MinT - Information on Result #1224621

Information on Result #1224621

Digital (31, 40, 262657)-net over F₃₂, using (u,Â u+v)-construction based on

digital (3, 7, 513)-net over F₃₂, using
- net defined by OOA [i] based on linear OOA(32⁷, 513, F₃₂, 4, 4) (dual of [(513, 4), 2045, 5]-NRT-code), using
  - OA 2-folding and stacking [i] based on linear OA(32⁷, 1026, F₃₂, 4) (dual of [1026, 1019, 5]-code), using
    - constructionÂ X applied to C_e(3) âŠ‚ C_e(2) [i] based on
      1. linear OA(32⁷, 1024, F₃₂, 4) (dual of [1024, 1017, 5]-code), using an extension C_e(3) of the primitive narrow-sense BCH-code C(I) with length 1023Â = 32²âˆ’1, defining interval IÂ =Â [1,3], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 4 [i]
      2. linear OA(32⁵, 1024, F₃₂, 3) (dual of [1024, 1019, 4]-code or 1024-cap in PG(4,32)), using an extension C_e(2) of the primitive narrow-sense BCH-code C(I) with length 1023Â = 32²âˆ’1, defining interval IÂ =Â [1,2], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 3 [i]
      3. linear OA(32⁰, 2, F₃₂, 0) (dual of [2, 2, 1]-code), using
        discarding factors / shortening the dual code based on linear OA(32⁰, s, F₃₂, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
        OA with only one run / dual of code without redundancy [i]
digital (24, 33, 262144)-net over F₃₂, using
- net defined by OOA [i] based on linear OOA(32³³, 262144, F₃₂, 9, 9) (dual of [(262144, 9), 2359263, 10]-NRT-code), using
  - OOA 4-folding and stacking with additional row [i] based on linear OA(32³³, 1048577, F₃₂, 9) (dual of [1048577, 1048544, 10]-code), using
    - the expurgated narrow-sense BCH-code C(I) with length 1048577Â | 32⁸âˆ’1, defining interval IÂ =Â [0,4], and minimum distance dÂ â‰¥ |{−4,−3,…,4}|+1Â =Â 10 (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.