MinT - Information on Result #577728

Information on Result #577728

There is no linear OOA(9⁶⁸, 45, F₉, 3, 64) (dual of [(45, 3), 67, 65]-NRT-code), because 1 times depth reduction would yield linear OOA(9⁶⁸, 45, F₉, 2, 64) (dual of [(45, 2), 22, 65]-NRT-code), but

28 step m-reduction [i] would yield linear OA(9⁴⁰, 45, F₉, 36) (dual of [45, 5, 37]-code), but
- constructionÂ Y1 [i] would yield
  1. OA(9³⁹, 41, S₉, 36), but
    - the (dual) Plotkin bound shows that MÂ â‰¥ 739 044147 071729 616580 416051 031916 488005 / 37 > 9³⁹ [i]
  2. OA(9⁵, 45, S₉, 4), but
    - discarding factors would yield OA(9⁵, 44, S₉, 4), but
      - the Rao or (dual) Hamming bound shows that MÂ â‰¥ 60897 > 9⁵ [i]

Mode: Bound (linear).

Optimality

Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.

Other Results with Identical Parameters

None.

Depending Results

None.