MinT - Best Known (70, 70+58, s)-Nets in Base 3

Best Known (70, 70+58, s)-Nets in Base 3

(70, 70+58, 68)-Net over F₃ — Constructive and digital

Digital (70, 128, 68)-net over F₃, using

trace code for nets [i] based on digital (6, 64, 34)-net over F₉, using
- net from sequence [i] based on digital (6, 33)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 6 and N(F) ≥ 34, using
    - a function field by SÃ©mirat [i]

(70, 70+58, 91)-Net over F₃ — Digital

Digital (70, 128, 91)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(70, 70+58, 716)-Net in Base 3 — Upper bound on s

There is no (70, 128, 717)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 11 933650 704935 139954 871733 553303 637083 072316 113866 925303 899083 > 3¹²⁸ [i]