MinT - Best Known (107, 150, s)-Nets in Base 3

Best Known (107, 150, s)-Nets in Base 3

(107, 150, 246)-Net over F₃ — Constructive and digital

Digital (107, 150, 246)-net over F₃, using

trace code for nets [i] based on digital (7, 50, 82)-net over F₂₇, using
- net from sequence [i] based on digital (7, 81)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 7 and N(F) ≥ 82, using
    - a function field by SÃ©mirat [i]

(107, 150, 405)-Net over F₃ — Digital

Digital (107, 150, 405)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(107, 150, 10517)-Net in Base 3 — Upper bound on s

There is no (107, 150, 10518)-net in base 3, because

1 times m-reduction [i] would yield (107, 149, 10518)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 123488 458846 261983 372944 609736 152394 932110 891575 837145 350016 661335 049061 > 3¹⁴⁹ [i]