MinT - Information on Result #1718258

Information on Result #1718258

Digital (139, 156, 1398104)-net over F₄, using net defined by OOA based on linear OOA(4¹⁵⁶, 1398104, F₄, 21, 17) (dual of [(1398104, 21), 29360028, 18]-NRT-code), using

OOA 3-folding and stacking with additional row [i] based on linear OOA(4¹⁵⁶, 4194313, F₄, 3, 17) (dual of [(4194313, 3), 12582783, 18]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(4¹⁵⁶, 4194315, F₄, 3, 17) (dual of [(4194315, 3), 12582789, 18]-NRT-code), using
  - embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OOA(4¹⁵⁶, 4194315, F₄, 2, 17) (dual of [(4194315, 2), 8388474, 18]-NRT-code), using
    - (u,Â u+v)-construction [i] based on
      1. linear OOA(4¹¹, 14, F₄, 2, 8) (dual of [(14, 2), 17, 9]-NRT-code), using
        extended algebraic-geometric NRT-code AG_e(2;F,19P) [i] based on function field F/F₄ with g(F) = 3 and N(F) ≥ 14, using
        an explicitly constructive algebraic function field [i]
      2. linear OOA(4¹⁴⁵, 4194301, F₄, 2, 17) (dual of [(4194301, 2), 8388457, 18]-NRT-code), using
        OOA 2-folding [i] based on linear OA(4¹⁴⁵, 8388602, F₄, 17) (dual of [8388602, 8388457, 18]-code), using
        discarding factors / shortening the dual code based on linear OA(4¹⁴⁵, large, F₄, 17) (dual of [large, large−145, 18]-code), using
        the expurgated narrow-sense BCH-code C(I) with length 16777217Â | 4²⁴âˆ’1, defining interval IÂ =Â [0,8], and minimum distance dÂ â‰¥ |{−8,−7,…,8}|+1Â =Â 18 (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.