MinT - Information on Result #599843

Information on Result #599843

There is no digital (20, 156, 173)-net over F₈, because extracting embedded orthogonal array would yield linear OA(8¹⁵⁶, 173, F₈, 136) (dual of [173, 17, 137]-code), but

constructionÂ Y1 [i] would yield
1. linear OA(8¹⁵⁵, 161, F₈, 136) (dual of [161, 6, 137]-code), but
  - constructionÂ Y1 [i] would yield
    1. linear OA(8¹⁵⁴, 157, F₈, 136) (dual of [157, 3, 137]-code), but
      - Griesmer bound [i]
    2. OA(8⁶, 161, S₈, 4), but
      - discarding factors would yield OA(8⁶, 104, S₈, 4), but
        the Rao or (dual) Hamming bound shows that MÂ â‰¥ 263173 > 8⁶ [i]
2. OA(8¹⁷, 173, S₈, 12), but
  - discarding factors would yield OA(8¹⁷, 158, S₈, 12), but
    - the Rao or (dual) Hamming bound shows that MÂ â‰¥ 2322 300560 650316 > 8¹⁷ [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 (20, 157, 173)-net over F₈	[i]	m-Reduction
2	No digital (20, 158, 173)-net over F₈	[i]
3	No digital (20, 159, 173)-net over F₈	[i]
4	No digital (20, 160, 173)-net over F₈	[i]
5	No digital (20, 161, 173)-net over F₈	[i]
6	No digital (20, 162, 173)-net over F₈	[i]
7	No digital (20, 163, 173)-net over F₈	[i]