MinT - Information on Result #1713170

Information on Result #1713170

Digital (123, 136, 2097174)-net over F₃, using net defined by OOA based on linear OOA(3¹³⁶, 2097174, F₃, 15, 13) (dual of [(2097174, 15), 31457474, 14]-NRT-code), using

OOA 2-folding and stacking with additional row [i] based on linear OOA(3¹³⁶, 4194349, F₃, 3, 13) (dual of [(4194349, 3), 12582911, 14]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3¹³⁶, 4194350, F₃, 3, 13) (dual of [(4194350, 3), 12582914, 14]-NRT-code), using
  - embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OOA(3¹³⁶, 4194350, F₃, 2, 13) (dual of [(4194350, 2), 8388564, 14]-NRT-code), using
    - (u,Â u+v)-construction [i] based on
      1. linear OOA(3¹⁵, 49, F₃, 2, 6) (dual of [(49, 2), 83, 7]-NRT-code), using
        embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OA(3¹⁵, 49, F₃, 6) (dual of [49, 34, 7]-code), using
        discarding factors / shortening the dual code based on linear OA(3¹⁵, 85, F₃, 6) (dual of [85, 70, 7]-code), using
        codes constructed by inverting constructionÂ Y₁ [i]
      2. linear OOA(3¹²¹, 4194301, F₃, 2, 13) (dual of [(4194301, 2), 8388481, 14]-NRT-code), using
        OOA 2-folding [i] based on linear OA(3¹²¹, 8388602, F₃, 13) (dual of [8388602, 8388481, 14]-code), using
        discarding factors / shortening the dual code based on linear OA(3¹²¹, large, F₃, 13) (dual of [large, large−121, 14]-code), using
        the expurgated narrow-sense BCH-code C(I) with length 14348908Â | 3³⁰âˆ’1, defining interval IÂ =Â [0,6], and minimum distance dÂ â‰¥ |{−6,−5,…,6}|+1Â =Â 14 (BCH-bound) [i]

Mode: 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.