MinT - Best Known (234−73, 234, s)-Nets in Base 3

Best Known (234−73, 234, s)-Nets in Base 3

(234−73, 234, 204)-Net over F₃ — Constructive and digital

Digital (161, 234, 204)-net over F₃, using

trace code for nets [i] based on digital (5, 78, 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]

(234−73, 234, 450)-Net over F₃ — Digital

Digital (161, 234, 450)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(234−73, 234, 8709)-Net in Base 3 — Upper bound on s

There is no (161, 234, 8710)-net in base 3, because

1 times m-reduction [i] would yield (161, 233, 8710)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 1481 441526 440932 514546 567058 750168 619338 101278 477137 977661 732042 027373 551004 268826 418264 333720 441593 315000 170569 > 3²³³ [i]