MinT - Information on Result #599777

Information on Result #599777

There is no digital (3, 24, 29)-net over F₇, because extracting embedded orthogonal array would yield linear OA(7²⁴, 29, F₇, 21) (dual of [29, 5, 22]-code), but

constructionÂ Y1 [i] would yield
1. OA(7²³, 25, S₇, 21), but
  - the (dual) Plotkin bound shows that MÂ â‰¥ 383 162462 761132 828802 / 11 > 7²³ [i]
2. OA(7⁵, 29, S₇, 4), but
  - the linear programming bound shows that MÂ â‰¥ 3 384381 / 197 > 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 (3, 25, 29)-net over F₇	[i]	m-Reduction
2	No digital (3, 26, 29)-net over F₇	[i]
3	No digital (3, 27, 29)-net over F₇	[i]
4	No digital (3, 28, 29)-net over F₇	[i]
5	No digital (3, 29, 29)-net over F₇	[i]
6	No digital (3, 30, 29)-net over F₇	[i]
7	No digital (3, 31, 29)-net over F₇	[i]
8	No digital (3, 32, 29)-net over F₇	[i]
9	No digital (3, 33, 29)-net over F₇	[i]
10	No digital (3, 34, 29)-net over F₇	[i]
11	No digital (3, 35, 29)-net over F₇	[i]
12	No digital (3, 36, 29)-net over F₇	[i]
13	No digital (3, 37, 29)-net over F₇	[i]
14	No digital (3, 38, 29)-net over F₇	[i]
15	No digital (3, 39, 29)-net over F₇	[i]
16	No digital (3, 40, 29)-net over F₇	[i]
17	No digital (3, 41, 29)-net over F₇	[i]
18	No digital (3, 42, 29)-net over F₇	[i]
19	No digital (3, 43, 29)-net over F₇	[i]
20	No digital (3, 44, 29)-net over F₇	[i]
21	No digital (3, 45, 29)-net over F₇	[i]
22	No digital (3, 46, 29)-net over F₇	[i]
23	No digital (3, 47, 29)-net over F₇	[i]
24	No digital (3, 48, 29)-net over F₇	[i]
25	No digital (3, 49, 29)-net over F₇	[i]
26	No digital (3, 50, 29)-net over F₇	[i]
27	No digital (3, 51, 29)-net over F₇	[i]
28	No digital (3, 52, 29)-net over F₇	[i]
29	No digital (3, 53, 29)-net over F₇	[i]
30	No digital (3, 54, 29)-net over F₇	[i]
31	No digital (3, 55, 29)-net over F₇	[i]
32	No digital (3, 56, 29)-net over F₇	[i]
33	No digital (3, 57, 29)-net over F₇	[i]
34	No digital (3, 58, 29)-net over F₇	[i]
35	No digital (3, 59, 29)-net over F₇	[i]
36	No digital (3, 60, 29)-net over F₇	[i]
37	No digital (3, 61, 29)-net over F₇	[i]
38	No digital (3, 62, 29)-net over F₇	[i]
39	No digital (3, 63, 29)-net over F₇	[i]
40	No digital (3, 64, 29)-net over F₇	[i]
41	No digital (3, 65, 29)-net over F₇	[i]
42	No digital (3, 66, 29)-net over F₇	[i]
43	No digital (3, 67, 29)-net over F₇	[i]
44	No digital (3, 68, 29)-net over F₇	[i]
45	No digital (3, 69, 29)-net over F₇	[i]
46	No digital (3, 70, 29)-net over F₇	[i]
47	No digital (3, 71, 29)-net over F₇	[i]
48	No digital (3, 72, 29)-net over F₇	[i]
49	No digital (3, 73, 29)-net over F₇	[i]
50	No digital (3, 74, 29)-net over F₇	[i]
51	No digital (3, 75, 29)-net over F₇	[i]
52	No digital (3, 76, 29)-net over F₇	[i]
53	No digital (3, 77, 29)-net over F₇	[i]
54	No digital (3, 78, 29)-net over F₇	[i]
55	No digital (3, 79, 29)-net over F₇	[i]
56	No digital (3, 80, 29)-net over F₇	[i]
57	No digital (3, 81, 29)-net over F₇	[i]
58	No digital (3, 82, 29)-net over F₇	[i]
59	No digital (3, 83, 29)-net over F₇	[i]
60	No digital (3, 84, 29)-net over F₇	[i]
61	No digital (3, 85, 29)-net over F₇	[i]
62	No digital (3, 86, 29)-net over F₇	[i]
63	No digital (3, 87, 29)-net over F₇	[i]
64	No digital (3, 88, 29)-net over F₇	[i]
65	No digital (3, 89, 29)-net over F₇	[i]
66	No digital (3, 90, 29)-net over F₇	[i]
67	No digital (3, 91, 29)-net over F₇	[i]
68	No digital (3, 92, 29)-net over F₇	[i]
69	No digital (3, 93, 29)-net over F₇	[i]
70	No digital (3, 94, 29)-net over F₇	[i]
71	No digital (3, 95, 29)-net over F₇	[i]
72	No digital (3, 96, 29)-net over F₇	[i]
73	No digital (3, 97, 29)-net over F₇	[i]
74	No digital (3, 98, 29)-net over F₇	[i]
75	No digital (3, 99, 29)-net over F₇	[i]
76	No digital (3, 100, 29)-net over F₇	[i]
77	No digital (3, 101, 29)-net over F₇	[i]
78	No digital (3, 102, 29)-net over F₇	[i]
79	No digital (3, 103, 29)-net over F₇	[i]
80	No digital (3, 104, 29)-net over F₇	[i]
81	No digital (3, 105, 29)-net over F₇	[i]
82	No digital (3, 106, 29)-net over F₇	[i]
83	No digital (3, 107, 29)-net over F₇	[i]
84	No digital (3, 108, 29)-net over F₇	[i]
85	No digital (3, 109, 29)-net over F₇	[i]
86	No digital (3, 110, 29)-net over F₇	[i]
87	No digital (3, m, 29)-net over F₇ for arbitrarily large m	[i]	m-Reduction from Arbitrarily Large Net