MinT - Information on Result #584821

Information on Result #584821

There is no linear OOA(3²⁴⁴, 239, F₃, 4, 168) (dual of [(239, 4), 712, 169]-NRT-code), because 2 times depth reduction would yield linear OOA(3²⁴⁴, 239, F₃, 2, 168) (dual of [(239, 2), 234, 169]-NRT-code), but

15 step m-reduction [i] would yield linear OA(3²²⁹, 239, F₃, 153) (dual of [239, 10, 154]-code), but
- constructionÂ Y1 [i] would yield
  1. linear OA(3²²⁸, 235, F₃, 153) (dual of [235, 7, 154]-code), but
    - residual code [i] would yield linear OA(3⁷⁵, 81, F₃, 51) (dual of [81, 6, 52]-code), but
      - â€œMaâ€ bound on codes from Brouwerâ€™s database [i]
  2. OA(3¹⁰, 239, S₃, 4), but
    - discarding factors would yield OA(3¹⁰, 172, S₃, 4), but
      - the Rao or (dual) Hamming bound shows that MÂ â‰¥ 59169 > 3¹⁰ [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.