MinT - Best Known (134−39, 134, s)-Nets in Base 3

Best Known (134−39, 134, s)-Nets in Base 3

(134−39, 134, 204)-Net over F₃ — Constructive and digital

Digital (95, 134, 204)-net over F₃, using

1 times m-reduction [i] based on digital (95, 135, 204)-net over F₃, using
- trace code for nets [i] based on digital (5, 45, 68)-net over F₂₇, using
  - net from sequence [i] based on digital (5, 67)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 5 and N(F) ≥ 68, using
      - a function field by SÃ©mirat [i]

(134−39, 134, 351)-Net over F₃ — Digital

Digital (95, 134, 351)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(134−39, 134, 8651)-Net in Base 3 — Upper bound on s

There is no (95, 134, 8652)-net in base 3, because

1 times m-reduction [i] would yield (95, 133, 8652)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 2866 145939 977140 009847 275027 694368 992160 789643 918493 127843 612369 > 3¹³³ [i]