MinT - Best Known (47, 47+22, s)-Nets in Base 3

Best Known (47, 47+22, s)-Nets in Base 3

(47, 47+22, 114)-Net over F₃ — Constructive and digital

Digital (47, 69, 114)-net over F₃, using

trace code for nets [i] based on digital (1, 23, 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]

(47, 47+22, 159)-Net over F₃ — Digital

Digital (47, 69, 159)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(47, 47+22, 2404)-Net in Base 3 — Upper bound on s

There is no (47, 69, 2405)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 837 941903 977498 200196 525213 675659 > 3⁶⁹ [i]