MinT - Information on Result #598907

Information on Result #598907

There is no digital (135, 245, 332)-net over F₂, because extracting embedded orthogonal array would yield linear OA(2²⁴⁵, 332, F₂, 110) (dual of [332, 87, 111]-code), but

constructionÂ Y1 [i] would yield
1. OA(2²⁴⁴, 300, S₂, 110), but
  - the linear programming bound shows that MÂ â‰¥ 727209 932038 995964 963694 786156 506719 769259 430085 807852 102717 045283 079365 167115 254635 995296 956416 / 21378 491075 472167 578125 > 2²⁴⁴ [i]
2. OA(2⁸⁷, 332, S₂, 32), but
  - discarding factors would yield OA(2⁸⁷, 302, S₂, 32), but
    - the Rao or (dual) Hamming bound shows that MÂ â‰¥ 161 699122 225452 699910 750634 > 2⁸⁷ [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 (135, 246, 332)-net over F₂	[i]	m-Reduction
2	No digital (135, 247, 332)-net over F₂	[i]
3	No digital (135, 248, 332)-net over F₂	[i]
4	No digital (135, 249, 332)-net over F₂	[i]
5	No digital (135, 250, 332)-net over F₂	[i]
6	No digital (135, 251, 332)-net over F₂	[i]
7	No digital (135, 252, 332)-net over F₂	[i]
8	No digital (135, 253, 332)-net over F₂	[i]
9	No digital (135, 254, 332)-net over F₂	[i]
10	No digital (135, 255, 332)-net over F₂	[i]
11	No digital (135, 256, 332)-net over F₂	[i]
12	No digital (135, 257, 332)-net over F₂	[i]
13	No digital (135, 258, 332)-net over F₂	[i]
14	No digital (135, 259, 332)-net over F₂	[i]
15	No digital (135, 260, 332)-net over F₂	[i]