MinT - Information on Result #1213423

Information on Result #1213423

Digital (116, 127, 3355460)-net over F₅, using (u,Â u+v)-construction based on

digital (35, 40, 4194301)-net over F₅, using
- net defined by OOA [i] based on linear OOA(5⁴⁰, 4194301, F₅, 5, 5) (dual of [(4194301, 5), 20971465, 6]-NRT-code), using
  - OOA 2-folding and stacking with additional row [i] based on linear OA(5⁴⁰, large, F₅, 5) (dual of [large, large−40, 6]-code), using
    - the primitive narrow-sense BCH-code C(I) with length 9765624Â = 5¹⁰âˆ’1, defining interval IÂ =Â [1,5], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 6 [i]
digital (76, 87, 1677730)-net over F₅, using
- (u,Â u+v)-construction [i] based on
  1. digital (1, 6, 10)-net over F₅, using
    - net from sequence [i] based on digital (1, 9)-sequence over F₅, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₅ with g(F) = 1 and N(F) ≥ 10, using
        an explicitly constructive algebraic function field [i]
  2. digital (70, 81, 1677720)-net over F₅, using
    - net defined by OOA [i] based on linear OOA(5⁸¹, 1677720, F₅, 11, 11) (dual of [(1677720, 11), 18454839, 12]-NRT-code), using
      - OOA 5-folding and stacking with additional row [i] based on linear OA(5⁸¹, 8388601, F₅, 11) (dual of [8388601, 8388520, 12]-code), using
        discarding factors / shortening the dual code based on linear OA(5⁸¹, large, F₅, 11) (dual of [large, large−81, 12]-code), using
        the expurgated narrow-sense BCH-code C(I) with length 9765626Â | 5²⁰âˆ’1, defining interval IÂ =Â [0,5], and minimum distance dÂ â‰¥ |{−5,−4,…,5}|+1Â =Â 12 (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.