MinT - Best Known (168−48, 168, s)-Nets in Base 3

Best Known (168−48, 168, s)-Nets in Base 3

(168−48, 168, 252)-Net over F₃ — Constructive and digital

Digital (120, 168, 252)-net over F₃, using

trace code for nets [i] based on digital (8, 56, 84)-net over F₂₇, using
- net from sequence [i] based on digital (8, 83)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 8 and N(F) ≥ 84, using
    - a function field by SÃ©mirat [i]

(168−48, 168, 449)-Net over F₃ — Digital

Digital (120, 168, 449)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(168−48, 168, 10696)-Net in Base 3 — Upper bound on s

There is no (120, 168, 10697)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 143 599951 491323 815355 066293 205561 352015 394476 252787 802341 809823 392893 456444 251617 > 3¹⁶⁸ [i]