MinT - Information on Result #1234806

Information on Result #1234806

Digital (41, 64, 6728)-net over F₂₅₆, using (u,Â u+v)-construction based on

digital (8, 19, 771)-net over F₂₅₆, using
- generalized (u,Â u+v)-construction [i] based on
  1. digital (0, 3, 257)-net over F₂₅₆, using
    - net from sequence [i] based on digital (0, 256)-sequence over F₂₅₆, using
      - generalized Faure sequence [i]
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅₆ with g(F) = 0 and N(F) ≥ 257, using
        the rational function field F₂₅₆(x) [i]
      - Niederreiter sequence [i]
  2. digital (0, 5, 257)-net over F₂₅₆, using
    - net from sequence [i] based on digital (0, 256)-sequence over F₂₅₆ (see above)
  3. digital (0, 11, 257)-net over F₂₅₆, using
    - net from sequence [i] based on digital (0, 256)-sequence over F₂₅₆ (see above)
digital (22, 45, 5957)-net over F₂₅₆, using
- net defined by OOA [i] based on linear OOA(256⁴⁵, 5957, F₂₅₆, 23, 23) (dual of [(5957, 23), 136966, 24]-NRT-code), using
  - OOA 11-folding and stacking with additional row [i] based on linear OA(256⁴⁵, 65528, F₂₅₆, 23) (dual of [65528, 65483, 24]-code), using
    - discarding factors / shortening the dual code based on linear OA(256⁴⁵, 65536, F₂₅₆, 23) (dual of [65536, 65491, 24]-code), using
      - an extension C_e(22) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 256²âˆ’1, defining interval IÂ =Â [1,22], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 23 [i]

Mode: Constructive and linear.

None.

None.