MinT - Best Known (68, 68+52, s)-Nets in Base 3

Best Known (68, 68+52, s)-Nets in Base 3

(68, 68+52, 80)-Net over F₃ — Constructive and digital

Digital (68, 120, 80)-net over F₃, using

trace code for nets [i] based on digital (8, 60, 40)-net over F₉, using
- net from sequence [i] based on digital (8, 39)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 8 and N(F) ≥ 40, using
    - a function field by SÃ©mirat [i]

(68, 68+52, 97)-Net over F₃ — Digital

Digital (68, 120, 97)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(68, 68+52, 814)-Net in Base 3 — Upper bound on s

There is no (68, 120, 815)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 1798 314236 420283 568954 941624 123675 363586 736081 024791 283757 > 3¹²⁰ [i]