MinT - Best Known (200−92, 200, s)-Nets in Base 3

Best Known (200−92, 200, s)-Nets in Base 3

(200−92, 200, 80)-Net over F₃ — Constructive and digital

Digital (108, 200, 80)-net over F₃, using

trace code for nets [i] based on digital (8, 100, 40)-net over F₉, using
- net from sequence [i] based on digital (8, 39)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 8 and N(F) ≥ 40, using
    - a function field by SÃ©mirat [i]

(200−92, 200, 126)-Net over F₃ — Digital

Digital (108, 200, 126)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(200−92, 200, 1023)-Net in Base 3 — Upper bound on s

There is no (108, 200, 1024)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 271875 764954 553278 734372 050084 968861 594563 286482 904417 200228 576044 533228 129078 472320 079872 546817 > 3²⁰⁰ [i]