MinT - Best Known (154, 154+48, s)-Nets in Base 3

Best Known (154, 154+48, s)-Nets in Base 3

(154, 154+48, 464)-Net over F₃ — Constructive and digital

Digital (154, 202, 464)-net over F₃, using

3² times duplication [i] based on digital (152, 200, 464)-net over F₃, using
- trace code for nets [i] based on digital (2, 50, 116)-net over F₈₁, using
  - net from sequence [i] based on digital (2, 115)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 2 and N(F) ≥ 116, using
      - a function field by SÃ©mirat [i]

(154, 154+48, 1053)-Net over F₃ — Digital

Digital (154, 202, 1053)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(154, 154+48, 50804)-Net in Base 3 — Upper bound on s

There is no (154, 202, 50805)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 2 391048 230390 544890 202596 891830 007337 631124 052093 110419 078855 225789 206620 246599 658844 695099 843361 > 3²⁰² [i]