MinT - Information on Result #1224659

Information on Result #1224659

Digital (33, 43, 209760)-net over F₃₂, using (u,Â u+v)-construction based on

digital (1, 6, 44)-net over F₃₂, using
- net from sequence [i] based on digital (1, 43)-sequence over F₃₂, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 1 and N(F) ≥ 44, using
    - a function field by SÃ©mirat [i]
digital (27, 37, 209716)-net over F₃₂, using
- net defined by OOA [i] based on linear OOA(32³⁷, 209716, F₃₂, 10, 10) (dual of [(209716, 10), 2097123, 11]-NRT-code), using
  - OA 5-folding and stacking [i] based on linear OA(32³⁷, 1048580, F₃₂, 10) (dual of [1048580, 1048543, 11]-code), using
    - constructionÂ X applied to C_e(9) âŠ‚ C_e(8) [i] based on
      1. linear OA(32³⁷, 1048576, F₃₂, 10) (dual of [1048576, 1048539, 11]-code), using an extension C_e(9) of the primitive narrow-sense BCH-code C(I) with length 1048575Â = 32⁴âˆ’1, defining interval IÂ =Â [1,9], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 10 [i]
      2. linear OA(32³³, 1048576, F₃₂, 9) (dual of [1048576, 1048543, 10]-code), using an extension C_e(8) of the primitive narrow-sense BCH-code C(I) with length 1048575Â = 32⁴âˆ’1, defining interval IÂ =Â [1,8], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 9 [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 (72, 82, 6712320)-net over F₃₂	[i]		Generalized (u,Â u+v)-Construction for Nets