MinT - Information on Result #1771933

Information on Result #1771933

Digital (223, 245, 4194411)-net over F₃, using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(3²⁴⁵, 4194411, F₃, 2, 22) (dual of [(4194411, 2), 8388577, 23]-NRT-code), using

(u,Â u+v)-construction [i] based on
1. linear OOA(3³⁴, 110, F₃, 2, 11) (dual of [(110, 2), 186, 12]-NRT-code), using
  - embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OA(3³⁴, 110, F₃, 11) (dual of [110, 76, 12]-code), using
    - discarding factors / shortening the dual code based on linear OA(3³⁴, 115, F₃, 11) (dual of [115, 81, 12]-code), using
      - constructionÂ X with VarÅ¡amov bound [i] based on
        linear OA(3³³, 113, F₃, 11) (dual of [113, 80, 12]-code), using
        a â€œBZâ€ code from Brouwerâ€™s database [i]
        linear OA(3³³, 114, F₃, 10) (dual of [114, 81, 11]-code), using Gilbertâ€“VarÅ¡amov bound and b^mÂ = 3³³Â > V_b^sâˆ’1(kâˆ’1)Â = 3192 777628 940355 [i]
        linear OA(3⁰, 1, F₃, 0) (dual of [1, 1, 1]-code), using
        discarding factors / shortening the dual code based on linear OA(3⁰, s, F₃, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
        OA with only one run / dual of code without redundancy [i]
2. linear OOA(3²¹¹, 4194301, F₃, 2, 22) (dual of [(4194301, 2), 8388391, 23]-NRT-code), using
  - OOA 2-folding [i] based on linear OA(3²¹¹, 8388602, F₃, 22) (dual of [8388602, 8388391, 23]-code), using
    - discarding factors / shortening the dual code based on linear OA(3²¹¹, large, F₃, 22) (dual of [large, large−211, 23]-code), using
      - the primitive expurgated narrow-sense BCH-code C(I) with length 14348906Â = 3¹⁵âˆ’1, defining interval IÂ =Â [0,21], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 23 [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.