MinT - Information on Result #589277

Information on Result #589277

There is no linear OOA(3¹⁷², 179, F₃, 5, 116) (dual of [(179, 5), 723, 117]-NRT-code), because 3 times depth reduction would yield linear OOA(3¹⁷², 179, F₃, 2, 116) (dual of [(179, 2), 186, 117]-NRT-code), but

2 step m-reduction [i] would yield linear OA(3¹⁷⁰, 179, F₃, 114) (dual of [179, 9, 115]-code), but
- constructionÂ Y1 [i] would yield
  1. linear OA(3¹⁶⁹, 175, F₃, 114) (dual of [175, 6, 115]-code), but
    - residual code [i] would yield linear OA(3⁵⁵, 60, F₃, 38) (dual of [60, 5, 39]-code), but
      - 2 times truncation [i] would yield linear OA(3⁵³, 58, F₃, 36) (dual of [58, 5, 37]-code), but
        residual code [i] would yield linear OA(3¹⁷, 21, F₃, 12) (dual of [21, 4, 13]-code), but
        â€œHNâ€ bound on codes from Brouwerâ€™s database [i]
  2. OA(3⁹, 179, S₃, 4), but
    - discarding factors would yield OA(3⁹, 100, S₃, 4), but
      - the Rao or (dual) Hamming bound shows that MÂ â‰¥ 20001 > 3⁹ [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.