MinT - Best Known (42, 42+30, s)-Nets in Base 3

Best Known (42, 42+30, s)-Nets in Base 3

(42, 42+30, 68)-Net over F₃ — Constructive and digital

Digital (42, 72, 68)-net over F₃, using

trace code for nets [i] based on digital (6, 36, 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]

(42, 42+30, 73)-Net over F₃ — Digital

Digital (42, 72, 73)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(42, 42+30, 612)-Net in Base 3 — Upper bound on s

There is no (42, 72, 613)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 22999 381337 875004 160962 921104 656891 > 3⁷² [i]