MinT - Best Known (102−42, 102, s)-Nets in Base 3

Best Known (102−42, 102, s)-Nets in Base 3

(102−42, 102, 80)-Net over F₃ — Constructive and digital

Digital (60, 102, 80)-net over F₃, using

2 times m-reduction [i] based on digital (60, 104, 80)-net over F₃, using
- trace code for nets [i] based on digital (8, 52, 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]

(102−42, 102, 99)-Net over F₃ — Digital

Digital (60, 102, 99)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(102−42, 102, 881)-Net in Base 3 — Upper bound on s

There is no (60, 102, 882)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 4 739496 397835 990654 282369 181845 251888 190331 246045 > 3¹⁰² [i]