MinT - Best Known (109−32, 109, s)-Nets in Base 3

Best Known (109−32, 109, s)-Nets in Base 3

(109−32, 109, 192)-Net over F₃ — Constructive and digital

Digital (77, 109, 192)-net over F₃, using

3¹ times duplication [i] based on digital (76, 108, 192)-net over F₃, using
- trace code for nets [i] based on digital (4, 36, 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]

(109−32, 109, 291)-Net over F₃ — Digital

Digital (77, 109, 291)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(109−32, 109, 6036)-Net in Base 3 — Upper bound on s

There is no (77, 109, 6037)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 10157 762299 049198 483407 504953 398818 620131 846915 501505 > 3¹⁰⁹ [i]