MinT - Best Known (234−78, 234, s)-Nets in Base 3

Best Known (234−78, 234, s)-Nets in Base 3

(234−78, 234, 162)-Net over F₃ — Constructive and digital

Digital (156, 234, 162)-net over F₃, using

14 times m-reduction [i] based on digital (156, 248, 162)-net over F₃, using
- trace code for nets [i] based on digital (32, 124, 81)-net over F₉, using
  - net from sequence [i] based on digital (32, 80)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 32 and N(F) ≥ 81, using
      - F₄ from the tower of function fields by Bezerra and GarcÃa over F₉ [i]

(234−78, 234, 365)-Net over F₃ — Digital

Digital (156, 234, 365)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(234−78, 234, 5573)-Net in Base 3 — Upper bound on s

There is no (156, 234, 5574)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 4439 672932 544136 335482 577265 035684 162427 481584 628851 997145 316224 605443 358728 982537 435419 337950 223775 609493 089241 > 3²³⁴ [i]