MinT - Best Known (69, 69+60, s)-Nets in Base 3

Best Known (69, 69+60, s)-Nets in Base 3

(69, 69+60, 60)-Net over F₃ — Constructive and digital

Digital (69, 129, 60)-net over F₃, using

1 times m-reduction [i] based on digital (69, 130, 60)-net over F₃, using
- trace code for nets [i] based on digital (4, 65, 30)-net over F₉, using
  - net from sequence [i] based on digital (4, 29)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 4 and N(F) ≥ 30, using
      - a function field by SÃ©mirat [i]

(69, 69+60, 85)-Net over F₃ — Digital

Digital (69, 129, 85)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(69, 69+60, 649)-Net in Base 3 — Upper bound on s

There is no (69, 129, 650)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 36 550376 970161 186769 707478 332089 864973 924186 277656 233277 577693 > 3¹²⁹ [i]