MinT - Best Known (150−58, 150, s)-Nets in Base 3

Best Known (150−58, 150, s)-Nets in Base 3

(150−58, 150, 148)-Net over F₃ — Constructive and digital

Digital (92, 150, 148)-net over F₃, using

trace code for nets [i] based on digital (17, 75, 74)-net over F₉, using
- net from sequence [i] based on digital (17, 73)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 17 and N(F) ≥ 74, using
    - a function field by GarcÃa and Quoos [i]

(150−58, 150, 161)-Net over F₃ — Digital

Digital (92, 150, 161)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(150−58, 150, 1685)-Net in Base 3 — Upper bound on s

There is no (92, 150, 1686)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 373144 351029 650046 304742 123911 799253 529664 663189 028180 531562 476672 621397 > 3¹⁵⁰ [i]