MinT - Information on Result #3177406

Information on Result #3177406

Digital (32, 53, 240)-net over F₃₂, using 1 times m-reduction based on digital (32, 54, 240)-net over F₃₂, using

(u,Â u+v)-construction [i] based on
1. digital (10, 21, 205)-net over F₃₂, using
  - net defined by OOA [i] based on linear OOA(32²¹, 205, F₃₂, 11, 11) (dual of [(205, 11), 2234, 12]-NRT-code), using
    - OOA 5-folding and stacking with additional row [i] based on linear OA(32²¹, 1026, F₃₂, 11) (dual of [1026, 1005, 12]-code), using
      - constructionÂ X applied to C_e(10) âŠ‚ C_e(9) [i] based on
        linear OA(32²¹, 1024, F₃₂, 11) (dual of [1024, 1003, 12]-code), using an extension C_e(10) of the primitive narrow-sense BCH-code C(I) with length 1023Â = 32²âˆ’1, defining interval IÂ =Â [1,10], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 11 [i]
        linear OA(32¹⁹, 1024, F₃₂, 10) (dual of [1024, 1005, 11]-code), using an extension C_e(9) of the primitive narrow-sense BCH-code C(I) with length 1023Â = 32²âˆ’1, defining interval IÂ =Â [1,9], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 10 [i]
        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]
2. digital (11, 33, 120)-net over F₃₂, using
  - net from sequence [i] based on digital (11, 119)-sequence over F₃₂, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 11 and N(F) ≥ 120, using
      - a function field by SÃ©mirat [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.