MinT - Best Known (109, 109+48, s)-Nets in Base 3

Best Known (109, 109+48, s)-Nets in Base 3

(109, 109+48, 192)-Net over F₃ — Constructive and digital

Digital (109, 157, 192)-net over F₃, using

3¹ times duplication [i] based on digital (108, 156, 192)-net over F₃, using
- trace code for nets [i] based on digital (4, 52, 64)-net over F₂₇, using
  - net from sequence [i] based on digital (4, 63)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 4 and N(F) ≥ 64, using
      - a function field by SÃ©mirat [i]

(109, 109+48, 339)-Net over F₃ — Digital

Digital (109, 157, 339)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(109, 109+48, 6455)-Net in Base 3 — Upper bound on s

There is no (109, 157, 6456)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 810 873044 445355 197967 505805 100091 135879 839484 424623 002381 134467 120147 922177 > 3¹⁵⁷ [i]