MinT - Best Known (105, 150, s)-Nets in Base 3

Best Known (105, 150, s)-Nets in Base 3

(105, 150, 204)-Net over F₃ — Constructive and digital

Digital (105, 150, 204)-net over F₃, using

trace code for nets [i] based on digital (5, 50, 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]

(105, 150, 347)-Net over F₃ — Digital

Digital (105, 150, 347)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(105, 150, 7691)-Net in Base 3 — Upper bound on s

There is no (105, 150, 7692)-net in base 3, because

1 times m-reduction [i] would yield (105, 149, 7692)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 123422 674137 539035 461903 141063 401813 912013 208168 940925 608455 964811 505673 > 3¹⁴⁹ [i]