MinT - Information on Result #1188838

Information on Result #1188838

Digital (103, 116, 1398133)-net over F₅, using net defined by OOA based on linear OOA(5¹¹⁶, 1398133, F₅, 15, 13) (dual of [(1398133, 15), 20971879, 14]-NRT-code), using

OOA 2-folding and stacking with additional row [i] based on linear OOA(5¹¹⁶, 2796267, F₅, 3, 13) (dual of [(2796267, 3), 8388685, 14]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(5¹⁵, 66, F₅, 3, 6) (dual of [(66, 3), 183, 7]-NRT-code), using
    - (u,Â u+v)-construction [i] based on
      1. linear OOA(5⁵, 66, F₅, 3, 3) (dual of [(66, 3), 193, 4]-NRT-code), using
        appending kth column [i] based on linear OOA(5⁵, 66, F₅, 2, 3) (dual of [(66, 2), 127, 4]-NRT-code), using
        OAs with strength 3, bÂ â‰ Â 2, and mÂ >Â 3 are always embeddable [i] based on linear OA(5⁵, 66, F₅, 3) (dual of [66, 61, 4]-code or 66-cap in PG(4,5)), using
        caps completed using a computer search [i]
      2. linear OOA(5¹⁰, 33, F₅, 3, 6) (dual of [(33, 3), 89, 7]-NRT-code), using
        extracting embedded OOA [i] based on digital (4, 10, 33)-net over F₅, using
        linear code embedding found in a computer search [i]
  2. linear OOA(5¹⁰¹, 2796201, F₅, 3, 13) (dual of [(2796201, 3), 8388502, 14]-NRT-code), using
    - OOA 3-folding [i] based on linear OA(5¹⁰¹, large, F₅, 13) (dual of [large, large−101, 14]-code), using
      - the expurgated narrow-sense BCH-code C(I) with length 9765626Â | 5²⁰âˆ’1, defining interval IÂ =Â [0,6], and minimum distance dÂ â‰¥ |{−6,−5,…,6}|+1Â =Â 14 (BCH-bound) [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.