MinT - Information on Result #3266008

Information on Result #3266008

Digital (63, 74, 3355440)-net over F₃₂, using 32² times duplication based on digital (61, 72, 3355440)-net over F₃₂, using

(u,Â u+v)-construction [i] based on
1. digital (16, 21, 4194301)-net over F₃₂, using
  - net defined by OOA [i] based on linear OOA(32²¹, 4194301, F₃₂, 5, 5) (dual of [(4194301, 5), 20971484, 6]-NRT-code), using
    - OOA 2-folding and stacking with additional row [i] based on linear OA(32²¹, large, F₃₂, 5) (dual of [large, large−21, 6]-code), using
      - the expurgated narrow-sense BCH-code C(I) with length 33554433Â | 32¹⁰âˆ’1, defining interval IÂ =Â [0,2], and minimum distance dÂ â‰¥ |{−2,−1,0,1,2}|+1Â =Â 6 (BCH-bound) [i]
2. digital (40, 51, 1677720)-net over F₃₂, using
  - net defined by OOA [i] based on linear OOA(32⁵¹, 1677720, F₃₂, 11, 11) (dual of [(1677720, 11), 18454869, 12]-NRT-code), using
    - OOA 5-folding and stacking with additional row [i] based on linear OA(32⁵¹, 8388601, F₃₂, 11) (dual of [8388601, 8388550, 12]-code), using
      - discarding factors / shortening the dual code based on linear OA(32⁵¹, large, F₃₂, 11) (dual of [large, large−51, 12]-code), using
        the expurgated narrow-sense BCH-code C(I) with length 33554433Â | 32¹⁰âˆ’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.