MinT - Information on Result #1224944

Information on Result #1224944

Digital (40, 55, 4769)-net over F₃₂, using (u,Â u+v)-construction based on

digital (5, 12, 88)-net over F₃₂, using
- (u,Â u+v)-construction [i] based on
  1. digital (1, 4, 1025)-net over F₃₂, using
    - net defined by OOA [i] based on linear OOA(32⁴, 1025, F₃₂, 3, 3) (dual of [(1025, 3), 3071, 4]-NRT-code), using
      - appending kth column [i] based on linear OOA(32⁴, 1025, F₃₂, 2, 3) (dual of [(1025, 2), 2046, 4]-NRT-code), using
        OAs with strength 3, bÂ â‰ Â 2, and mÂ >Â 3 are always embeddable [i] based on linear OA(32⁴, 1025, F₃₂, 3) (dual of [1025, 1021, 4]-code or 1025-cap in PG(3,32)), using
        ovoid in PG(3,Â 32) [i]
  2. digital (1, 8, 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 (28, 43, 4681)-net over F₃₂, using
- net defined by OOA [i] based on linear OOA(32⁴³, 4681, F₃₂, 15, 15) (dual of [(4681, 15), 70172, 16]-NRT-code), using
  - OOA 7-folding and stacking with additional row [i] based on linear OA(32⁴³, 32768, F₃₂, 15) (dual of [32768, 32725, 16]-code), using
    - an extension C_e(14) of the primitive narrow-sense BCH-code C(I) with length 32767Â = 32³âˆ’1, defining interval IÂ =Â [1,14], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 15 [i]

Mode: Constructive and linear.

None.

None.