MinT - Information on Result #1178978

Information on Result #1178978

Digital (44, 49, 4194314)-net over F₃, using net defined by OOA based on linear OOA(3⁴⁹, 4194314, F₃, 5, 5) (dual of [(4194314, 5), 20971521, 6]-NRT-code), using

appending kth column [i] based on linear OOA(3⁴⁹, 4194314, F₃, 4, 5) (dual of [(4194314, 4), 16777207, 6]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(3³, 13, F₃, 4, 2) (dual of [(13, 4), 49, 3]-NRT-code), using
    - appending 2 arbitrary columns [i] based on linear OOA(3³, 13, F₃, 2, 2) (dual of [(13, 2), 23, 3]-NRT-code), using
      - appending kth column [i] based on linear OA(3³, 13, F₃, 2) (dual of [13, 10, 3]-code), using
        Hamming code H(3,3) [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.