MinT - Best Known (102, 102+68, s)-Nets in Base 3

Best Known (102, 102+68, s)-Nets in Base 3

(102, 102+68, 148)-Net over F₃ — Constructive and digital

Digital (102, 170, 148)-net over F₃, using

trace code for nets [i] based on digital (17, 85, 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]

(102, 102+68, 163)-Net over F₃ — Digital

Digital (102, 170, 163)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(102, 102+68, 1611)-Net in Base 3 — Upper bound on s

There is no (102, 170, 1612)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 1307 539914 814864 679769 468012 998761 043236 687392 806647 343697 338948 258057 050368 372969 > 3¹⁷⁰ [i]