MinT - Best Known (67, 67+26, s)-Nets in Base 3

Best Known (67, 67+26, s)-Nets in Base 3

(67, 67+26, 204)-Net over F₃ — Constructive and digital

Digital (67, 93, 204)-net over F₃, using

trace code for nets [i] based on digital (5, 31, 68)-net over F₂₇, using
- net from sequence [i] based on digital (5, 67)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 5 and N(F) ≥ 68, using
    - a function field by SÃ©mirat [i]

(67, 67+26, 311)-Net over F₃ — Digital

Digital (67, 93, 311)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(67, 67+26, 7326)-Net in Base 3 — Upper bound on s

There is no (67, 93, 7327)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 235 921185 038052 917851 546394 418088 475463 091239 > 3⁹³ [i]