MinT - Information on Result #599145

Information on Result #599145

There is no digital (64, 193, 203)-net over F₃, because extracting embedded orthogonal array would yield linear OA(3¹⁹³, 203, F₃, 129) (dual of [203, 10, 130]-code), but

constructionÂ Y1 [i] would yield
1. linear OA(3¹⁹², 199, F₃, 129) (dual of [199, 7, 130]-code), but
  - residual code [i] would yield linear OA(3⁶³, 69, F₃, 43) (dual of [69, 6, 44]-code), but
    - â€œMaâ€ bound on codes from Brouwerâ€™s database [i]
2. OA(3¹⁰, 203, S₃, 4), but
  - discarding factors would yield OA(3¹⁰, 172, S₃, 4), but
    - the Rao or (dual) Hamming bound shows that MÂ â‰¥ 59169 > 3¹⁰ [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 (64, 194, 203)-net over F₃	[i]	m-Reduction
2	No digital (64, 195, 203)-net over F₃	[i]
3	No digital (64, 196, 203)-net over F₃	[i]
4	No digital (64, 197, 203)-net over F₃	[i]
5	No digital (64, 198, 203)-net over F₃	[i]
6	No digital (64, 199, 203)-net over F₃	[i]
7	No digital (64, 200, 203)-net over F₃	[i]
8	No digital (64, 201, 203)-net over F₃	[i]
9	No digital (64, 202, 203)-net over F₃	[i]
10	No digital (64, 203, 203)-net over F₃	[i]
11	No digital (64, 204, 203)-net over F₃	[i]
12	No digital (64, 205, 203)-net over F₃	[i]
13	No digital (64, 206, 203)-net over F₃	[i]
14	No digital (64, 207, 203)-net over F₃	[i]
15	No digital (64, 208, 203)-net over F₃	[i]
16	No digital (64, 209, 203)-net over F₃	[i]
17	No digital (64, 210, 203)-net over F₃	[i]
18	No digital (64, 211, 203)-net over F₃	[i]
19	No digital (64, 212, 203)-net over F₃	[i]
20	No digital (64, 213, 203)-net over F₃	[i]
21	No digital (64, 214, 203)-net over F₃	[i]
22	No digital (64, 215, 203)-net over F₃	[i]
23	No digital (64, 216, 203)-net over F₃	[i]
24	No digital (64, 217, 203)-net over F₃	[i]
25	No digital (64, 218, 203)-net over F₃	[i]
26	No digital (64, 219, 203)-net over F₃	[i]
27	No digital (64, 220, 203)-net over F₃	[i]
28	No digital (64, 221, 203)-net over F₃	[i]
29	No digital (64, 222, 203)-net over F₃	[i]
30	No digital (64, 223, 203)-net over F₃	[i]
31	No digital (64, 224, 203)-net over F₃	[i]
32	No digital (64, 225, 203)-net over F₃	[i]
33	No digital (64, 226, 203)-net over F₃	[i]
34	No digital (64, 227, 203)-net over F₃	[i]
35	No digital (64, 228, 203)-net over F₃	[i]
36	No digital (64, 229, 203)-net over F₃	[i]
37	No digital (64, 230, 203)-net over F₃	[i]
38	No digital (64, 231, 203)-net over F₃	[i]
39	No digital (64, 232, 203)-net over F₃	[i]
40	No digital (64, 233, 203)-net over F₃	[i]
41	No digital (64, 234, 203)-net over F₃	[i]
42	No digital (64, 235, 203)-net over F₃	[i]
43	No digital (64, 236, 203)-net over F₃	[i]
44	No digital (64, 237, 203)-net over F₃	[i]
45	No digital (64, 238, 203)-net over F₃	[i]
46	No digital (64, 239, 203)-net over F₃	[i]
47	No digital (64, 240, 203)-net over F₃	[i]
48	No digital (64, 241, 203)-net over F₃	[i]
49	No digital (64, 242, 203)-net over F₃	[i]
50	No digital (64, 243, 203)-net over F₃	[i]
51	No digital (64, 244, 203)-net over F₃	[i]
52	No digital (64, 245, 203)-net over F₃	[i]
53	No digital (64, 246, 203)-net over F₃	[i]
54	No digital (64, 247, 203)-net over F₃	[i]
55	No digital (64, 248, 203)-net over F₃	[i]
56	No digital (64, 249, 203)-net over F₃	[i]
57	No digital (64, 250, 203)-net over F₃	[i]