MinT - Best Known (109, 156, s)-Nets in Base 3

Best Known (109, 156, s)-Nets in Base 3

(109, 156, 204)-Net over F₃ — Constructive and digital

Digital (109, 156, 204)-net over F₃, using

trace code for nets [i] based on digital (5, 52, 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]

(109, 156, 354)-Net over F₃ — Digital

Digital (109, 156, 354)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(109, 156, 7718)-Net in Base 3 — Upper bound on s

There is no (109, 156, 7719)-net in base 3, because

1 times m-reduction [i] would yield (109, 155, 7719)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 89 978335 062519 861565 108167 462857 394991 193822 624781 579742 699077 784897 732595 > 3¹⁵⁵ [i]