MinT - Best Known (89−40, 89, s)-Nets in Base 3

Best Known (89−40, 89, s)-Nets in Base 3

(89−40, 89, 60)-Net over F₃ — Constructive and digital

Digital (49, 89, 60)-net over F₃, using

1 times m-reduction [i] based on digital (49, 90, 60)-net over F₃, using
- trace code for nets [i] based on digital (4, 45, 30)-net over F₉, using
  - net from sequence [i] based on digital (4, 29)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 4 and N(F) ≥ 30, using
      - a function field by SÃ©mirat [i]

(89−40, 89, 70)-Net over F₃ — Digital

Digital (49, 89, 70)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(89−40, 89, 532)-Net in Base 3 — Upper bound on s

There is no (49, 89, 533)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 2 996919 156432 248161 375734 674520 537191 140497 > 3⁸⁹ [i]