MinT - Best Known (65, 93, s)-Nets in Base 3

Best Known (65, 93, s)-Nets in Base 3

(65, 93, 156)-Net over F₃ — Constructive and digital

Digital (65, 93, 156)-net over F₃, using

trace code for nets [i] based on digital (3, 31, 52)-net over F₂₇, using
- net from sequence [i] based on digital (3, 51)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 3 and N(F) ≥ 52, using
    - a function field by SÃ©mirat [i]

(65, 93, 237)-Net over F₃ — Digital

Digital (65, 93, 237)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(65, 93, 4452)-Net in Base 3 — Upper bound on s

There is no (65, 93, 4453)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 236 336654 600050 100688 111345 072094 771808 034081 > 3⁹³ [i]