MinT - Information on Result #1178979

Information on Result #1178979

Digital (45, 50, 4194341)-net over F₃, using net defined by OOA based on linear OOA(3⁵⁰, 4194341, F₃, 5, 5) (dual of [(4194341, 5), 20971655, 6]-NRT-code), using

appending kth column [i] based on linear OOA(3⁵⁰, 4194341, F₃, 4, 5) (dual of [(4194341, 4), 16777314, 6]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(3⁴, 40, F₃, 4, 2) (dual of [(40, 4), 156, 3]-NRT-code), using
    - appending 2 arbitrary columns [i] based on linear OOA(3⁴, 40, F₃, 2, 2) (dual of [(40, 2), 76, 3]-NRT-code), using
      - appending kth column [i] based on linear OA(3⁴, 40, F₃, 2) (dual of [40, 36, 3]-code), using
        Hamming code H(4,3) [i]
  2. linear OOA(3⁴⁶, 4194301, F₃, 4, 5) (dual of [(4194301, 4), 16777158, 6]-NRT-code), using
    - OOA 2-folding and stacking with additional row [i] based on linear OA(3⁴⁶, large, F₃, 5) (dual of [large, large−46, 6]-code), using
      - the primitive expurgated narrow-sense BCH-code C(I) with length 14348906Â = 3¹⁵âˆ’1, defining interval IÂ =Â [0,4], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 6 [i]

Mode: Constructive and 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.