MinT - Best Known (168−51, 168, s)-Nets in Base 3

Best Known (168−51, 168, s)-Nets in Base 3

(168−51, 168, 204)-Net over F₃ — Constructive and digital

Digital (117, 168, 204)-net over F₃, using

trace code for nets [i] based on digital (5, 56, 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]

(168−51, 168, 367)-Net over F₃ — Digital

Digital (117, 168, 367)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(168−51, 168, 7805)-Net in Base 3 — Upper bound on s

There is no (117, 168, 7806)-net in base 3, because

1 times m-reduction [i] would yield (117, 167, 7806)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 47 840663 377475 316830 902574 497177 751365 104416 052223 131227 065961 558229 186621 210957 > 3¹⁶⁷ [i]