MinT - Information on Result #1771733

Information on Result #1771733

Digital (221, 243, 4194386)-net over F₃, using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(3²⁴³, 4194386, F₃, 2, 22) (dual of [(4194386, 2), 8388529, 23]-NRT-code), using

(u,Â u+v)-construction [i] based on
1. linear OOA(3³², 85, F₃, 2, 11) (dual of [(85, 2), 138, 12]-NRT-code), using
  - embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OA(3³², 85, F₃, 11) (dual of [85, 53, 12]-code), using
    - discarding factors / shortening the dual code based on linear OA(3³², 87, F₃, 11) (dual of [87, 55, 12]-code), using
      - (u,Â u+v)-construction [i] based on
        linear OA(3⁵, 6, F₃, 5) (dual of [6, 1, 6]-code or 6-arc in PG(4,3)), using
        dual of repetition code with length 6 [i]
        linear OA(3²⁷, 81, F₃, 11) (dual of [81, 54, 12]-code), using
        an extension C_e(10) of the primitive narrow-sense BCH-code C(I) with length 80Â = 3⁴âˆ’1, defining interval IÂ =Â [1,10], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 11 [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.