MinT - Best Known (68, 68+60, s)-Nets in Base 3

Best Known (68, 68+60, s)-Nets in Base 3

(68, 68+60, 60)-Net over F₃ — Constructive and digital

Digital (68, 128, 60)-net over F₃, using

trace code for nets [i] based on digital (4, 64, 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]

(68, 68+60, 82)-Net over F₃ — Digital

Digital (68, 128, 82)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(68, 68+60, 624)-Net in Base 3 — Upper bound on s

There is no (68, 128, 625)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 11 850187 054561 523332 559534 792285 376235 477426 484930 070168 971801 > 3¹²⁸ [i]