MinT - Best Known (238−102, 238, s)-Nets in Base 3

Best Known (238−102, 238, s)-Nets in Base 3

(238−102, 238, 148)-Net over F₃ — Constructive and digital

Digital (136, 238, 148)-net over F₃, using

trace code for nets [i] based on digital (17, 119, 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]

(238−102, 238, 179)-Net over F₃ — Digital

Digital (136, 238, 179)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(238−102, 238, 1622)-Net in Base 3 — Upper bound on s

There is no (136, 238, 1623)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 361839 188491 601830 859123 828658 872923 622194 736917 723654 562542 354050 091656 182851 868715 599171 102213 655099 434506 495227 > 3²³⁸ [i]