MinT - Information on Result #587475

Information on Result #587475

There is no linear OOA(3¹⁴, 30, F₃, 5, 9) (dual of [(30, 5), 136, 10]-NRT-code), because 4 times depth reduction would yield linear OA(3¹⁴, 30, F₃, 9) (dual of [30, 16, 10]-code), but

constructionÂ Y1 [i] would yield
1. linear OA(3¹³, 19, F₃, 9) (dual of [19, 6, 10]-code), but
  - constructionÂ Y1 [i] would yield
    1. linear OA(3¹², 15, F₃, 9) (dual of [15, 3, 10]-code), but
      - Griesmer bound [i]
    2. OA(3⁶, 19, S₃, 4), but
      - the linear programming bound shows that MÂ â‰¥ 51975 / 67 > 3⁶ [i]
2. linear OA(3¹⁶, 30, F₃, 11) (dual of [30, 14, 12]-code), but
  - discarding factors / shortening the dual code would yield linear OA(3¹⁶, 24, F₃, 11) (dual of [24, 8, 12]-code), but
    - â€œBSâ€ bound on codes from Brouwerâ€™s database [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.