MinT - Best Known (168−38, 168, s)-Nets in Base 3

Best Known (168−38, 168, s)-Nets in Base 3

(168−38, 168, 600)-Net over F₃ — Constructive and digital

Digital (130, 168, 600)-net over F₃, using

trace code for nets [i] based on digital (4, 42, 150)-net over F₈₁, using
- net from sequence [i] based on digital (4, 149)-sequence over F₈₁, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 4 and N(F) ≥ 150, using
    - a function field by SÃ©mirat [i]

(168−38, 168, 1093)-Net over F₃ — Digital

Digital (130, 168, 1093)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(168−38, 168, 65587)-Net in Base 3 — Upper bound on s

There is no (130, 168, 65588)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 143 372395 560174 059538 712257 838144 132223 467030 253166 451373 053162 564713 143866 737009 > 3¹⁶⁸ [i]