MinT - Best Known (81−34, 81, s)-Nets in Base 3

Best Known (81−34, 81, s)-Nets in Base 3

(81−34, 81, 68)-Net over F₃ — Constructive and digital

Digital (47, 81, 68)-net over F₃, using

1 times m-reduction [i] based on digital (47, 82, 68)-net over F₃, using
- trace code for nets [i] based on digital (6, 41, 34)-net over F₉, using
  - net from sequence [i] based on digital (6, 33)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 6 and N(F) ≥ 34, using
      - a function field by SÃ©mirat [i]

(81−34, 81, 78)-Net over F₃ — Digital

Digital (47, 81, 78)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(81−34, 81, 657)-Net in Base 3 — Upper bound on s

There is no (47, 81, 658)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 454 263611 996887 823278 920739 835216 877957 > 3⁸¹ [i]