MinT - Information on Result #3151995

Information on Result #3151995

There is no digital (20, 172, 170)-net over F₈, because 8 times m-reduction would yield digital (20, 164, 170)-net over F₈, but

extracting embedded orthogonal array [i] would yield 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]

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

None.