MinT - Information on Result #1224788

Information on Result #1224788

Digital (54, 66, 1398177)-net over F₃₂, using (u,Â u+v)-construction based on

digital (4, 10, 77)-net over F₃₂, using
- (u,Â u+v)-construction [i] based on
  1. digital (0, 3, 33)-net over F₃₂, using
    - net from sequence [i] based on digital (0, 32)-sequence over F₃₂, using
      - generalized Faure sequence [i]
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 0 and N(F) ≥ 33, using
        the rational function field F₃₂(x) [i]
      - Niederreiter sequence [i]
  2. digital (1, 7, 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 (44, 56, 1398100)-net over F₃₂, using
- net defined by OOA [i] based on linear OOA(32⁵⁶, 1398100, F₃₂, 12, 12) (dual of [(1398100, 12), 16777144, 13]-NRT-code), using
  - OA 6-folding and stacking [i] based on linear OA(32⁵⁶, 8388600, F₃₂, 12) (dual of [8388600, 8388544, 13]-code), using
    - discarding factors / shortening the dual code based on linear OA(32⁵⁶, large, F₃₂, 12) (dual of [large, large−56, 13]-code), using
      - the primitive expurgated narrow-sense BCH-code C(I) with length 33554431Â = 32⁵âˆ’1, defining interval IÂ =Â [0,11], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 13 [i]

Mode: Constructive and linear.

None.

The following results depend on this result:

	Result		This result only	Method
1	Digital (80, 92, 2796354)-net over F₃₂	[i]		(u,Â u+v)-Construction for Nets