MinT - Best Known (143−63, 143, s)-Nets in Base 3

Best Known (143−63, 143, s)-Nets in Base 3

(143−63, 143, 80)-Net over F₃ — Constructive and digital

Digital (80, 143, 80)-net over F₃, using

1 times m-reduction [i] based on digital (80, 144, 80)-net over F₃, using
- trace code for nets [i] based on digital (8, 72, 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]

(143−63, 143, 107)-Net over F₃ — Digital

Digital (80, 143, 107)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(143−63, 143, 921)-Net in Base 3 — Upper bound on s

There is no (80, 143, 922)-net in base 3, because

1 times m-reduction [i] would yield (80, 142, 922)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 57 023274 293635 207891 660034 180207 435580 820653 085875 125516 876853 305625 > 3¹⁴² [i]