MinT - Information on Result #599910

Information on Result #599910

There is no digital (5, 85, 92)-net over F₁₆, because extracting embedded orthogonal array would yield linear OA(16⁸⁵, 92, F₁₆, 80) (dual of [92, 7, 81]-code), but

constructionÂ Y1 [i] would yield
1. OA(16⁸⁴, 86, S₁₆, 80), but
  - the (dual) Plotkin bound shows that MÂ â‰¥ 4 479489 484355 608421 114884 561136 888556 243290 994469 299069 799978 201927 583742 360321 890761 754986 543214 231552 / 27 > 16⁸⁴ [i]
2. OA(16⁷, 92, S₁₆, 6), but
  - discarding factors would yield OA(16⁷, 80, S₁₆, 6), but
    - the Rao or (dual) Hamming bound shows that MÂ â‰¥ 278 002201 > 16⁷ [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 (5, 86, 92)-net over F₁₆	[i]	m-Reduction
2	No digital (5, 87, 92)-net over F₁₆	[i]
3	No digital (5, 88, 92)-net over F₁₆	[i]
4	No digital (5, 89, 92)-net over F₁₆	[i]
5	No digital (5, 90, 92)-net over F₁₆	[i]
6	No digital (5, 91, 92)-net over F₁₆	[i]
7	No digital (5, 92, 92)-net over F₁₆	[i]
8	No digital (5, 93, 92)-net over F₁₆	[i]
9	No digital (5, 94, 92)-net over F₁₆	[i]
10	No digital (5, 95, 92)-net over F₁₆	[i]
11	No digital (5, 96, 92)-net over F₁₆	[i]
12	No digital (5, 97, 92)-net over F₁₆	[i]
13	No digital (5, 98, 92)-net over F₁₆	[i]
14	No digital (5, 99, 92)-net over F₁₆	[i]
15	No digital (5, 100, 92)-net over F₁₆	[i]
16	No digital (5, 101, 92)-net over F₁₆	[i]
17	No digital (5, 102, 92)-net over F₁₆	[i]
18	No digital (5, 103, 92)-net over F₁₆	[i]
19	No digital (5, 104, 92)-net over F₁₆	[i]
20	No digital (5, 105, 92)-net over F₁₆	[i]
21	No digital (5, 106, 92)-net over F₁₆	[i]
22	No digital (5, 107, 92)-net over F₁₆	[i]
23	No digital (5, 108, 92)-net over F₁₆	[i]
24	No digital (5, 109, 92)-net over F₁₆	[i]
25	No digital (5, 110, 92)-net over F₁₆	[i]
26	No digital (5, 111, 92)-net over F₁₆	[i]
27	No digital (5, 112, 92)-net over F₁₆	[i]
28	No digital (5, 113, 92)-net over F₁₆	[i]
29	No digital (5, 114, 92)-net over F₁₆	[i]
30	No digital (5, 115, 92)-net over F₁₆	[i]
31	No digital (5, 116, 92)-net over F₁₆	[i]
32	No digital (5, 117, 92)-net over F₁₆	[i]
33	No digital (5, 118, 92)-net over F₁₆	[i]
34	No digital (5, 119, 92)-net over F₁₆	[i]
35	No digital (5, 120, 92)-net over F₁₆	[i]
36	No digital (5, 121, 92)-net over F₁₆	[i]
37	No digital (5, 122, 92)-net over F₁₆	[i]
38	No digital (5, 123, 92)-net over F₁₆	[i]
39	No digital (5, 124, 92)-net over F₁₆	[i]
40	No digital (5, 125, 92)-net over F₁₆	[i]
41	No digital (5, 126, 92)-net over F₁₆	[i]
42	No digital (5, 127, 92)-net over F₁₆	[i]
43	No digital (5, 128, 92)-net over F₁₆	[i]
44	No digital (5, 129, 92)-net over F₁₆	[i]
45	No digital (5, 130, 92)-net over F₁₆	[i]
46	No digital (5, m, 92)-net over F₁₆ for arbitrarily large m	[i]	m-Reduction from Arbitrarily Large Net