MinT - Information on Result #1229356

Information on Result #1229356

Digital (138, 153, 1198451)-net over F₄, using (u,Â u+v)-construction based on

digital (13, 20, 80)-net over F₄, using
- generalized (u,Â u+v)-construction [i] based on
  1. digital (0, 1, 20)-net over F₄, using
    - s-reduction based on digital (0, 1, s)-net over F₄ for arbitrarily large s, using
      - construction for strength kÂ =Â 1 [i]
  2. digital (1, 3, 20)-net over F₄, using
    - s-reduction based on digital (1, 3, 21)-net over F₄, using
      - kÂ =Â 2 construction [i]
  3. digital (2, 5, 20)-net over F₄, using
    - s-reduction based on digital (2, 5, 41)-net over F₄, using
      - net defined by OOA [i] based on linear OOA(4⁵, 41, F₄, 3, 3) (dual of [(41, 3), 118, 4]-NRT-code), using
        appending kth column [i] based on linear OOA(4⁵, 41, F₄, 2, 3) (dual of [(41, 2), 77, 4]-NRT-code), using
        OAs with strength 3, bÂ â‰ Â 2, and mÂ >Â 3 are always embeddable [i] based on linear OA(4⁵, 41, F₄, 3) (dual of [41, 36, 4]-code or 41-cap in PG(4,4)), using
        a cap found by Tallinii [i]
  4. digital (4, 11, 20)-net over F₄, using
    - linear code embedding found in a computer search [i]
digital (118, 133, 1198371)-net over F₄, using
- net defined by OOA [i] based on linear OOA(4¹³³, 1198371, F₄, 15, 15) (dual of [(1198371, 15), 17975432, 16]-NRT-code), using
  - OOA 7-folding and stacking with additional row [i] based on linear OA(4¹³³, 8388598, F₄, 15) (dual of [8388598, 8388465, 16]-code), using
    - discarding factors / shortening the dual code based on linear OA(4¹³³, large, F₄, 15) (dual of [large, large−133, 16]-code), using
      - the primitive expurgated narrow-sense BCH-code C(I) with length 16777215Â = 4¹²âˆ’1, defining interval IÂ =Â [0,14], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 16 [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.