MinT - Best Known (45, 66, s)-Nets in Base 3

Best Known (45, 66, s)-Nets in Base 3

(45, 66, 114)-Net over F₃ — Constructive and digital

Digital (45, 66, 114)-net over F₃, using

trace code for nets [i] based on digital (1, 22, 38)-net over F₂₇, using
- net from sequence [i] based on digital (1, 37)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 1 and N(F) ≥ 38, using
    - a function field by SÃ©mirat [i]

(45, 66, 156)-Net over F₃ — Digital

Digital (45, 66, 156)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(45, 66, 2849)-Net in Base 3 — Upper bound on s

There is no (45, 66, 2850)-net in base 3, because

1 times m-reduction [i] would yield (45, 65, 2850)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 10 313779 660911 892977 633225 155621 > 3⁶⁵ [i]