MinT - Information on Result #599847

Information on Result #599847

There is no digital (21, 165, 182)-net over F₈, because extracting embedded orthogonal array would yield linear OA(8¹⁶⁵, 182, F₈, 144) (dual of [182, 17, 145]-code), but

constructionÂ Y1 [i] would yield
1. linear OA(8¹⁶⁴, 170, F₈, 144) (dual of [170, 6, 145]-code), but
  - constructionÂ Y1 [i] would yield
    1. linear OA(8¹⁶³, 166, F₈, 144) (dual of [166, 3, 145]-code), but
      - Griesmer bound [i]
    2. OA(8⁶, 170, 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, 182, 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 (21, 166, 182)-net over F₈	[i]	m-Reduction
2	No digital (21, 167, 182)-net over F₈	[i]
3	No digital (21, 168, 182)-net over F₈	[i]
4	No digital (21, 169, 182)-net over F₈	[i]
5	No digital (21, 170, 182)-net over F₈	[i]
6	No digital (21, 171, 182)-net over F₈	[i]
7	No digital (21, 172, 182)-net over F₈	[i]