 37)-net over F₇	[i]
69	No digital (4, 101, 37)-net over F₇	[i]
70	No digital (4, 102, 37)-net over F₇	[i]
71	No digital (4, 103, 37)-net over F₇	[i]
72	No digital (4, 104, 37)-net over F₇	[i]
73	No digital (4, 105, 37)-net over F₇	[i]
74	No digital (4, 106, 37)-net over F₇	[i]
75	No digital (4, 107, 37)-net over F₇	[i]
76	No digital (4, 108, 37)-net over F₇	[i]
77	No digital (4, 109, 37)-net over F₇	[i]
78	No digital (4, 110, 37)-net over F₇	[i]
79	No digital (4, m, 37)-net over F₇ for arbitrarily large m	[i]	m-Reduction from Arbitrarily Large Net