MinT - Information on Result #1227675

Information on Result #1227675

Digital (34, 47, 88755)-net over F₈₁, using (u,Â u+v)-construction based on

digital (4, 10, 182)-net over F₈₁, using
- (u,Â u+v)-construction [i] based on
  1. digital (0, 3, 82)-net over F₈₁, using
    - net from sequence [i] based on digital (0, 81)-sequence over F₈₁, using
      - generalized Faure sequence [i]
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 0 and N(F) ≥ 82, using
        the rational function field F₈₁(x) [i]
      - Niederreiter sequence [i]
  2. digital (1, 7, 100)-net over F₈₁, using
    - net from sequence [i] based on digital (1, 99)-sequence over F₈₁, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 1 and N(F) ≥ 100, using
        a function field by SÃ©mirat [i]
digital (24, 37, 88573)-net over F₈₁, using
- net defined by OOA [i] based on linear OOA(81³⁷, 88573, F₈₁, 13, 13) (dual of [(88573, 13), 1151412, 14]-NRT-code), using
  - OOA 6-folding and stacking with additional row [i] based on linear OA(81³⁷, 531439, F₈₁, 13) (dual of [531439, 531402, 14]-code), using
    - discarding factors / shortening the dual code based on linear OA(81³⁷, 531441, F₈₁, 13) (dual of [531441, 531404, 14]-code), using
      - an extension C_e(12) of the primitive narrow-sense BCH-code C(I) with length 531440Â = 81³âˆ’1, defining interval IÂ =Â [1,12], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 13 [i]

Mode: Constructive and linear.

None.

None.