MinT - Information on Result #1225199

Information on Result #1225199

Digital (70, 90, 104922)-net over F₃₂, using (u,Â u+v)-construction based on

digital (3, 13, 64)-net over F₃₂, using
- net from sequence [i] based on digital (3, 63)-sequence over F₃₂, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 3 and N(F) ≥ 64, using
    - a function field by SÃ©mirat [i]
digital (57, 77, 104858)-net over F₃₂, using
- net defined by OOA [i] based on linear OOA(32⁷⁷, 104858, F₃₂, 20, 20) (dual of [(104858, 20), 2097083, 21]-NRT-code), using
  - OA 10-folding and stacking [i] based on linear OA(32⁷⁷, 1048580, F₃₂, 20) (dual of [1048580, 1048503, 21]-code), using
    - constructionÂ X applied to C_e(19) âŠ‚ C_e(18) [i] based on
      1. linear OA(32⁷⁷, 1048576, F₃₂, 20) (dual of [1048576, 1048499, 21]-code), using an extension C_e(19) of the primitive narrow-sense BCH-code C(I) with length 1048575Â = 32⁴âˆ’1, defining interval IÂ =Â [1,19], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 20 [i]
      2. linear OA(32⁷³, 1048576, F₃₂, 19) (dual of [1048576, 1048503, 20]-code), using an extension C_e(18) of the primitive narrow-sense BCH-code C(I) with length 1048575Â = 32⁴âˆ’1, defining interval IÂ =Â [1,18], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 19 [i]
      3. linear OA(32⁰, 4, F₃₂, 0) (dual of [4, 4, 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]

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

The following results depend on this result:

	Result		This result only	Method
1	Digital (71, 91, 104922)-net over F₃₂	[i]		Net Duplication