MinT - Best Known (70, 70+30, s)-Nets in Base 3

Best Known (70, 70+30, s)-Nets in Base 3

(70, 70+30, 156)-Net over F₃ — Constructive and digital

Digital (70, 100, 156)-net over F₃, using

3¹ times duplication [i] based on digital (69, 99, 156)-net over F₃, using
- trace code for nets [i] based on digital (3, 33, 52)-net over F₂₇, using
  - net from sequence [i] based on digital (3, 51)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 3 and N(F) ≥ 52, using
      - a function field by SÃ©mirat [i]

(70, 70+30, 253)-Net over F₃ — Digital

Digital (70, 100, 253)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(70, 70+30, 4855)-Net in Base 3 — Upper bound on s

There is no (70, 100, 4856)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 515857 071177 894655 814626 968096 826795 226189 159841 > 3¹⁰⁰ [i]