MinT - Information on Result #1229358

Information on Result #1229358

Digital (177, 192, 4793564)-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 (157, 172, 4793484)-net over F₄, using
- trace code for nets [i] based on digital (28, 43, 1198371)-net over F₂₅₆, using
  - net defined by OOA [i] based on linear OOA(256⁴³, 1198371, F₂₅₆, 15, 15) (dual of [(1198371, 15), 17975522, 16]-NRT-code), using
    - OOA 7-folding and stacking with additional row [i] based on linear OA(256⁴³, 8388598, F₂₅₆, 15) (dual of [8388598, 8388555, 16]-code), using
      - discarding factors / shortening the dual code based on linear OA(256⁴³, large, F₂₅₆, 15) (dual of [large, large−43, 16]-code), using
        the primitive expurgated narrow-sense BCH-code C(I) with length 16777215Â = 256³âˆ’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.