MinT - Information on Result #599233

Information on Result #599233

There is no digital (76, 229, 239)-net over F₃, because extracting embedded orthogonal array would yield linear OA(3²²⁹, 239, F₃, 153) (dual of [239, 10, 154]-code), but

constructionÂ Y1 [i] would yield
1. linear OA(3²²⁸, 235, F₃, 153) (dual of [235, 7, 154]-code), but
  - residual code [i] would yield linear OA(3⁷⁵, 81, F₃, 51) (dual of [81, 6, 52]-code), but
    - â€œMaâ€ bound on codes from Brouwerâ€™s database [i]
2. OA(3¹⁰, 239, 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 (76, 230, 239)-net over F₃	[i]	m-Reduction
2	No digital (76, 231, 239)-net over F₃	[i]
3	No digital (76, 232, 239)-net over F₃	[i]
4	No digital (76, 233, 239)-net over F₃	[i]
5	No digital (76, 234, 239)-net over F₃	[i]
6	No digital (76, 235, 239)-net over F₃	[i]
7	No digital (76, 236, 239)-net over F₃	[i]
8	No digital (76, 237, 239)-net over F₃	[i]
9	No digital (76, 238, 239)-net over F₃	[i]
10	No digital (76, 239, 239)-net over F₃	[i]
11	No digital (76, 240, 239)-net over F₃	[i]
12	No digital (76, 241, 239)-net over F₃	[i]
13	No digital (76, 242, 239)-net over F₃	[i]
14	No digital (76, 243, 239)-net over F₃	[i]
15	No digital (76, 244, 239)-net over F₃	[i]
16	No digital (76, 245, 239)-net over F₃	[i]
17	No digital (76, 246, 239)-net over F₃	[i]
18	No digital (76, 247, 239)-net over F₃	[i]
19	No digital (76, 248, 239)-net over F₃	[i]
20	No digital (76, 249, 239)-net over F₃	[i]
21	No digital (76, 250, 239)-net over F₃	[i]